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Theory · Learning Theory

Leonardo Defilippis, Yatin Dandi, Pierre Mergny, Florent Krzakala, Bruno Loureiro

We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of neural networks, results beyond the single-index setting remain elusive. In this work, we introduce spectral algorithms based on the linearization of a message passing scheme tailored to this problem. Our main contribution is to show that the proposed methods achieve the optimal reconstruction threshold. Leveraging a high-dimensional characterization of the algorithms, we show that above the critical threshold the leading eigenvector correlates with the relevant index subspace, a phenomenon reminiscent of the Baik–Ben Arous–Peche (BBP) transition in spiked models arising in random matrix theory. Supported by numerical experiments and a rigorous theoretical framework, our work bridges critical gaps in the computational limits of weak learnability in multi-index model.

Optimization · Neural Network Optimization

Runze Xia, Richard Jiang

Recent advances in Vision Transformers (ViTs) have shown remarkable performance across vision tasks, yet their deep, uniform layer structure introduces significant computational overhead. In this work, we explore the emergent dynamics of ViT layers through the lens of energy-based memory systems, drawing a connection between self-attention and modern Hopfield networks. We introduce a novel metric—Layer Instability Index (LII)—derived from the operational softmax mode and its variability, to quantify the metastability of each Transformer layer over time. Our analysis reveals that certain layers exhibit consistent convergence to attractor-like states, suggesting functional specialisation and early stabilisation. Leveraging this insight, we propose an adaptive training framework that dynamically freezes or skips stable layers based on their energy landscape behavior. Our method reduces training costs while maintaining or improving accuracy. Extensive experiments on ViT-S/B/L on CUB-200-2011, CIFAR-10/100, Food-101, Stanford Dogs, and Beans demonstrate the generality and efficiency of our approach. This work provides new theoretical and practical perspectives for energy-aware optimisation of deep Transformer models.

Applications · Genetics, Cell Biology, etc

Zhenyi Zhang, Zihan Wang, Yuhao Sun, Tiejun Li, Peijie Zhou

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schrödinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schrödinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy. Code is available at: https://github.com/zhenyiizhang/CytoBridge-NeurIPS.

Optimization · Neural Network Optimization

Anirudh Chakravarthy, Shuai Zheng, Xin Huang, Sachithra Hemachandra, Xiao Zhang, Yuning Chai, Zhao Chen

The fine-tuning of pre-trained models has become ubiquitous in generative AI, computer vision, and robotics. Although much attention has been paid to improving the efficiency of fine-tuning model, there has been less scholarship around fine-tuning specifically for improved model performance. To remedy this gap, we present PROFIT, one of the first optimizers designed to incrementally fine-tune converged models on new tasks and/or datasets. Unlike traditional optimizers such as SGD or Adam, which make minimal assumptions due to random initializations, PROFIT takes the properties of a converged model into account explicitly to regularize the optimization process. Employing a temporal gradient-orthogonalization process, PROFIT outperforms fine-tuning methods in various tasks, from image classification to multimodal language model training to large-scale motion prediction. Moreover, PROFIT is encapsulated as a modular optimizer, which makes it easy to integrate directly into any training pipeline with minimal engineering effort.

Computer Vision · Everything Else

Jae-Young Yim, Dongwook Kim, Jae-Young Sim

Large-scale datasets are usually required to train deep neural networks; however, they increase computational complexity, hindering practical applications. Recently, dataset distillation for images and texts has attracted considerable attention, as it reduces the original dataset to a small synthetic one to alleviate the computational burden of training while preserving essential task-relevant information. However, dataset distillation for 3D point clouds remains largely unexplored, as point clouds exhibit fundamentally different characteristics from those of images, making this task more challenging. In this paper, we propose a distribution-matching-based distillation framework for 3D point clouds that jointly optimizes the geometric structures and orientations of synthetic 3D objects. To address the semantic misalignment caused by the unordered nature of point clouds, we introduce a Semantically Aligned Distribution Matching (SADM) loss, which is computed on the sorted features within each channel. Moreover, to handle rotational variations, we jointly learn optimal rotation angles while updating the synthetic dataset to better align with the original feature distribution. Extensive experiments on widely used benchmark datasets demonstrate that the proposed method consistently outperforms existing dataset distillation approaches, achieving higher accuracy and strong cross-architecture generalization.

Applications · Neuroscience, Cognitive Science

Niklas Dexheimer, Sascha Gaudlitz, Johannes Schmidt-Hieber

Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability simplex. Despite the constant injection of noise and the non-convexity of the underlying optimization problem, one can rigorously prove that the considered Hebbian learning dynamic identifies the presynaptic neuron with the highest activity and that the convergence is exponentially fast in the number of iterations. This is non-standard and surprising as typically noisy gradient descent with fixed noise level only converges to a stationary regime where the noise causes the dynamic to fluctuate around a minimiser.

