Daily Papers

Neural networks (NNs) are increasingly used in always-on safety-critical applications deployed on hardware accelerators (NN-HAs) employing various memory technologies. Reliable continuous operation of NN is essential for safety-critical applications. During online operation, NNs are susceptible to single and multiple permanent and soft errors due to factors such as radiation, aging, and thermal effects. Explicit NN-HA testing methods cannot detect transient faults during inference, are unsuitable for always-on applications, and require extensive test vector generation and storage. Therefore, in this paper, we propose the uncertainty fingerprint approach representing the online fault status of NN. Furthermore, we propose a dual head NN topology specifically designed to produce uncertainty fingerprints and the primary prediction of the NN in a single shot. During the online operation, by matching the uncertainty fingerprint, we can concurrently self-test NNs with up to 100% coverage with a low false positive rate while maintaining a similar performance of the primary task. Compared to existing works, memory overhead is reduced by up to 243.7 MB, multiply and accumulate (MAC) operation is reduced by up to 10000times, and false-positive rates are reduced by up to 89%.

End-to-end vision-based imitation learning has demonstrated promising results in autonomous driving by learning control commands directly from expert demonstrations. However, traditional approaches rely on either regressionbased models, which provide precise control but lack confidence estimation, or classification-based models, which offer confidence scores but suffer from reduced precision due to discretization. This limitation makes it challenging to quantify the reliability of predicted actions and apply corrections when necessary. In this work, we introduce a dual-head neural network architecture that integrates both regression and classification heads to improve decision reliability in imitation learning. The regression head predicts continuous driving actions, while the classification head estimates confidence, enabling a correction mechanism that adjusts actions in low-confidence scenarios, enhancing driving stability. We evaluate our approach in a closed-loop setting within the CARLA simulator, demonstrating its ability to detect uncertain actions, estimate confidence, and apply real-time corrections. Experimental results show that our method reduces lane deviation and improves trajectory accuracy by up to 50%, outperforming conventional regression-only models. These findings highlight the potential of classification-guided confidence estimation in enhancing the robustness of vision-based imitation learning for autonomous driving. The source code is available at https://github.com/ElaheDlv/Confidence_Aware_IL.

Deep neural networks perform remarkably well on image classification tasks but remain vulnerable to carefully crafted adversarial perturbations. This work revisits linear dimensionality reduction as a simple, data-adapted defense. We empirically compare standard Principal Component Analysis (PCA) with its sparse variant (SPCA) as front-end feature extractors for downstream classifiers, and we complement these experiments with a theoretical analysis. On the theory side, we derive exact robustness certificates for linear heads applied to SPCA features: for both ell_infty and ell_2 threat models (binary and multiclass), the certified radius grows as the dual norms of W^top u shrink, where W is the projection and u the head weights. We further show that for general (non-linear) heads, sparsity reduces operator-norm bounds through a Lipschitz composition argument, predicting lower input sensitivity. Empirically, with a small non-linear network after the projection, SPCA consistently degrades more gracefully than PCA under strong white-box and black-box attacks while maintaining competitive clean accuracy. Taken together, the theory identifies the mechanism (sparser projections reduce adversarial leverage) and the experiments verify that this benefit persists beyond the linear setting. Our code is available at https://github.com/killian31/SPCARobustness.

Vision-language models (VLMs) have achieved remarkable success across diverse tasks by leveraging rich textual information with minimal labeled data. However, deploying such large models remains challenging, particularly in resource-constrained environments. Knowledge distillation (KD) offers a well-established solution to this problem; however, recent KD approaches from VLMs often involve multi-stage training or additional tuning, increasing computational overhead and optimization complexity. In this paper, we propose texttt{D}ual-texttt{H}ead texttt{O}ptimization (texttt{DHO}) -- a simple yet effective KD framework that transfers knowledge from VLMs to compact, task-specific models in semi-supervised settings. Specifically, we introduce dual prediction heads that independently learn from labeled data and teacher predictions, and propose to linearly combine their outputs during inference. We observe that DHO mitigates gradient conflicts between supervised and distillation signals, enabling more effective feature learning than single-head KD baselines. As a result, extensive experiments show that DHO consistently outperforms baselines across multiple domains and fine-grained datasets. Notably, on ImageNet, it achieves state-of-the-art performance, improving accuracy by 3% and 0.1% with 1% and 10% labeled data, respectively, while using fewer parameters.

Activity difference based learning algorithms-such as contrastive Hebbian learning and equilibrium propagation-have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.

This work aims to tackle the Parkinson's disease (PD) detection problem from the speech signal in a bilingual setting by proposing an ad-hoc dual-head deep neural architecture for type-based binary classification. One head is specialized for diadochokinetic patterns. The other head looks for natural speech patterns present in continuous spoken utterances. Only one of the two heads is operative accordingly to the nature of the input. Speech representations are extracted from self-supervised learning (SSL) models and wavelet transforms. Adaptive layers, convolutional bottlenecks, and contrastive learning are exploited to reduce variations across languages. Our solution is assessed against two distinct datasets, EWA-DB, and PC-GITA, which cover Slovak and Spanish languages, respectively. Results indicate that conventional models trained on a single language dataset struggle with cross-linguistic generalization, and naive combinations of datasets are suboptimal. In contrast, our model improves generalization on both languages, simultaneously.

Inspired by the Many-Worlds Interpretation (MWI), this work introduces a novel neural network architecture that splits the same input signal into parallel branches at each layer, utilizing a Hyper Rectified Activation, referred to as ANDHRA. The branched layers do not merge and form separate network paths, leading to multiple network heads for output prediction. For a network with a branching factor of 2 at three levels, the total number of heads is 2^3 = 8 . The individual heads are jointly trained by combining their respective loss values. However, the proposed architecture requires additional parameters and memory during training due to the additional branches. During inference, the experimental results on CIFAR-10/100 demonstrate that there exists one individual head that outperforms the baseline accuracy, achieving statistically significant improvement with equal parameters and computational cost.

We build a dual-way neural dictionary to retrieve words given definitions, and produce definitions for queried words. The model learns the two tasks simultaneously and handles unknown words via embeddings. It casts a word or a definition to the same representation space through a shared layer, then generates the other form in a multi-task fashion. Our method achieves promising automatic scores on previous benchmarks without extra resources. Human annotators prefer the model's outputs in both reference-less and reference-based evaluation, indicating its practicality. Analysis suggests that multiple objectives benefit learning.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

Attention is a powerful and ubiquitous mechanism for allowing neural models to focus on particular salient pieces of information by taking their weighted average when making predictions. In particular, multi-headed attention is a driving force behind many recent state-of-the-art NLP models such as Transformer-based MT models and BERT. These models apply multiple attention mechanisms in parallel, with each attention "head" potentially focusing on different parts of the input, which makes it possible to express sophisticated functions beyond the simple weighted average. In this paper we make the surprising observation that even if models have been trained using multiple heads, in practice, a large percentage of attention heads can be removed at test time without significantly impacting performance. In fact, some layers can even be reduced to a single head. We further examine greedy algorithms for pruning down models, and the potential speed, memory efficiency, and accuracy improvements obtainable therefrom. Finally, we analyze the results with respect to which parts of the model are more reliant on having multiple heads, and provide precursory evidence that training dynamics play a role in the gains provided by multi-head attention.

We propose Dual PatchNorm: two Layer Normalization layers (LayerNorms), before and after the patch embedding layer in Vision Transformers. We demonstrate that Dual PatchNorm outperforms the result of exhaustive search for alternative LayerNorm placement strategies in the Transformer block itself. In our experiments, incorporating this trivial modification, often leads to improved accuracy over well-tuned Vision Transformers and never hurts.

We introduce a novel architecture design that enhances expressiveness by incorporating multiple head classifiers (\ie, classification heads) instead of relying on channel expansion or additional building blocks. Our approach employs attention-based aggregation, utilizing pairwise feature similarity to enhance multiple lightweight heads with minimal resource overhead. We compute the Gramian matrices to reinforce class tokens in an attention layer for each head. This enables the heads to learn more discriminative representations, enhancing their aggregation capabilities. Furthermore, we propose a learning algorithm that encourages heads to complement each other by reducing correlation for aggregation. Our models eventually surpass state-of-the-art CNNs and ViTs regarding the accuracy-throughput trade-off on ImageNet-1K and deliver remarkable performance across various downstream tasks, such as COCO object instance segmentation, ADE20k semantic segmentation, and fine-grained visual classification datasets. The effectiveness of our framework is substantiated by practical experimental results and further underpinned by generalization error bound. We release the code publicly at: https://github.com/Lab-LVM/imagenet-models.

Mixture-of-Experts (MoE) networks have been proposed as an efficient way to scale up model capacity and implement conditional computing. However, the study of MoE components mostly focused on the feedforward layer in Transformer architecture. This paper proposes the Mixture of Attention Heads (MoA), a new architecture that combines multi-head attention with the MoE mechanism. MoA includes a set of attention heads that each has its own set of parameters. Given an input, a router dynamically selects a subset of k attention heads per token. This conditional computation schema allows MoA to achieve stronger performance than the standard multi-head attention layer. Furthermore, the sparsely gated MoA can easily scale up the number of attention heads and the number of parameters while preserving computational efficiency. In addition to the performance improvements, MoA also automatically differentiates heads' utilities, providing a new perspective to discuss the model's interpretability. We conducted experiments on several important tasks, including Machine Translation and Masked Language Modeling. Experiments have shown promising results on several tasks against strong baselines that involve large and very deep models.

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

This paper presents our submitted system to SemEval 2021 Task 4: Reading Comprehension of Abstract Meaning. Our system uses a large pre-trained language model as the encoder and an additional dual multi-head co-attention layer to strengthen the relationship between passages and question-answer pairs, following the current state-of-the-art model DUMA. The main difference is that we stack the passage-question and question-passage attention modules instead of calculating parallelly to simulate re-considering process. We also add a layer normalization module to improve the performance of our model. Furthermore, to incorporate our known knowledge about abstract concepts, we retrieve the definitions of candidate answers from WordNet and feed them to the model as extra inputs. Our system, called WordNet-enhanced DUal Multi-head Co-Attention (WN-DUMA), achieves 86.67% and 89.99% accuracy on the official blind test set of subtask 1 and subtask 2 respectively.

Recent approaches to multi-task learning (MTL) have focused on modelling connections between tasks at the decoder level. This leads to a tight coupling between tasks, which need retraining if a new task is inserted or removed. We argue that MTL is a stepping stone towards universal feature learning (UFL), which is the ability to learn generic features that can be applied to new tasks without retraining. We propose Medusa to realize this goal, designing task heads with dual attention mechanisms. The shared feature attention masks relevant backbone features for each task, allowing it to learn a generic representation. Meanwhile, a novel Multi-Scale Attention head allows the network to better combine per-task features from different scales when making the final prediction. We show the effectiveness of Medusa in UFL (+13.18% improvement), while maintaining MTL performance and being 25% more efficient than previous approaches.

With the emergence of pre-trained vision-language models like CLIP, how to adapt them to various downstream classification tasks has garnered significant attention in recent research. The adaptation strategies can be typically categorized into three paradigms: zero-shot adaptation, few-shot adaptation, and the recently-proposed training-free few-shot adaptation. Most existing approaches are tailored for a specific setting and can only cater to one or two of these paradigms. In this paper, we introduce a versatile adaptation approach that can effectively work under all three settings. Specifically, we propose the dual memory networks that comprise dynamic and static memory components. The static memory caches training data knowledge, enabling training-free few-shot adaptation, while the dynamic memory preserves historical test features online during the testing process, allowing for the exploration of additional data insights beyond the training set. This novel capability enhances model performance in the few-shot setting and enables model usability in the absence of training data. The two memory networks employ the same flexible memory interactive strategy, which can operate in a training-free mode and can be further enhanced by incorporating learnable projection layers. Our approach is tested across 11 datasets under the three task settings. Remarkably, in the zero-shot scenario, it outperforms existing methods by over 3\% and even shows superior results against methods utilizing external training data. Additionally, our method exhibits robust performance against natural distribution shifts. Codes are available at https://github.com/YBZh/DMN.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns: a diagonal and homogeneous pattern in the key-query (KQ) weights, and a last-entry-only and zero-sum pattern in the output-value (OV) weights. Remarkably, these patterns consistently appear from gradient-based training starting from random initialization. Our analysis reveals that such emergent structures enable multi-head attention to approximately implement a debiased gradient descent predictor -- one that outperforms single-head attention and nearly achieves Bayesian optimality up to proportional factor. Furthermore, compared to linear transformers, the softmax attention readily generalizes to sequences longer than those seen during training. We also extend our study to scenarios with non-isotropic covariates and multi-task linear regression. In the former, multi-head attention learns to implement a form of pre-conditioned gradient descent. In the latter, we uncover an intriguing regime where the interplay between head number and task number triggers a superposition phenomenon that efficiently resolves multi-task in-context learning. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution, paving the way for deeper understanding and broader applications of in-context learning.

We investigate methods for combining multiple self-supervised tasks--i.e., supervised tasks where data can be collected without manual labeling--in order to train a single visual representation. First, we provide an apples-to-apples comparison of four different self-supervised tasks using the very deep ResNet-101 architecture. We then combine tasks to jointly train a network. We also explore lasso regularization to encourage the network to factorize the information in its representation, and methods for "harmonizing" network inputs in order to learn a more unified representation. We evaluate all methods on ImageNet classification, PASCAL VOC detection, and NYU depth prediction. Our results show that deeper networks work better, and that combining tasks--even via a naive multi-head architecture--always improves performance. Our best joint network nearly matches the PASCAL performance of a model pre-trained on ImageNet classification, and matches the ImageNet network on NYU depth prediction.

Scaling pre-trained language models has resulted in large performance gains in various natural language processing tasks but comes with a large cost in memory requirements. Inspired by the position embeddings in transformers, we aim to simplify and reduce the memory footprint of the multi-head attention (MHA) mechanism. We propose an alternative module that uses only a single shared projection matrix and multiple head embeddings (MHE), i.e. one per head. We empirically demonstrate that our MHE attention is substantially more memory efficient compared to alternative attention mechanisms while achieving high predictive performance retention ratio to vanilla MHA on several downstream tasks. MHE attention only requires a negligible fraction of additional parameters (3nd, where n is the number of attention heads and d the size of the head embeddings) compared to a single-head attention, while MHA requires (3n^2-3n)d^2-3nd additional parameters.

Convolutional Neural Networks (CNNs) are pivotal in image classification tasks due to their robust feature extraction capabilities. However, their high computational and memory requirements pose challenges for deployment in resource-constrained environments. This paper introduces a methodology to construct lightweight CNNs while maintaining competitive accuracy. The approach integrates two stages of training; dual-input-output model and transfer learning with progressive unfreezing. The dual-input-output model train on original and augmented datasets, enhancing robustness. Progressive unfreezing is applied to the unified model to optimize pre-learned features during fine-tuning, enabling faster convergence and improved model accuracy. The methodology was evaluated on three benchmark datasets; handwritten digit MNIST, fashion MNIST, and CIFAR-10. The proposed model achieved a state-of-the-art accuracy of 99% on the handwritten digit MNIST and 89% on fashion MNIST, with only 14,862 parameters and a model size of 0.17 MB. While performance on CIFAR-10 was comparatively lower (65% with less than 20,00 parameters), the results highlight the scalability of this method. The final model demonstrated fast inference times and low latency, making it suitable for real-time applications. Future directions include exploring advanced augmentation techniques, improving architectural scalability for complex datasets, and extending the methodology to tasks beyond classification. This research underscores the potential for creating efficient, scalable, and task-specific CNNs for diverse applications.

Standard transformers entangle all computation in a single residual stream, obscuring which components perform which functions. We introduce the Dual-Stream Transformer, which decomposes the residual stream into two functionally distinct components: a token stream updated by attention and a context stream updated by feed-forward networks. Information flow between attention heads is controlled through a hierarchy of mixing strategies, from fully independent (maximum interpretability) to dense (standard transformer behavior). This design exposes a tunable tradeoff between interpretability and performance. We measure this tradeoff on language modeling tasks at 29M parameters. Fully independent head mixing increases validation loss by 8\% relative to dense baselines. The recommended Kronecker mixing strategy, which permits scalar communication between heads while preserving within-head structure, costs only 2.5\%. All configurations maintain functional generation under attention amplification (scaling logits by factors up to 16 at inference time), with degradation ranging from 16\% to 27\%. This robustness suggests the architectures learn discrete algorithms that operate independently of soft probabilistic mixing. The architecture provides a foundation for interpretable language models where internal structure is exposed by design. This work was partially supported by DARPA Contract HR001125C0302.

Recent studies show that the attention heads in Transformer are not equal. We relate this phenomenon to the imbalance training of multi-head attention and the model dependence on specific heads. To tackle this problem, we propose a simple masking method: HeadMask, in two specific ways. Experiments show that translation improvements are achieved on multiple language pairs. Subsequent empirical analyses also support our assumption and confirm the effectiveness of the method.

Multi-head attention layers, as used in the Transformer neural sequence model, are a powerful alternative to RNNs for moving information across and between sequences. While training these layers is generally fast and simple, due to parallelizability across the length of the sequence, incremental inference (where such paralleization is impossible) is often slow, due to the memory-bandwidth cost of repeatedly loading the large "keys" and "values" tensors. We propose a variant called multi-query attention, where the keys and values are shared across all of the different attention "heads", greatly reducing the size of these tensors and hence the memory bandwidth requirements of incremental decoding. We verify experimentally that the resulting models can indeed be much faster to decode, and incur only minor quality degradation from the baseline.

Designing neural networks typically relies on manual trial and error or a neural architecture search (NAS) followed by weight training. The former is time-consuming and labor-intensive, while the latter often discretizes architecture search and weight optimization. In this paper, we propose a fundamentally different approach that simultaneously optimizes both the architecture and the weights of a neural network. Our framework first trains a universal multi-scale autoencoder that embeds both architectural and parametric information into a continuous latent space, where functionally similar neural networks are mapped closer together. Given a dataset, we then randomly initialize a point in the embedding space and update it via gradient descent to obtain the optimal neural network, jointly optimizing its structure and weights. The optimization process incorporates sparsity and compactness penalties to promote efficient models. Experiments on synthetic regression tasks demonstrate that our method effectively discovers sparse and compact neural networks with strong performance.

Multi-head attentive neural architectures have achieved state-of-the-art results on a variety of natural language processing tasks. Evidence has shown that they are overparameterized; attention heads can be pruned without significant performance loss. In this work, we instead "reallocate" them -- the model learns to activate different heads on different inputs. Drawing connections between multi-head attention and mixture of experts, we propose the mixture of attentive experts model (MAE). MAE is trained using a block coordinate descent algorithm that alternates between updating (1) the responsibilities of the experts and (2) their parameters. Experiments on machine translation and language modeling show that MAE outperforms strong baselines on both tasks. Particularly, on the WMT14 English to German translation dataset, MAE improves over "transformer-base" by 0.8 BLEU, with a comparable number of parameters. Our analysis shows that our model learns to specialize different experts to different inputs.

Visual document understanding typically requires separate retrieval and generation models, doubling memory and system complexity. We present Hydra, a dual-head approach that provides both ColBERT-style late-interaction retrieval and autoregressive generation from a single vision-language model (VLM). A single LoRA adapter, trained only for retrieval, is toggled at inference: enabling it produces multi-vector embeddings; disabling it recovers the base model's generation quality -- byte-identical outputs in 100% of 10,500 greedy and stochastic samples, with max delta-ANLS = 0.0044 across 15,301 samples on four VQA benchmarks (three informative; ChartQA is near-zero for both models under greedy decoding) when compared against an independent base-model pipeline. We identify three engineering requirements (attention-mode restoration, lm_head preservation, KV-cache-aware decoding) whose omission silently breaks generation despite correct weight recovery. On ViDoRe V1, Hydra (4B) is within 1 percentage point of a controlled single-head baseline in a single training run, with higher aggregate scores on V2 and V3 that are concentrated on a subset of tasks; multi-seed experiments are needed to confirm these trends. The single-model design reduces peak GPU memory by 41%, though adapter switching introduces throughput overhead under concurrent serving loads. An ablation shows that GritLM-style joint training provides no benefit within the LoRA-based (r=16) training regime. A proof-of-concept extension to Qwen2.5-Omni-3B demonstrates that the mechanism generalizes to audio retrieval and video embedding, with speech generation.

Despite being the workhorse of deep learning, the backpropagation algorithm is no panacea. It enforces sequential layer updates, thus preventing efficient parallelization of the training process. Furthermore, its biological plausibility is being challenged. Alternative schemes have been devised; yet, under the constraint of synaptic asymmetry, none have scaled to modern deep learning tasks and architectures. Here, we challenge this perspective, and study the applicability of Direct Feedback Alignment to neural view synthesis, recommender systems, geometric learning, and natural language processing. In contrast with previous studies limited to computer vision tasks, our findings show that it successfully trains a large range of state-of-the-art deep learning architectures, with performance close to fine-tuned backpropagation. At variance with common beliefs, our work supports that challenging tasks can be tackled in the absence of weight transport.

In this work, we upgrade the multi-head attention mechanism, the core of the Transformer model, to improve efficiency while maintaining or surpassing the previous accuracy level. We show that multi-head attention can be expressed in the summation form. Drawing on the insight that not all attention heads hold equal significance, we propose Mixture-of-Head attention (MoH), a new architecture that treats attention heads as experts in the Mixture-of-Experts (MoE) mechanism. MoH has two significant advantages: First, MoH enables each token to select the appropriate attention heads, enhancing inference efficiency without compromising accuracy or increasing the number of parameters. Second, MoH replaces the standard summation in multi-head attention with a weighted summation, introducing flexibility to the attention mechanism and unlocking extra performance potential. Extensive experiments on ViT, DiT, and LLMs demonstrate that MoH outperforms multi-head attention by using only 50%-90% of the attention heads. Moreover, we demonstrate that pre-trained multi-head attention models, such as LLaMA3-8B, can be further continue-tuned into our MoH models. Notably, MoH-LLaMA3-8B achieves an average accuracy of 64.0% across 14 benchmarks, outperforming LLaMA3-8B by 2.4% by utilizing only 75% of the attention heads. We believe the proposed MoH is a promising alternative to multi-head attention and provides a strong foundation for developing advanced and efficient attention-based models.