Deep Learning · Robustness

Jinyong Jeong, Hyungu Kahng, Seoung Bum Kim

Distribution shifts between training and test data undermine the reliability of deep neural networks, challenging real-world applications across domains and subpopulations. While distributionally robust optimization (DRO) methods like GroupDRO aim to improve robustness by optimizing worst-case performance over predefined groups, their use of a single global classifier can be restrictive when facing substantial inter-environment variability. We propose Multi-Expert Distributionally Robust Optimization (MEDRO), a novel extension of GroupDRO designed to address such complex shifts. MEDRO employs a shared feature extractor with $m$ environment-specific expert classifier heads, and introduces a min-max objective over all $m^{2}$ expert-environment pairings, explicitly modeling cross-environment risks. This expanded uncertainty set captures fine-grained distributional variations that a single classifier might overlook. Empirical evaluations on a range of standard distribution shift benchmarks demonstrate that MEDRO often achieves robust predictive performance compared to existing methods. Furthermore, MEDRO offers practical inference strategies, such as ensembling or gating mechanisms, for typical scenarios where environment labels are unavailable at test time. Our findings suggest MEDRO as a promising step toward resilient and generalizable machine learning under real-world distribution shifts.

Applications · Neuroscience, Cognitive Science

Trinity Chung, Yuchen Shen, Nathan Kong, Aran Nayebi

Tactile sensing remains far less understood in neuroscience and less effective in artificial systems compared to more mature modalities such as vision and language. We bridge these gaps by introducing a novel Encoder-Attender-Decoder (EAD) framework to systematically explore the space of task-optimized temporal neural networks trained on realistic tactile input sequences from a customized rodent whisker-array simulator. We identify convolutional recurrent neural networks (ConvRNNs) as superior encoders to purely feedforward and state-space architectures for tactile categorization. Crucially, these ConvRNN-encoder-based EAD models achieve neural representations closely matching rodent somatosensory cortex, saturating the explainable neural variability and revealing a clear linear relationship between supervised categorization performance and neural alignment. Furthermore, contrastive self-supervised ConvRNN-encoder-based EADs, trained with tactile-specific augmentations, match supervised neural fits, serving as an ethologically-relevant, label-free proxy. For neuroscience, our findings highlight nonlinear recurrent processing as important for general-purpose tactile representations in somatosensory cortex, providing the first quantitative characterization of the underlying inductive biases in this system. For embodied AI, our results emphasize the importance of recurrent EAD architectures to handle realistic tactile inputs, along with tailored self-supervised learning methods for achieving robust tactile perception with the same type of sensors animals use to sense in unstructured environments.

Optimization · Neural Network Optimization

Marlon Becker, Frederick Altrock, Benjamin Risse

The recently proposed optimization algorithm for deep neural networks Sharpness Aware Minimization (SAM) suggests perturbing parameters before gradient calculation by a gradient ascent step to guide the optimization into parameter space regions of flat loss. While significant generalization improvements and thus reduction of overfitting could be demonstrated, the computational costs are doubled due to the additionally needed gradient calculation, making SAM unfeasible in case of limited computationally capacities. Motivated by Nesterov Accelerated Gradient (NAG) we propose Momentum-SAM (MSAM), which perturbs parameters in the direction of the accumulated momentum vector to achieve low sharpness without significant computational overhead or memory demands over SGD or Adam. We evaluate MSAM in detail and reveal insights on separable mechanisms of NAG, SAM and MSAM regarding training optimization and generalization.

Applications · Language, Speech and Dialog

Akhiad Bercovich, Mohammed Dabbah, Omri Puny, Ido Galil, Amnon Geifman, Yonatan Geifman, Izik Golan, Ehud Karpas, Itay Levy, Zach Moshe 等

We introduce \textit{FFN Fusion}, an architectural optimization technique that reduces sequential computation in large language models by identifying and exploiting natural opportunities for parallelization. Our key insight is that sequences of Feed-Forward Network (FFN) layers, particularly those remaining after the removal of specific attention layers, can often be parallelized with minimal accuracy impact. We develop a principled methodology for identifying and fusing such sequences, transforming them into parallel operations that significantly reduce inference latency while preserving model behavior. Applying these techniques to Llama-3.1-405B-Instruct, we create a 253B model (253B-Base), an efficient and soon-to-be publicly available model that achieves a 1.71$\times$ speedup in inference latency and 35$\times$ lower per-token cost while maintaining strong performance across benchmarks. Most intriguingly, we find that even full transformer blocks containing both attention and FFN layers can sometimes be parallelized, suggesting new directions for neural architecture design.