We present DualFocus, a novel framework for integrating macro and micro perspectives within multi-modal large language models (MLLMs) to enhance vision-language task performance. Current MLLMs typically singularly focus on inputs at a predefined resolution, resulting in deficiencies in detailed questions involving local regions. We introduced a DualFocus mechanism where the model concentrates on the image from a macro perspective, responses to the question, and identifies suitable sub-regions to zoom in for subsequent micro perspective analysis. Via the integration of answers from both macro and micro perspectives, the model is adept at addressing tasks that encompass global, detailed, and combined considerations. To endows the DualFocus mechanism in MLLMs, we curated a tailored dataset derived from the Visual Genome (VG) and adapted it to align with the training regimen of DualFocus. Through comparative studies across different model sizes and benchmarks, we demonstrate DualFocus's superiority in balancing detailed examination with holistic insight, significantly reducing hallucination instances in MLLMs and improving their performance in various vision-language tasks.

Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning has attracted considerable interest as a biologically plausible alternative to backpropagation. Nevertheless, its exclusive reliance on local information, without consideration of global task objectives, fundamentally limits its scalability. Inspired by the biological synergy between neuromodulators and local plasticity, we introduce a novel model-agnostic Global-guided Hebbian Learning (GHL) framework, which seamlessly integrates local and global information to scale up across diverse networks and tasks. In specific, the local component employs Oja's rule with competitive learning to ensure stable and effective local updates. Meanwhile, the global component introduces a sign-based signal that guides the direction of local Hebbian plasticity updates. Extensive experiments demonstrate that our method consistently outperforms existing Hebbian approaches. Notably, on large-scale network and complex datasets like ImageNet, our framework achieves the competitive results and significantly narrows the gap with standard backpropagation.

In contrastive learning, two views of an original image, generated by different augmentations, are considered a positive pair, and their similarity is required to be high. Similarly, two views of distinct images form a negative pair, with encouraged low similarity. Typically, a single similarity measure, provided by a lone projection head, evaluates positive and negative sample pairs. However, due to diverse augmentation strategies and varying intra-sample similarity, views from the same image may not always be similar. Additionally, owing to inter-sample similarity, views from different images may be more akin than those from the same image. Consequently, enforcing high similarity for positive pairs and low similarity for negative pairs may be unattainable, and in some cases, such enforcement could detrimentally impact performance. To address this challenge, we propose using multiple projection heads, each producing a distinct set of features. Our pre-training loss function emerges from a solution to the maximum likelihood estimation over head-wise posterior distributions of positive samples given observations. This loss incorporates the similarity measure over positive and negative pairs, each re-weighted by an individual adaptive temperature, regulated to prevent ill solutions. Our approach, Adaptive Multi-Head Contrastive Learning (AMCL), can be applied to and experimentally enhances several popular contrastive learning methods such as SimCLR, MoCo, and Barlow Twins. The improvement remains consistent across various backbones and linear probing epochs, and becomes more significant when employing multiple augmentation methods.

Dual encoders perform retrieval by encoding documents and queries into dense lowdimensional vectors, scoring each document by its inner product with the query. We investigate the capacity of this architecture relative to sparse bag-of-words models and attentional neural networks. Using both theoretical and empirical analysis, we establish connections between the encoding dimension, the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents. Building on these insights, we propose a simple neural model that combines the efficiency of dual encoders with some of the expressiveness of more costly attentional architectures, and explore sparse-dense hybrids to capitalize on the precision of sparse retrieval. These models outperform strong alternatives in large-scale retrieval.

Gaze estimation methods estimate gaze from facial appearance with a single camera. However, due to the limited view of a single camera, the captured facial appearance cannot provide complete facial information and thus complicate the gaze estimation problem. Recently, camera devices are rapidly updated. Dual cameras are affordable for users and have been integrated in many devices. This development suggests that we can further improve gaze estimation performance with dual-view gaze estimation. In this paper, we propose a dual-view gaze estimation network (DV-Gaze). DV-Gaze estimates dual-view gaze directions from a pair of images. We first propose a dual-view interactive convolution (DIC) block in DV-Gaze. DIC blocks exchange dual-view information during convolution in multiple feature scales. It fuses dual-view features along epipolar lines and compensates for the original feature with the fused feature. We further propose a dual-view transformer to estimate gaze from dual-view features. Camera poses are encoded to indicate the position information in the transformer. We also consider the geometric relation between dual-view gaze directions and propose a dual-view gaze consistency loss for DV-Gaze. DV-Gaze achieves state-of-the-art performance on ETH-XGaze and EVE datasets. Our experiments also prove the potential of dual-view gaze estimation. We release codes in https://github.com/yihuacheng/DVGaze.

In large language models built upon the Transformer architecture, recent studies have shown that inter-head interaction can enhance attention performance. Motivated by this, we propose Multi-head Explicit Attention (MEA), a simple yet effective attention variant that explicitly models cross-head interaction. MEA consists of two key components: a Head-level Linear Composition (HLC) module that separately applies learnable linear combinations to the key and value vectors across heads, thereby enabling rich inter-head communication; and a head-level Group Normalization layer that aligns the statistical properties of the recombined heads. MEA shows strong robustness in pretraining, which allows the use of larger learning rates that lead to faster convergence, ultimately resulting in lower validation loss and improved performance across a range of tasks. Furthermore, we explore the parameter efficiency of MEA by reducing the number of attention heads and leveraging HLC to reconstruct them using low-rank "virtual heads". This enables a practical key-value cache compression strategy that reduces KV-cache memory usage by 50% with negligible performance loss on knowledge-intensive and scientific reasoning tasks, and only a 3.59% accuracy drop for Olympiad-level mathematical benchmarks.

Bidirectional transformers are the foundation of many sequence modeling tasks across natural, biological, and chemical language domains, but they are permutation-invariant without explicit positional embeddings. In contrast, unidirectional attention inherently encodes positional information through its triangular mask, enabling models to operate without positional embeddings altogether. Here, we introduce Dual Triangle Attention, a novel bidirectional attention mechanism that separates the query-key subspace of each attention head into two complementary triangular masks: one that attends to past-and-self positions and one that attends to future-and-self positions. This design provides bidirectional context while maintaining the causal mask's implicit positional inductive bias in both directions. Using PyTorch's flex_attention, Dual Triangle Attention is implemented as a single compiled kernel call with no additional parameters beyond standard multi-head attention. We evaluated Dual Triangle Attention across three settings: (1) a synthetic argmax position probe, (2) masked language modeling (MLM) on natural language, and (3) MLM on protein sequences. In the argmax task, both Dual Triangle Attention and causal attention learn positional information without explicit positional embeddings, whereas standard bidirectional attention cannot. In the MLM experiments, Dual Triangle Attention with Rotary Positional Embeddings (RoPE) achieved the best context extension performance and strong performance across the board. These findings suggest that Dual Triangle Attention is a viable attention mechanism for bidirectional transformers, with or without positional embeddings.

An effective technique for obtaining high-quality representations is adding a projection head on top of the encoder during training, then discarding it and using the pre-projection representations. Despite its proven practical effectiveness, the reason behind the success of this technique is poorly understood. The pre-projection representations are not directly optimized by the loss function, raising the question: what makes them better? In this work, we provide a rigorous theoretical answer to this question. We start by examining linear models trained with self-supervised contrastive loss. We reveal that the implicit bias of training algorithms leads to layer-wise progressive feature weighting, where features become increasingly unequal as we go deeper into the layers. Consequently, lower layers tend to have more normalized and less specialized representations. We theoretically characterize scenarios where such representations are more beneficial, highlighting the intricate interplay between data augmentation and input features. Additionally, we demonstrate that introducing non-linearity into the network allows lower layers to learn features that are completely absent in higher layers. Finally, we show how this mechanism improves the robustness in supervised contrastive learning and supervised learning. We empirically validate our results through various experiments on CIFAR-10/100, UrbanCars and shifted versions of ImageNet. We also introduce a potential alternative to projection head, which offers a more interpretable and controllable design.

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with H heads, dimension d, and context size n < d, featuring Theta(Hd^2) parameters, can memorize Omega(Hn) examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator's saturation property. We validate our findings through experiments on synthetic data.

Image deblurring task is an ill-posed one, where exists infinite feasible solutions for blurry image. Modern deep learning approaches usually discard the learning of blur kernels and directly employ end-to-end supervised learning. Popular deblurring datasets define the label as one of the feasible solutions. However, we argue that it's not reasonable to specify a label directly, especially when the label is sampled from a random distribution. Therefore, we propose to make the network learn the distribution of feasible solutions, and design based on this consideration a novel multi-head output architecture and corresponding loss function for distribution learning. Our approach enables the model to output multiple feasible solutions to approximate the target distribution. We further propose a novel parameter multiplexing method that reduces the number of parameters and computational effort while improving performance. We evaluated our approach on multiple image-deblur models, including the current state-of-the-art NAFNet. The improvement of best overall (pick the highest score among multiple heads for each validation image) PSNR outperforms the compared baselines up to 0.11~0.18dB. The improvement of the best single head (pick the best-performed head among multiple heads on validation set) PSNR outperforms the compared baselines up to 0.04~0.08dB. The codes are available at https://github.com/Liu-SD/multi-output-deblur.

This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an O(log n{mu}) upper bound on the time it takes for all neurons to achieve good alignment with the input data, where n is the number of data points and mu measures how well the data are separated. After the early alignment phase, the loss converges to zero at a O(1{t}) rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.

Typical deep visual recognition models are capable of performing the one task they were trained on. In this paper, we tackle the extremely difficult problem of combining completely distinct models with different initializations, each solving a separate task, into one multi-task model without any additional training. Prior work in model merging permutes one model to the space of the other then adds them together. While this works for models trained on the same task, we find that this fails to account for the differences in models trained on disjoint tasks. Thus, we introduce "ZipIt!", a general method for merging two arbitrary models of the same architecture that incorporates two simple strategies. First, in order to account for features that aren't shared between models, we expand the model merging problem to additionally allow for merging features within each model by defining a general "zip" operation. Second, we add support for partially zipping the models up until a specified layer, naturally creating a multi-head model. We find that these two changes combined account for a staggering 20-60% improvement over prior work, making the merging of models trained on disjoint tasks feasible.

Activation compressed training provides a solution towards reducing the memory cost of training deep neural networks~(DNNs). However, state-of-the-art work combines a search of quantization bit-width with the training, which makes the procedure complicated and less transparent. To this end, we propose a simple and effective method to compress DNN training. Our method is motivated by an instructive observation: DNN backward propagation mainly utilizes the low-frequency component (LFC) of the activation maps, while the majority of memory is for caching the high-frequency component (HFC) during the training. This indicates the HFC of activation maps is highly redundant and compressible during DNN training, which inspires our proposed Dual Activation Precision (DIVISION). During the training, DIVISION preserves the high-precision copy of LFC and compresses the HFC into a light-weight copy with low numerical precision. This can significantly reduce the memory cost without negatively affecting the precision of backward propagation such that DIVISION maintains competitive model accuracy. Experiment results show DIVISION has better comprehensive performance than state-of-the-art methods, including over 10x compression of activation maps and competitive training throughput, without loss of model accuracy.

Art style classification remains a formidable challenge in computational aesthetics due to the scarcity of expertly labeled datasets and the intricate, often nonlinear interplay of stylistic elements. While recent dual-teacher self-supervised frameworks reduce reliance on labeled data, their linear projection layers and localized focus struggle to model global compositional context and complex style-feature interactions. We enhance the dual-teacher knowledge distillation framework to address these limitations by replacing conventional MLP projection and prediction heads with Kolmogorov-Arnold Networks (KANs). Our approach retains complementary guidance from two teacher networks, one emphasizing localized texture and brushstroke patterns, the other capturing broader stylistic hierarchies while leveraging KANs' spline-based activations to model nonlinear feature correlations with mathematical precision. Experiments on WikiArt and Pandora18k demonstrate that our approach outperforms the base dual teacher architecture in Top-1 accuracy. Our findings highlight the importance of KANs in disentangling complex style manifolds, leading to better linear probe accuracy than MLP projections.

In this study, we introduce the Multi-Head Explainer (MHEX), a versatile and modular framework that enhances both the explainability and accuracy of Convolutional Neural Networks (CNNs) and Transformer-based models. MHEX consists of three core components: an Attention Gate that dynamically highlights task-relevant features, Deep Supervision that guides early layers to capture fine-grained details pertinent to the target class, and an Equivalent Matrix that unifies refined local and global representations to generate comprehensive saliency maps. Our approach demonstrates superior compatibility, enabling effortless integration into existing residual networks like ResNet and Transformer architectures such as BERT with minimal modifications. Extensive experiments on benchmark datasets in medical imaging and text classification show that MHEX not only improves classification accuracy but also produces highly interpretable and detailed saliency scores.

There has been an explosion of interest in designing high-performance Transformers. While Transformers have delivered significant performance improvements, training such networks is extremely memory intensive owing to storing all intermediate activations that are needed for gradient computation during backpropagation, especially for long sequences. To this end, we present Mesa, a memory-saving training framework for Transformers. Specifically, Mesa uses exact activations during forward pass while storing a low-precision version of activations to reduce memory consumption during training. The low-precision activations are then dequantized during back-propagation to compute gradients. Besides, to address the heterogeneous activation distributions in the multi-head self-attention layers, we propose a head-wise activation quantization strategy, which quantizes activations based on the statistics of each head to minimize the approximation error. To further boost training efficiency, we learn quantization parameters by running estimates. More importantly, by re-investing the saved memory in employing a larger batch size or scaling up model size, we may further improve the performance under constrained computational resources. Extensive experiments on ImageNet, CIFAR-100 and ADE20K demonstrate that Mesa can achieve flexible memory-savings (up to 50%) during training while achieving comparable or even better performance. Code is available at https://github.com/ziplab/Mesa.

Attention layers -- which map a sequence of inputs to a sequence of outputs -- are core building blocks of the Transformer architecture which has achieved significant breakthroughs in modern artificial intelligence. This paper presents a rigorous theoretical study on the learning and generalization of a single multi-head attention layer, with a sequence of key vectors and a separate query vector as input. We consider the random feature setting where the attention layer has a large number of heads, with randomly sampled frozen query and key matrices, and trainable value matrices. We show that such a random-feature attention layer can express a broad class of target functions that are permutation invariant to the key vectors. We further provide quantitative excess risk bounds for learning these target functions from finite samples, using random feature attention with finitely many heads. Our results feature several implications unique to the attention structure compared with existing random features theory for neural networks, such as (1) Advantages in the sample complexity over standard two-layer random-feature networks; (2) Concrete and natural classes of functions that can be learned efficiently by a random-feature attention layer; and (3) The effect of the sampling distribution of the query-key weight matrix (the product of the query and key matrix), where Gaussian random weights with a non-zero mean result in better sample complexities over the zero-mean counterpart for learning certain natural target functions. Experiments on simulated data corroborate our theoretical findings and further illustrate the interplay between the sample size and the complexity of the target function.

The costly self-attention layers in modern Transformers require memory and compute quadratic in sequence length. Existing approximation methods usually underperform and fail to obtain significant speedups in practice. Here we present SwitchHead - a novel method that reduces both compute and memory requirements and achieves wall-clock speedup, while matching the language modeling performance of baseline Transformers with the same parameter budget. SwitchHead uses Mixture-of-Experts (MoE) layers for the value and output projections and requires 4 to 8 times fewer attention matrices than standard Transformers. Our novel attention can also be combined with MoE MLP layers, resulting in an efficient fully-MoE "SwitchAll" Transformer model. Our code is public.

This paper describes a system designed to distinguish between AI-generated and human-written scientific excerpts in the DAGPap24 competition hosted within the Fourth Workshop on Scientific Document Processing. In this competition the task is to find artificially generated token-level text fragments in documents of a scientific domain. Our work focuses on the use of a multi-task learning architecture with two heads. The application of this approach is justified by the specificity of the task, where class spans are continuous over several hundred characters. We considered different encoder variations to obtain a state vector for each token in the sequence, as well as a variation in splitting fragments into tokens to further feed into the input of a transform-based encoder. This approach allows us to achieve a 9% quality improvement relative to the baseline solution score on the development set (from 0.86 to 0.95) using the average macro F1-score, as well as a score of 0.96 on a closed test part of the dataset from the competition.

Learning with auxiliary tasks can improve the ability of a primary task to generalise. However, this comes at the cost of manually labelling auxiliary data. We propose a new method which automatically learns appropriate labels for an auxiliary task, such that any supervised learning task can be improved without requiring access to any further data. The approach is to train two neural networks: a label-generation network to predict the auxiliary labels, and a multi-task network to train the primary task alongside the auxiliary task. The loss for the label-generation network incorporates the loss of the multi-task network, and so this interaction between the two networks can be seen as a form of meta learning with a double gradient. We show that our proposed method, Meta AuXiliary Learning (MAXL), outperforms single-task learning on 7 image datasets, without requiring any additional data. We also show that MAXL outperforms several other baselines for generating auxiliary labels, and is even competitive when compared with human-defined auxiliary labels. The self-supervised nature of our method leads to a promising new direction towards automated generalisation. Source code can be found at https://github.com/lorenmt/maxl.

Developing Intelligent Systems involves artificial intelligence approaches including artificial neural networks. Here, we present a tutorial of Deep Neural Networks (DNNs), and some insights about the origin of the term "deep"; references to deep learning are also given. Restricted Boltzmann Machines, which are the core of DNNs, are discussed in detail. An example of a simple two-layer network, performing unsupervised learning for unlabeled data, is shown. Deep Belief Networks (DBNs), which are used to build networks with more than two layers, are also described. Moreover, examples for supervised learning with DNNs performing simple prediction and classification tasks, are presented and explained. This tutorial includes two intelligent pattern recognition applications: hand- written digits (benchmark known as MNIST) and speech recognition.

While the Transformer architecture dominates many fields, its quadratic self-attention complexity hinders its use in large-scale applications. Linear attention offers an efficient alternative, but its direct application often degrades performance, with existing fixes typically re-introducing computational overhead through extra modules (e.g., depthwise separable convolution) that defeat the original purpose. In this work, we identify a key failure mode in these methods: global context collapse, where the model loses representational diversity. To address this, we propose Multi-Head Linear Attention (MHLA), which preserves this diversity by computing attention within divided heads along the token dimension. We prove that MHLA maintains linear complexity while recovering much of the expressive power of softmax attention, and verify its effectiveness across multiple domains, achieving a 3.6\% improvement on ImageNet classification, a 6.3\% gain on NLP, a 12.6\% improvement on image generation, and a 41\% enhancement on video generation under the same time complexity.

The ability of deep neural networks (DNNs) come from extracting and interpreting features from the data provided. By exploiting intermediate features in DNNs instead of relying on hard labels, we craft adversarial perturbation that generalize more effectively, boosting black-box transferability. These features ubiquitously come from supervised learning in previous work. Inspired by the exceptional synergy between self-supervised learning and the Transformer architecture, this paper explores whether exploiting self-supervised Vision Transformer (ViT) representations can improve adversarial transferability. We present dSVA -- a generative dual self-supervised ViT features attack, that exploits both global structural features from contrastive learning (CL) and local textural features from masked image modeling (MIM), the self-supervised learning paradigm duo for ViTs. We design a novel generative training framework that incorporates a generator to create black-box adversarial examples, and strategies to train the generator by exploiting joint features and the attention mechanism of self-supervised ViTs. Our findings show that CL and MIM enable ViTs to attend to distinct feature tendencies, which, when exploited in tandem, boast great adversarial generalizability. By disrupting dual deep features distilled by self-supervised ViTs, we are rewarded with remarkable black-box transferability to models of various architectures that outperform state-of-the-arts. Code available at https://github.com/spencerwooo/dSVA.

We propose split-brain autoencoders, a straightforward modification of the traditional autoencoder architecture, for unsupervised representation learning. The method adds a split to the network, resulting in two disjoint sub-networks. Each sub-network is trained to perform a difficult task -- predicting one subset of the data channels from another. Together, the sub-networks extract features from the entire input signal. By forcing the network to solve cross-channel prediction tasks, we induce a representation within the network which transfers well to other, unseen tasks. This method achieves state-of-the-art performance on several large-scale transfer learning benchmarks.

Few algorithms for supervised training of spiking neural networks exist that can deal with patterns of multiple spikes, and their computational properties are largely unexplored. We demonstrate in a set of simulations that the ReSuMe learning algorithm can be successfully applied to layered neural networks. Input and output patterns are encoded as spike trains of multiple precisely timed spikes, and the network learns to transform the input trains into target output trains. This is done by combining the ReSuMe learning algorithm with multiplicative scaling of the connections of downstream neurons. We show in particular that layered networks with one hidden layer can learn the basic logical operations, including Exclusive-Or, while networks without hidden layer cannot, mirroring an analogous result for layered networks of rate neurons. While supervised learning in spiking neural networks is not yet fit for technical purposes, exploring computational properties of spiking neural networks advances our understanding of how computations can be done with spike trains.

The teacher-student framework, prevalent in semi-supervised semantic segmentation, mainly employs the exponential moving average (EMA) to update a single teacher's weights based on the student's. However, EMA updates raise a problem in that the weights of the teacher and student are getting coupled, causing a potential performance bottleneck. Furthermore, this problem may become more severe when training with more complicated labels such as segmentation masks but with few annotated data. This paper introduces Dual Teacher, a simple yet effective approach that employs dual temporary teachers aiming to alleviate the coupling problem for the student. The temporary teachers work in shifts and are progressively improved, so consistently prevent the teacher and student from becoming excessively close. Specifically, the temporary teachers periodically take turns generating pseudo-labels to train a student model and maintain the distinct characteristics of the student model for each epoch. Consequently, Dual Teacher achieves competitive performance on the PASCAL VOC, Cityscapes, and ADE20K benchmarks with remarkably shorter training times than state-of-the-art methods. Moreover, we demonstrate that our approach is model-agnostic and compatible with both CNN- and Transformer-based models. Code is available at https://github.com/naver-ai/dual-teacher.

Dual encoder architectures like CLIP models map two types of inputs into a shared embedding space and predict similarities between them. Despite their success, it is, however, not understood how these models compare their two inputs. Common first-order feature-attribution methods can only provide limited insights into dual-encoders since their predictions depend on feature-interactions rather than on individual features. In this paper, we first derive a second-order method enabling the attribution of predictions by any differentiable dual encoder onto feature-interactions between its inputs. Second, we apply our method to CLIP models and show that they learn fine-grained correspondences between parts of captions and regions in images. They match objects across input modes also account for mismatches. This visual-linguistic grounding ability, however, varies heavily between object classes and exhibits pronounced out-of-domain effects. We can identify individual errors as well as systematic failure categories including object coverage, unusual scenes and correlated contexts.

We propose a cross-modal attention distillation framework to train a dual-encoder model for vision-language understanding tasks, such as visual reasoning and visual question answering. Dual-encoder models have a faster inference speed than fusion-encoder models and enable the pre-computation of images and text during inference. However, the shallow interaction module used in dual-encoder models is insufficient to handle complex vision-language understanding tasks. In order to learn deep interactions of images and text, we introduce cross-modal attention distillation, which uses the image-to-text and text-to-image attention distributions of a fusion-encoder model to guide the training of our dual-encoder model. In addition, we show that applying the cross-modal attention distillation for both pre-training and fine-tuning stages achieves further improvements. Experimental results demonstrate that the distilled dual-encoder model achieves competitive performance for visual reasoning, visual entailment and visual question answering tasks while enjoying a much faster inference speed than fusion-encoder models. Our code and models will be publicly available at https://github.com/kugwzk/Distilled-DualEncoder.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Mixture-of-Experts (MoE) enhances model performance while maintaining computational efficiency, making it well-suited for large-scale applications. However, expert in exist MoE paradigm works as an individual, thereby lacking high-quality expert interactions. Moreover, they have not been effectively extended to attention block, which constrains further efficiency improvements. To tackle these issues, we propose Union-of-Experts (UoE), which decomposes transformer into an equitant group of experts, and then implement dynamic routing on input data and experts. Our approach advances MoE design with three key innovations: (1) We conducted equitant expert decomposition on both MLP blocks and attention blocks based on matrix partition in tensor parallelism. (2) We developed two routing paradigms: patch wise data selection and expert selection, to apply routing across different levels. (3) We design the architecture of UoE model, including Selective Multi-Head Attention (SMHA) and Union-of-MLP-Experts (UoME). (4) We develop parallel implementation of UoE's routing and computation operation, and optimize efficiency based on the hardware processing analysis. The experiments demonstrate that the model employed with UoE surpass Full Attention, state-of-art MoEs and efficient transformers in several tasks across image and natural language domains. The source codes are available at https://github.com/YujiaoYang-work/UoE.

Backpropagation is the standard method for achieving state-of-the-art accuracy in neural network training, but it often imposes high memory costs and lacks biological plausibility. In this paper, we introduce the Mono-Forward algorithm, a purely local layerwise learning method inspired by Hinton's Forward-Forward framework. Unlike backpropagation, Mono-Forward optimizes each layer solely with locally available information, eliminating the reliance on global error signals. We evaluated Mono-Forward on multi-layer perceptrons and convolutional neural networks across multiple benchmarks, including MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100. The test results show that Mono-Forward consistently matches or surpasses the accuracy of backpropagation across all tasks, with significantly reduced and more even memory usage, better parallelizability, and a comparable convergence rate.

Multi-head self-attention (MHSA) is a key component of Transformers, a widely popular architecture in both language and vision. Multiple heads intuitively enable different parallel processes over the same input. Yet, they also obscure the attribution of each input patch to the output of a model. We propose a novel 1-head Transformer Attention Bottleneck (TAB) layer, inserted after the traditional MHSA architecture, to serve as an attention bottleneck for interpretability and intervention. Unlike standard self-attention, TAB constrains the total attention over all patches to in [0, 1]. That is, when the total attention is 0, no visual information is propagated further into the network and the vision-language model (VLM) would default to a generic, image-independent response. To demonstrate the advantages of TAB, we train VLMs with TAB to perform image difference captioning. Over three datasets, our models perform similarly to baseline VLMs in captioning but the bottleneck is superior in localizing changes and in identifying when no changes occur. TAB is the first architecture to enable users to intervene by editing attention, which often produces expected outputs by VLMs.

The differing representation spaces required for visual understanding and generation pose a challenge in unifying them within the autoregressive paradigm of large language models. A vision tokenizer trained for reconstruction excels at capturing low-level perceptual details, making it well-suited for visual generation but lacking high-level semantic representations for understanding tasks. Conversely, a vision encoder trained via contrastive learning aligns well with language but struggles to decode back into the pixel space for generation tasks. To bridge this gap, we propose DualToken, a method that unifies representations for both understanding and generation within a single tokenizer. However, directly integrating reconstruction and semantic objectives in a single tokenizer creates conflicts, leading to degraded performance in both reconstruction quality and semantic performance. Instead of forcing a single codebook to handle both semantic and perceptual information, DualToken disentangles them by introducing separate codebooks for high and low-level features, effectively transforming their inherent conflict into a synergistic relationship. As a result, DualToken achieves state-of-the-art performance in both reconstruction and semantic tasks while demonstrating remarkable effectiveness in downstream MLLM understanding and generation tasks. Notably, we also show that DualToken, as a unified tokenizer, surpasses the naive combination of two distinct types vision encoders, providing superior performance within a unified MLLM.

Multi-Head Mixture-of-Experts (MH-MoE) demonstrates superior performance by using the multi-head mechanism to collectively attend to information from various representation spaces within different experts. In this paper, we present a novel implementation of MH-MoE that maintains both FLOPs and parameter parity with sparse Mixture of Experts models. Experimental results on language models show that the new implementation yields quality improvements over both vanilla MoE and fine-grained MoE models. Additionally, our experiments demonstrate that MH-MoE is compatible with 1-bit Large Language Models (LLMs) such as BitNet.

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the order of their execution is learned. In this work, we further expand this approach and also learn the underlying internal structure of modules in terms of the ordering and combination of simple and elementary arithmetic operators. Our results show that one is indeed able to simultaneously learn both internal module structure and module sequencing without extra supervisory signals for module execution sequencing. With this approach, we report performance comparable to models using hand-designed modules.

The structure of biological neural circuits-modular, hierarchical, and sparsely interconnected-reflects an efficient trade-off between wiring cost, functional specialization, and robustness. These principles offer valuable insights for artificial neural network (ANN) design, especially as networks grow in depth and scale. Sparsity, in particular, has been widely explored for reducing memory and computation, improving speed, and enhancing generalization. Motivated by systems neuroscience findings, we explore how patterns of functional connectivity in the mouse visual cortex-specifically, ensemble-to-ensemble communication, can inform ANN design. We introduce G2GNet, a novel architecture that imposes sparse, modular connectivity across feedforward layers. Despite having significantly fewer parameters than fully connected models, G2GNet achieves superior accuracy on standard vision benchmarks. To our knowledge, this is the first architecture to incorporate biologically observed functional connectivity patterns as a structural bias in ANN design. We complement this static bias with a dynamic sparse training (DST) mechanism that prunes and regrows edges during training. We also propose a Hebbian-inspired rewiring rule based on activation correlations, drawing on principles of biological plasticity. G2GNet achieves up to 75% sparsity while improving accuracy by up to 4.3% on benchmarks, including Fashion-MNIST, CIFAR-10, and CIFAR-100, outperforming dense baselines with far fewer computations.

The Transformer architecture processes sequences by implementing a form of neural message-passing that consists of iterative information retrieval (attention), followed by local processing (position-wise MLP). Two types of information are essential under this general computational paradigm: "sensory" information about individual objects, and "relational" information describing the relationships between objects. Standard attention naturally encodes the former, but does not explicitly encode the latter. In this paper, we present an extension of Transformers where multi-head attention is augmented with two distinct types of attention heads, each routing information of a different type. The first type is the standard attention mechanism of Transformers, which captures object-level features, while the second type is a novel attention mechanism we propose to explicitly capture relational information. The two types of attention heads each possess different inductive biases, giving the resulting architecture greater efficiency and versatility. The promise of this approach is demonstrated empirically across a range of tasks.

Transformer architectures have revolutionized artificial intelligence (AI) through their attention mechanisms, yet the computational principles underlying their success remain opaque. We present a novel theoretical framework that reinterprets the core computation of attention as Pavlovian conditioning. Our model finds a direct mathematical analogue in linear attention, which simplifies the analysis of the underlying associative process. We demonstrate that attention's queries, keys, and values can be mapped to the three elements of classical conditioning: test stimuli that probe associations, conditional stimuli (CS) that serve as retrieval cues, and unconditional stimuli (US) that contain response information. Through this lens, we suggest that each attention operation constructs a transient associative memory via a Hebbian rule, where CS-US pairs form dynamic associations that test stimuli can later retrieve. Our framework yields several theoretical insights grounded in this linearized model: (1) a capacity theorem showing that attention heads can store O(d_k) associations before interference degrades retrieval; (2) an error propagation analysis revealing fundamental architectural trade-offs of balancing model depth, width, and head redundancy to maintain reliability; and (3) an understanding of how biologically plausible learning rules could enhance transformer architectures. By establishing this deep connection, we suggest that the success of modern AI may stem not from architectural novelty alone, but from implementing computational principles that biology optimized over millions of years of evolution.

Computational workloads composing traditional Transformer models are starkly bifurcated. Multi-Head Attention (MHA) is memory-bound, with low arithmetic intensity, while feedforward layers are compute-bound. This dichotomy has long motivated research into specialized hardware to mitigate the MHA bottleneck. This paper argues that recent architectural shifts, namely Multi-head Latent Attention (MLA) and Mixture-of-Experts (MoE), challenge the premise of specialized attention hardware. We make two key observations. First, the arithmetic intensity of MLA is over two orders of magnitude greater than that of MHA, shifting it close to a compute-bound regime well-suited for modern accelerators like GPUs. Second, by distributing MoE experts across a pool of accelerators, their arithmetic intensity can be tuned through batching to match that of the dense layers, creating a more balanced computational profile. These findings reveal a diminishing need for specialized attention hardware. The central challenge for next-generation Transformers is no longer accelerating a single memory-bound layer. Instead, the focus must shift to designing balanced systems with sufficient compute, memory capacity, memory bandwidth, and high-bandwidth interconnects to manage the diverse demands of large-scale models.

Attention based Transformer architecture has enabled significant advances in the field of natural language processing. In addition to new pre-training techniques, recent improvements crucially rely on working with a relatively larger embedding dimension for tokens. Unfortunately, this leads to models that are prohibitively large to be employed in the downstream tasks. In this paper we identify one of the important factors contributing to the large embedding size requirement. In particular, our analysis highlights that the scaling between the number of heads and the size of each head in the current architecture gives rise to a low-rank bottleneck in attention heads, causing this limitation. We further validate this in our experiments. As a solution we propose to set the head size of an attention unit to input sequence length, and independent of the number of heads, resulting in multi-head attention layers with provably more expressive power. We empirically show that this allows us to train models with a relatively smaller embedding dimension and with better performance scaling.

Solving multi-label recognition (MLR) for images in the low-label regime is a challenging task with many real-world applications. Recent work learns an alignment between textual and visual spaces to compensate for insufficient image labels, but loses accuracy because of the limited amount of available MLR annotations. In this work, we utilize the strong alignment of textual and visual features pretrained with millions of auxiliary image-text pairs and propose Dual Context Optimization (DualCoOp) as a unified framework for partial-label MLR and zero-shot MLR. DualCoOp encodes positive and negative contexts with class names as part of the linguistic input (i.e. prompts). Since DualCoOp only introduces a very light learnable overhead upon the pretrained vision-language framework, it can quickly adapt to multi-label recognition tasks that have limited annotations and even unseen classes. Experiments on standard multi-label recognition benchmarks across two challenging low-label settings demonstrate the advantages of our approach over state-of-the-art methods.

In recent years, deep learning has been a revolution in the field of machine learning, for computer vision in particular. In this approach, a deep (multilayer) artificial neural network (ANN) is trained in a supervised manner using backpropagation. Huge amounts of labeled examples are required, but the resulting classification accuracy is truly impressive, sometimes outperforming humans. Neurons in an ANN are characterized by a single, static, continuous-valued activation. Yet biological neurons use discrete spikes to compute and transmit information, and the spike times, in addition to the spike rates, matter. Spiking neural networks (SNNs) are thus more biologically realistic than ANNs, and arguably the only viable option if one wants to understand how the brain computes. SNNs are also more hardware friendly and energy-efficient than ANNs, and are thus appealing for technology, especially for portable devices. However, training deep SNNs remains a challenge. Spiking neurons' transfer function is usually non-differentiable, which prevents using backpropagation. Here we review recent supervised and unsupervised methods to train deep SNNs, and compare them in terms of accuracy, but also computational cost and hardware friendliness. The emerging picture is that SNNs still lag behind ANNs in terms of accuracy, but the gap is decreasing, and can even vanish on some tasks, while the SNNs typically require much fewer operations.

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Two principles: the complementary principle and the consensus principle are widely acknowledged in the literature of multi-view learning. However, the current design of multi-head self-attention, an instance of multi-view learning, prioritizes the complementarity while ignoring the consensus. To address this problem, we propose an enhanced multi-head self-attention (EMHA). First, to satisfy the complementary principle, EMHA removes the one-to-one mapping constraint among queries and keys in multiple subspaces and allows each query to attend to multiple keys. On top of that, we develop a method to fully encourage consensus among heads by introducing two interaction models, namely inner-subspace interaction and cross-subspace interaction. Extensive experiments on a wide range of language tasks (e.g., machine translation, abstractive summarization and grammar correction, language modeling), show its superiority, with a very modest increase in model size. Our code would be available at: https://github.com/zhengkid/EIT-Enhanced-Interactive-Transformer.

We interpret the function of individual neurons in CLIP by automatically describing them using text. Analyzing the direct effects (i.e. the flow from a neuron through the residual stream to the output) or the indirect effects (overall contribution) fails to capture the neurons' function in CLIP. Therefore, we present the "second-order lens", analyzing the effect flowing from a neuron through the later attention heads, directly to the output. We find that these effects are highly selective: for each neuron, the effect is significant for <2% of the images. Moreover, each effect can be approximated by a single direction in the text-image space of CLIP. We describe neurons by decomposing these directions into sparse sets of text representations. The sets reveal polysemantic behavior - each neuron corresponds to multiple, often unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we mass-produce "semantic" adversarial examples by generating images with concepts spuriously correlated to the incorrect class. Additionally, we use the second-order effects for zero-shot segmentation and attribute discovery in images. Our results indicate that a scalable understanding of neurons can be used for model deception and for introducing new model capabilities.

Click-through rate (CTR) prediction is one of the fundamental tasks for online advertising and recommendation. While multi-layer perceptron (MLP) serves as a core component in many deep CTR prediction models, it has been widely recognized that applying a vanilla MLP network alone is inefficient in learning multiplicative feature interactions. As such, many two-stream interaction models (e.g., DeepFM and DCN) have been proposed by integrating an MLP network with another dedicated network for enhanced CTR prediction. As the MLP stream learns feature interactions implicitly, existing research focuses mainly on enhancing explicit feature interactions in the complementary stream. In contrast, our empirical study shows that a well-tuned two-stream MLP model that simply combines two MLPs can even achieve surprisingly good performance, which has never been reported before by existing work. Based on this observation, we further propose feature gating and interaction aggregation layers that can be easily plugged to make an enhanced two-stream MLP model, FinalMLP. In this way, it not only enables differentiated feature inputs but also effectively fuses stream-level interactions across two streams. Our evaluation results on four open benchmark datasets as well as an online A/B test in our industrial system show that FinalMLP achieves better performance than many sophisticated two-stream CTR models. Our source code will be available at MindSpore/models.

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

We revisit continual learning~(CL), which enables pre-trained vision transformers (ViTs) to sequentially fine-tune on new downstream tasks over time. However, as the scale of these models increases, catastrophic forgetting remains a more serious challenge. Recent studies highlight a crossover between CL techniques and parameter-efficient fine-tuning (PEFT), which focuses on fine-tuning only a small set of trainable parameters to adapt to downstream tasks, such as low-rank adaptation (LoRA). While LoRA achieves faster convergence and requires fewer trainable parameters, it has seldom been explored in the context of continual learning. To address this gap, we propose a novel PEFT-CL method called Dual Low-Rank Adaptation (DualLoRA), which introduces both an orthogonal LoRA adapter and a residual LoRA adapter parallel to pre-trained weights in each layer. These components are orchestrated by a dynamic memory mechanism to strike a balance between stability and plasticity. Additionally, we propose a scheme to predict task identity with confidence and calibrate the model's outputs accordingly. On ViT-based models, we demonstrate that DualLoRA offers significant advantages in accuracy, inference speed, and computation efficiency in training over existing CL methods across multiple benchmarks.

The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote compositionality remains an open issue, with recent efforts concentrating mainly on linearized networks. We conduct a theoretical study that attempts to demystify compositionality in standard non-linear networks through the second-order Taylor approximation of the loss function. The proposed formulation highlights the importance of staying within the pre-training basin to achieve composable modules. Moreover, it provides the basis for two dual incremental training algorithms: the one from the perspective of multiple models trained individually, while the other aims to optimize the composed model as a whole. We probe their application in incremental classification tasks and highlight some valuable skills. In fact, the pool of incrementally learned modules not only supports the creation of an effective multi-task model but also enables unlearning and specialization in certain tasks. Code available at https://github.com/aimagelab/mammoth.

The multi-modal nature of many vision problems calls for neural network architectures that can perform multiple tasks concurrently. Typically, such architectures have been handcrafted in the literature. However, given the size and complexity of the problem, this manual architecture exploration likely exceeds human design abilities. In this paper, we propose a principled approach, rooted in differentiable neural architecture search, to automatically define branching (tree-like) structures in the encoding stage of a multi-task neural network. To allow flexibility within resource-constrained environments, we introduce a proxyless, resource-aware loss that dynamically controls the model size. Evaluations across a variety of dense prediction tasks show that our approach consistently finds high-performing branching structures within limited resource budgets.

A large-scale labeled dataset is a key factor for the success of supervised deep learning in computer vision. However, a limited number of annotated data is very common, especially in ophthalmic image analysis, since manual annotation is time-consuming and labor-intensive. Self-supervised learning (SSL) methods bring huge opportunities for better utilizing unlabeled data, as they do not need massive annotations. With an attempt to use as many as possible unlabeled ophthalmic images, it is necessary to break the dimension barrier, simultaneously making use of both 2D and 3D images. In this paper, we propose a universal self-supervised Transformer framework, named Uni4Eye, to discover the inherent image property and capture domain-specific feature embedding in ophthalmic images. Uni4Eye can serve as a global feature extractor, which builds its basis on a Masked Image Modeling task with a Vision Transformer (ViT) architecture. We employ a Unified Patch Embedding module to replace the origin patch embedding module in ViT for jointly processing both 2D and 3D input images. Besides, we design a dual-branch multitask decoder module to simultaneously perform two reconstruction tasks on the input image and its gradient map, delivering discriminative representations for better convergence. We evaluate the performance of our pre-trained Uni4Eye encoder by fine-tuning it on six downstream ophthalmic image classification tasks. The superiority of Uni4Eye is successfully established through comparisons to other state-of-the-art SSL pre-training methods.

Vision transformers have been applied successfully for image recognition tasks. There have been either multi-headed self-attention based (ViT dosovitskiy2020image, DeIT, touvron2021training) similar to the original work in textual models or more recently based on spectral layers (Fnetlee2021fnet, GFNetrao2021global, AFNOguibas2021efficient). We hypothesize that both spectral and multi-headed attention plays a major role. We investigate this hypothesis through this work and observe that indeed combining spectral and multi-headed attention layers provides a better transformer architecture. We thus propose the novel Spectformer architecture for transformers that combines spectral and multi-headed attention layers. We believe that the resulting representation allows the transformer to capture the feature representation appropriately and it yields improved performance over other transformer representations. For instance, it improves the top-1 accuracy by 2\% on ImageNet compared to both GFNet-H and LiT. SpectFormer-S reaches 84.25\% top-1 accuracy on ImageNet-1K (state of the art for small version). Further, Spectformer-L achieves 85.7\% that is the state of the art for the comparable base version of the transformers. We further ensure that we obtain reasonable results in other scenarios such as transfer learning on standard datasets such as CIFAR-10, CIFAR-100, Oxford-IIIT-flower, and Standford Car datasets. We then investigate its use in downstream tasks such of object detection and instance segmentation on the MS-COCO dataset and observe that Spectformer shows consistent performance that is comparable to the best backbones and can be further optimized and improved. Hence, we believe that combined spectral and attention layers are what are needed for vision transformers.

Transformer has recently gained considerable popularity in low-level vision tasks, including image super-resolution (SR). These networks utilize self-attention along different dimensions, spatial or channel, and achieve impressive performance. This inspires us to combine the two dimensions in Transformer for a more powerful representation capability. Based on the above idea, we propose a novel Transformer model, Dual Aggregation Transformer (DAT), for image SR. Our DAT aggregates features across spatial and channel dimensions, in the inter-block and intra-block dual manner. Specifically, we alternately apply spatial and channel self-attention in consecutive Transformer blocks. The alternate strategy enables DAT to capture the global context and realize inter-block feature aggregation. Furthermore, we propose the adaptive interaction module (AIM) and the spatial-gate feed-forward network (SGFN) to achieve intra-block feature aggregation. AIM complements two self-attention mechanisms from corresponding dimensions. Meanwhile, SGFN introduces additional non-linear spatial information in the feed-forward network. Extensive experiments show that our DAT surpasses current methods. Code and models are obtainable at https://github.com/zhengchen1999/DAT.

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training dynamics. While prior work has identified that individual neurons learn single-frequency Fourier features and phase alignment, it does not fully explain how these features combine into a global solution. We bridge this gap by formalizing a diversification condition that emerges during training when overparametrized, consisting of two parts: phase symmetry and frequency diversification. We prove that these properties allow the network to collectively approximate a flawed indicator function on the correct logic for the modular addition task. While individual neurons produce noisy signals, the phase symmetry enables a majority-voting scheme that cancels out noise, allowing the network to robustly identify the correct sum. Furthermore, we explain the emergence of these features under random initialization via a lottery ticket mechanism. Our gradient flow analysis proves that frequencies compete within each neuron, with the "winner" determined by its initial spectral magnitude and phase alignment. From a technical standpoint, we provide a rigorous characterization of the layer-wise phase coupling dynamics and formalize the competitive landscape using the ODE comparison lemma. Finally, we use these insights to demystify grokking, characterizing it as a three-stage process involving memorization followed by two generalization phases, driven by the competition between loss minimization and weight decay.

Neural Memory Networks (NMNs) have received increased attention in recent years compared to deep architectures that use a constrained memory. Despite their new appeal, the success of NMNs hinges on the ability of the gradient-based optimiser to perform incremental training of the NMN controllers, determining how to leverage their high capacity for knowledge retrieval. This means that while excellent performance can be achieved when the training data is consistent and well distributed, rare data samples are hard to learn from as the controllers fail to incorporate them effectively during model training. Drawing inspiration from the human cognition process, in particular the utilisation of neuromodulators in the human brain, we propose to decouple the learning process of the NMN controllers to allow them to achieve flexible, rapid adaptation in the presence of new information. This trait is highly beneficial for meta-learning tasks where the memory controllers must quickly grasp abstract concepts in the target domain, and adapt stored knowledge. This allows the NMN controllers to quickly determine which memories are to be retained and which are to be erased, and swiftly adapt their strategy to the new task at hand. Through both quantitative and qualitative evaluations on multiple public benchmarks, including classification and regression tasks, we demonstrate the utility of the proposed approach. Our evaluations not only highlight the ability of the proposed NMN architecture to outperform the current state-of-the-art methods, but also provide insights on how the proposed augmentations help achieve such superior results. In addition, we demonstrate the practical implications of the proposed learning strategy, where the feedback path can be shared among multiple neural memory networks as a mechanism for knowledge sharing.

A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one direction, and a generator in the opposite direction for the same data. The learning process of BL tries to reproduce the neuroplasticity stated in Hebbian theory using only backward propagation of errors. In this paper, two novel learning techniques are introduced which use BL for improving robustness to white noise static and adversarial examples. The first method is bidirectional propagation of errors, which the error propagation occurs in backward and forward directions. Motivated by the fact that its generative model receives as input a constant vector per class, we introduce as a second method the hybrid adversarial networks (HAN). Its generative model receives a random vector as input and its training is based on generative adversarial networks (GAN). To assess the performance of BL, we perform experiments using several architectures with fully and convolutional layers, with and without bias. Experimental results show that both methods improve robustness to white noise static and adversarial examples, and even increase accuracy, but have different behavior depending on the architecture and task, being more beneficial to use the one or the other. Nevertheless, HAN using a convolutional architecture with batch normalization presents outstanding robustness, reaching state-of-the-art accuracy on adversarial examples of hand-written digits.

We revisit a basic question in sequence modeling: is explicit self-attention actually necessary for strong performance and reasoning? We argue that standard multi-head attention is best seen as a form of tensor lifting: hidden vectors are mapped into a high-dimensional space of pairwise interactions, and learning proceeds by constraining this lifted tensor through gradient descent. This mechanism is extremely expressive but mathematically opaque, because after many layers it becomes very hard to describe the model with a small family of explicit invariants. To explore an alternative, we propose an attention-free architecture based on Grassmann flows. Instead of forming an L by L attention matrix, our Causal Grassmann layer (i) linearly reduces token states, (ii) encodes local token pairs as two-dimensional subspaces on a Grassmann manifold via Plucker coordinates, and (iii) fuses these geometric features back into the hidden states through gated mixing. Information therefore propagates by controlled deformations of low-rank subspaces over multi-scale local windows, so the core computation lives on a finite-dimensional manifold rather than in an unstructured tensor space. On the Wikitext-2 language modeling benchmark, purely Grassmann-based models with 13 to 18 million parameters achieve validation perplexities within about 10 to 15 percent of size-matched Transformers. On the SNLI natural language inference task, a Grassmann-Plucker head on top of DistilBERT slightly outperforms a Transformer head, with best validation and test accuracies of 0.8550 and 0.8538 compared to 0.8545 and 0.8511. We analyze the complexity of Grassmann mixing, show linear scaling in sequence length for fixed rank, and argue that such manifold-based designs offer a more structured route toward geometric and invariant-based interpretations of neural reasoning.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards "token uniformity". Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix. On the other hand, skip connections and MLPs stop the output from degeneration. Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.

In this work, we consider the optimization process of minibatch stochastic gradient descent (SGD) on a 2-layer neural network with data separated by a quadratic ground truth function. We prove that with data drawn from the d-dimensional Boolean hypercube labeled by the quadratic ``XOR'' function y = -x_ix_j, it is possible to train to a population error o(1) with d :polylog(d) samples. Our result considers simultaneously training both layers of the two-layer-neural network with ReLU activations via standard minibatch SGD on the logistic loss. To our knowledge, this work is the first to give a sample complexity of O(d) for efficiently learning the XOR function on isotropic data on a standard neural network with standard training. Our main technique is showing that the network evolves in two phases: a signal-finding phase where the network is small and many of the neurons evolve independently to find features, and a signal-heavy phase, where SGD maintains and balances the features. We leverage the simultaneous training of the layers to show that it is sufficient for only a small fraction of the neurons to learn features, since those neurons will be amplified by the simultaneous growth of their second layer weights.

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks and Boltzmann machines are versions of the Ising model, a model extensively studied in statistical mechanics for over a century. In the first part of this chapter, we provide an overview of the principles, models, and applications of ANNs, highlighting their connections to statistical mechanics and statistical learning theory. Artificial neural networks can be seen as high-dimensional mathematical functions, and understanding the geometric properties of their loss landscapes (i.e., the high-dimensional space on which one wishes to find extrema or saddles) can provide valuable insights into their optimization behavior, generalization abilities, and overall performance. Visualizing these functions can help us design better optimization methods and improve their generalization abilities. Thus, the second part of this chapter focuses on quantifying geometric properties and visualizing loss functions associated with deep ANNs.

Neural networks can approximate complex functions, but they struggle to perform exact arithmetic operations over real numbers. The lack of inductive bias for arithmetic operations leaves neural networks without the underlying logic necessary to extrapolate on tasks such as addition, subtraction, and multiplication. We present two new neural network components: the Neural Addition Unit (NAU), which can learn exact addition and subtraction; and the Neural Multiplication Unit (NMU) that can multiply subsets of a vector. The NMU is, to our knowledge, the first arithmetic neural network component that can learn to multiply elements from a vector, when the hidden size is large. The two new components draw inspiration from a theoretical analysis of recently proposed arithmetic components. We find that careful initialization, restricting parameter space, and regularizing for sparsity is important when optimizing the NAU and NMU. Our proposed units NAU and NMU, compared with previous neural units, converge more consistently, have fewer parameters, learn faster, can converge for larger hidden sizes, obtain sparse and meaningful weights, and can extrapolate to negative and small values.

Self-attention-based vision transformers (ViTs) have emerged as a highly competitive architecture in computer vision. Unlike convolutional neural networks (CNNs), ViTs are capable of global information sharing. With the development of various structures of ViTs, ViTs are increasingly advantageous for many vision tasks. However, the quadratic complexity of self-attention renders ViTs computationally intensive, and their lack of inductive biases of locality and translation equivariance demands larger model sizes compared to CNNs to effectively learn visual features. In this paper, we propose a light-weight and efficient vision transformer model called DualToken-ViT that leverages the advantages of CNNs and ViTs. DualToken-ViT effectively fuses the token with local information obtained by convolution-based structure and the token with global information obtained by self-attention-based structure to achieve an efficient attention structure. In addition, we use position-aware global tokens throughout all stages to enrich the global information, which further strengthening the effect of DualToken-ViT. Position-aware global tokens also contain the position information of the image, which makes our model better for vision tasks. We conducted extensive experiments on image classification, object detection and semantic segmentation tasks to demonstrate the effectiveness of DualToken-ViT. On the ImageNet-1K dataset, our models of different scales achieve accuracies of 75.4% and 79.4% with only 0.5G and 1.0G FLOPs, respectively, and our model with 1.0G FLOPs outperforms LightViT-T using global tokens by 0.7%.

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of first-order approximations telescoping out into a single empirically operational tool for practical analysis. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena in the literature -- including double descent, grokking, linear mode connectivity, and the challenges of applying deep learning on tabular data -- highlighting that this model allows us to construct and extract metrics that help predict and understand the a priori unexpected performance of neural networks. We also demonstrate that this model presents a pedagogical formalism allowing us to isolate components of the training process even in complex contemporary settings, providing a lens to reason about the effects of design choices such as architecture & optimization strategy, and reveals surprising parallels between neural network learning and gradient boosting.

It has been shown that dual encoders trained on one domain often fail to generalize to other domains for retrieval tasks. One widespread belief is that the bottleneck layer of a dual encoder, where the final score is simply a dot-product between a query vector and a passage vector, is too limited to make dual encoders an effective retrieval model for out-of-domain generalization. In this paper, we challenge this belief by scaling up the size of the dual encoder model {\em while keeping the bottleneck embedding size fixed.} With multi-stage training, surprisingly, scaling up the model size brings significant improvement on a variety of retrieval tasks, especially for out-of-domain generalization. Experimental results show that our dual encoders, Generalizable T5-based dense Retrievers (GTR), outperform %ColBERT~khattab2020colbert and existing sparse and dense retrievers on the BEIR dataset~thakur2021beir significantly. Most surprisingly, our ablation study finds that GTR is very data efficient, as it only needs 10\% of MS Marco supervised data to achieve the best out-of-domain performance. All the GTR models are released at https://tfhub.dev/google/collections/gtr/1.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

Fine-tuning pretrained large models to downstream tasks is an important problem, which however suffers from huge memory overhead due to large-scale parameters. This work strives to reduce memory overhead in fine-tuning from perspectives of activation function and layer normalization. To this end, we propose the Approximate Backpropagation (Approx-BP) theory, which provides the theoretical feasibility of decoupling the forward and backward passes. We apply our Approx-BP theory to backpropagation training and derive memory-efficient alternatives of GELU and SiLU activation functions, which use derivative functions of ReLUs in the backward pass while keeping their forward pass unchanged. In addition, we introduce a Memory-Sharing Backpropagation strategy, which enables the activation memory to be shared by two adjacent layers, thereby removing activation memory usage redundancy. Our method neither induces extra computation nor reduces training efficiency. We conduct extensive experiments with pretrained vision and language models, and the results demonstrate that our proposal can reduce up to sim30% of the peak memory usage. Our code is released at https://github.com/yyyyychen/LowMemoryBP.

Attention-based mechanisms are widely used in machine learning, most prominently in transformers. However, hyperparameters such as the rank of the attention matrices and the number of heads are scaled nearly the same way in all realizations of this architecture, without theoretical justification. In this work we show that there are dramatic trade-offs between the rank and number of heads of the attention mechanism. Specifically, we present a simple and natural target function that can be represented using a single full-rank attention head for any context length, but that cannot be approximated by low-rank attention unless the number of heads is exponential in the embedding dimension, even for short context lengths. Moreover, we prove that, for short context lengths, adding depth allows the target to be approximated by low-rank attention. For long contexts, we conjecture that full-rank attention is necessary. Finally, we present experiments with off-the-shelf transformers that validate our theoretical findings.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

RGB-D salient object detection (SOD), aiming to highlight prominent regions of a given scene by jointly modeling RGB and depth information, is one of the challenging pixel-level prediction tasks. Recently, the dual-attention mechanism has been devoted to this area due to its ability to strengthen the detection process. However, most existing methods directly fuse attentional cross-modality features under a manual-mandatory fusion paradigm without considering the inherent discrepancy between the RGB and depth, which may lead to a reduction in performance. Moreover, the long-range dependencies derived from global and local information make it difficult to leverage a unified efficient fusion strategy. Hence, in this paper, we propose the GL-DMNet, a novel dual mutual learning network with global-local awareness. Specifically, we present a position mutual fusion module and a channel mutual fusion module to exploit the interdependencies among different modalities in spatial and channel dimensions. Besides, we adopt an efficient decoder based on cascade transformer-infused reconstruction to integrate multi-level fusion features jointly. Extensive experiments on six benchmark datasets demonstrate that our proposed GL-DMNet performs better than 24 RGB-D SOD methods, achieving an average improvement of ~3% across four evaluation metrics compared to the second-best model (S3Net). Codes and results are available at https://github.com/kingkung2016/GL-DMNet.

Mixture-of-Experts (MoE) architectures are often considered a natural fit for continual learning because sparse routing should localize updates and reduce interference, yet MoE Transformers still forget substantially even with sparse, well-balanced expert utilization. We attribute this gap to a pre-routing bottleneck: multi-head attention concatenates head-specific signals into a single post-attention router input, forcing routing to act on co-occurring feature compositions rather than separable head channels. We show that this router input simultaneously encodes multiple separately decodable semantic and structural factors with uneven head support, and that different feature compositions induce weakly aligned parameter-gradient directions; as a result, routing maps many distinct compositions to the same route. We quantify this collision effect via a route-wise effective composition number N_{eff} and find that higher N_{eff} is associated with larger old-task loss increases after continual training. Motivated by these findings, we propose MH-MoE, which performs head-wise routing over sub-representations to increase routing granularity and reduce composition collisions. On TRACE with Qwen3-0.6B/8B, MH-MoE effectively mitigates forgetting, reducing BWT on Qwen3-0.6B from 11.2% (LoRAMoE) to 4.5%.

Convolutional architectures have proven extremely successful for vision tasks. Their hard inductive biases enable sample-efficient learning, but come at the cost of a potentially lower performance ceiling. Vision Transformers (ViTs) rely on more flexible self-attention layers, and have recently outperformed CNNs for image classification. However, they require costly pre-training on large external datasets or distillation from pre-trained convolutional networks. In this paper, we ask the following question: is it possible to combine the strengths of these two architectures while avoiding their respective limitations? To this end, we introduce gated positional self-attention (GPSA), a form of positional self-attention which can be equipped with a ``soft" convolutional inductive bias. We initialise the GPSA layers to mimic the locality of convolutional layers, then give each attention head the freedom to escape locality by adjusting a gating parameter regulating the attention paid to position versus content information. The resulting convolutional-like ViT architecture, ConViT, outperforms the DeiT on ImageNet, while offering a much improved sample efficiency. We further investigate the role of locality in learning by first quantifying how it is encouraged in vanilla self-attention layers, then analysing how it is escaped in GPSA layers. We conclude by presenting various ablations to better understand the success of the ConViT. Our code and models are released publicly at https://github.com/facebookresearch/convit.

Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently provided an equivalent convex training problem. However, extending this result to deeper networks remains to be an open problem. In this paper, we prove that the duality gap for deeper linear networks with vector outputs is non-zero. In contrast, we show that the zero duality gap can be obtained by stacking standard deep networks in parallel, which we call a parallel architecture, and modifying the regularization. Therefore, we prove the strong duality and existence of equivalent convex problems that enable globally optimal training of deep networks. As a by-product of our analysis, we demonstrate that the weight decay regularization on the network parameters explicitly encourages low-rank solutions via closed-form expressions. In addition, we show that strong duality holds for three-layer standard ReLU networks given rank-1 data matrices.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

Recurrent neural networks (RNNs) in the brain and in silico excel at solving tasks with intricate temporal dependencies. Long timescales required for solving such tasks can arise from properties of individual neurons (single-neuron timescale, tau, e.g., membrane time constant in biological neurons) or recurrent interactions among them (network-mediated timescale). However, the contribution of each mechanism for optimally solving memory-dependent tasks remains poorly understood. Here, we train RNNs to solve N-parity and N-delayed match-to-sample tasks with increasing memory requirements controlled by N by simultaneously optimizing recurrent weights and taus. We find that for both tasks RNNs develop longer timescales with increasing N, but depending on the learning objective, they use different mechanisms. Two distinct curricula define learning objectives: sequential learning of a single-N (single-head) or simultaneous learning of multiple Ns (multi-head). Single-head networks increase their tau with N and are able to solve tasks for large N, but they suffer from catastrophic forgetting. However, multi-head networks, which are explicitly required to hold multiple concurrent memories, keep tau constant and develop longer timescales through recurrent connectivity. Moreover, we show that the multi-head curriculum increases training speed and network stability to ablations and perturbations, and allows RNNs to generalize better to tasks beyond their training regime. This curriculum also significantly improves training GRUs and LSTMs for large-N tasks. Our results suggest that adapting timescales to task requirements via recurrent interactions allows learning more complex objectives and improves the RNN's performance.

Ever since their conception, Transformers have taken over traditional sequence models in many tasks, such as NLP, image classification, and video/audio processing, for their fast training and superior performance. Much of the merit is attributable to positional encoding and multi-head attention. However, Transformers fall short in learning long-range dependencies mainly due to the quadratic complexity scaled with context length, in terms of both time and space. Consequently, over the past five years, a myriad of methods has been proposed to make Transformers more efficient. In this work, we first take a step back, study and compare existing solutions to long-sequence modeling in terms of their pure mathematical formulation. Specifically, we summarize them using a unified template, given their shared nature of token mixing. Through benchmarks, we then demonstrate that long context length does yield better performance, albeit application-dependent, and traditional Transformer models fall short in taking advantage of long-range dependencies. Next, inspired by emerging sparse models of huge capacity, we propose a machine learning system for handling million-scale dependencies. As a proof of concept, we evaluate the performance of one essential component of this system, namely, the distributed multi-head attention. We show that our algorithm can scale up attention computation by almost 40times using four GeForce RTX 4090 GPUs, compared to vanilla multi-head attention mechanism. We believe this study is an instrumental step towards modeling million-scale dependencies.

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.

This paper introduces the sparse modular addition task and examines how transformers learn it. We focus on transformers with embeddings in R^2 and introduce a visual sandbox that provides comprehensive visualizations of each layer throughout the training process. We reveal a type of circuit, called "clustering heads," which learns the problem's invariants. We analyze the training dynamics of these circuits, highlighting two-stage learning, loss spikes due to high curvature or normalization layers, and the effects of initialization and curriculum learning.

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

We introduce Bootstrap Your Own Latent (BYOL), a new approach to self-supervised image representation learning. BYOL relies on two neural networks, referred to as online and target networks, that interact and learn from each other. From an augmented view of an image, we train the online network to predict the target network representation of the same image under a different augmented view. At the same time, we update the target network with a slow-moving average of the online network. While state-of-the art methods rely on negative pairs, BYOL achieves a new state of the art without them. BYOL reaches 74.3% top-1 classification accuracy on ImageNet using a linear evaluation with a ResNet-50 architecture and 79.6% with a larger ResNet. We show that BYOL performs on par or better than the current state of the art on both transfer and semi-supervised benchmarks. Our implementation and pretrained models are given on GitHub.

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the performance of resource sharing in many engineering areas, as learning tools and in combinatorial optimization, where they are seen as neural systems, and also as models of neurological aspects of living beings. In this article we focus on their learning capabilities, and more specifically, we present a practical guide for using the RNN to solve supervised learning problems. We give a general description of these models using almost indistinctly the terminology of Queuing Theory and the neural one. We present the standard learning procedures used by RNNs, adapted from similar well-established improvements in the standard NN field. We describe in particular a set of learning algorithms covering techniques based on the use of first order and, then, of second order derivatives. We also discuss some issues related to these objects and present new perspectives about their use in supervised learning problems. The tutorial describes their most relevant applications, and also provides a large bibliography.

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but recent reports of memorization of the training set raise the question of whether these networks are learning the "true" continuous density of the data. Here, we show that two DNNs trained on non-overlapping subsets of a dataset learn nearly the same score function, and thus the same density, when the number of training images is large enough. In this regime of strong generalization, diffusion-generated images are distinct from the training set, and are of high visual quality, suggesting that the inductive biases of the DNNs are well-aligned with the data density. We analyze the learned denoising functions and show that the inductive biases give rise to a shrinkage operation in a basis adapted to the underlying image. Examination of these bases reveals oscillating harmonic structures along contours and in homogeneous regions. We demonstrate that trained denoisers are inductively biased towards these geometry-adaptive harmonic bases since they arise not only when the network is trained on photographic images, but also when it is trained on image classes supported on low-dimensional manifolds for which the harmonic basis is suboptimal. Finally, we show that when trained on regular image classes for which the optimal basis is known to be geometry-adaptive and harmonic, the denoising performance of the networks is near-optimal.

Mixtures of Experts combine the outputs of several "expert" networks, each of which specializes in a different part of the input space. This is achieved by training a "gating" network that maps each input to a distribution over the experts. Such models show promise for building larger networks that are still cheap to compute at test time, and more parallelizable at training time. In this this work, we extend the Mixture of Experts to a stacked model, the Deep Mixture of Experts, with multiple sets of gating and experts. This exponentially increases the number of effective experts by associating each input with a combination of experts at each layer, yet maintains a modest model size. On a randomly translated version of the MNIST dataset, we find that the Deep Mixture of Experts automatically learns to develop location-dependent ("where") experts at the first layer, and class-specific ("what") experts at the second layer. In addition, we see that the different combinations are in use when the model is applied to a dataset of speech monophones. These demonstrate effective use of all expert combinations.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.