Optimization · Neural Network Optimization

Bhavya Vasudeva, Jung Lee, Vatsal Sharan, Mahdi Soltanolkotabi

Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient descent (GD), remains limited. In practice, neural networks (NNs) trained with SGD are known to exhibit simplicity bias --- a tendency to find simple solutions. In contrast, we show that Adam is more resistant to such simplicity bias. First, we investigate the differences in the implicit biases of Adam and GD when training two-layer ReLU NNs on a binary classification task with Gaussian data. We find that GD exhibits a simplicity bias, resulting in a linear decision boundary with a suboptimal margin, whereas Adam leads to much richer and more diverse features, producing a nonlinear boundary that is closer to the Bayes' optimal predictor. This richer decision boundary also allows Adam to achieve higher test accuracy both in-distribution and under certain distribution shifts. We theoretically prove these results by analyzing the population gradients. Next, to corroborate our theoretical findings, we present extensive empirical results showing that this property of Adam leads to superior generalization across various datasets with spurious correlations where NNs trained with SGD are known to show simplicity bias and do not generalize well under certain distributional shifts.

Optimization · Neural Network Optimization

chao zhou, Tom Jacobs, Advait Gadhikar, Rebekka Burkholz

Finetuning large pretrained neural networks is known to be resource-intensive, both in terms of memory and computational cost. To mitigate this, a common approach is to restrict training to a subset of the model parameters. By analyzing the relationship between gradients and weights during finetuning, we observe a notable pattern: large gradients are often associated with small-magnitude weights. This correlation is more pronounced in fine-tuning settings than in training from scratch. Motivated by this observation, we propose \textsc{NanoAdam}, which dynamically updates only the small-magnitude weights during fine-tuning and offers several practical advantages: first, the criterion is \emph{gradient-free}—the parameter subset can be determined without gradient computation; second, it preserves large-magnitude weights, which are likely to encode critical features learned during pre-training, thereby reducing the risk of catastrophic forgetting; thirdly, it permits the use of larger learning rates and consistently leads to better generalization performance in experiments. We demonstrate this for both NLP and vision tasks.

Applications · Chemistry and Drug Discovery

Sihan Wang, Wenjie Du, Qing Zhu, Yang Wang

Artificial intelligence (AI) has played a transformative role in chemical research, greatly facilitating the prediction of small molecule properties, simulation of catalytic processes, and material design. These advances are driven by increases in computing power, open source machine learning frameworks, and extensive chemical datasets. However, a persistent challenge is the limited amount of high-quality real-world data, while models calculated based on large amounts of theoretical data are often costly and difficult to deploy, which hinders the applicability of AI models in real-world scenarios. In this study, we enhance the prediction of solute-solvent properties by proposing a novel sample selection method: the iterative core subset extraction (CSIE) framework. CSIE iteratively updates the core sample subset based on information gain to remove redundant features in theoretical data and optimize the performance of the model on real chemical datasets. Furthermore, we introduce an asymmetric molecular interaction graph neural network (AMGNN) that combines positional information and bidirectional edge connections to simulate real-world chemical reaction scenarios to better capture solute-solvent interactions. Experimental results show that our method can accurately extract the core subset and improve the prediction accuracy.

Deep Learning · Graph Neural Networks

Andrei Manolache, Luiz Chamon, Mathias Niepert

Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects. Strictly equivariant models may struggle to fit the data, while unconstrained models lack a principled way to leverage partial symmetries. Even when the data is fully symmetric, enforcing equivariance can hurt training by limiting the model to a restricted region of the parameter space. Guided by homotopy principles, where an optimization problem is solved by gradually transforming a simpler problem into a complex one, we introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model and gradually reduces its deviation from equivariance. This gradual tightening smooths training early on and settles the model at a data-driven equilibrium, balancing between equivariance and non-equivariance. Across multiple architectures and tasks, our method consistently improves performance metrics, sample efficiency, and robustness to input perturbations compared with strictly equivariant models and heuristic equivariance relaxations.

Applications · Physics

Rafael Bischof, Michal Piovarci, Michael Kraus, Siddhartha Mishra, Bernd Bickel

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parameterizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that treats the residual of the generated PINN as "delta PDE" and performs another forward pass to generate a corrective PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves a >100× lower $L_2$ loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.

Applications

Inguk Choi, Woo-Jin Shin, Sang-Hyun Cho, Hyun-Jung Kim

Reinforcement Learning (RL) has shown promising results in solving Job Scheduling Problems (JSPs), automatically deriving powerful dispatching rules from data without relying on expert knowledge. However, most RL-based methods train only a single decision-maker, which limits exploration capability and leaves significant room for performance improvement. Moreover, designing reward functions for different JSP variants remains a challenging and labor-intensive task. To address these limitations, we introduce a novel and generic learning framework that optimizes multiple policies sharing a common objective and a single neural network, while enabling each policy to learn specialized and diverse strategies. The model optimization process is fully guided in a self-supervised manner, eliminating the need for reward functions. In addition, we develop a training scheme that adaptively controls the imitation intensity to reflect the quality of self-labels. Experimental results show that our method effectively addresses the aforementioned challenges and significantly outperforms state-of-the-art RL methods across six JSP variants. Furthermore, our approach also demonstrates strong performance on other combinatorial optimization problems, highlighting its versatility beyond JSPs.

Deep Learning · Robustness

Daniel Wesego, Pedram Rooshenas

Deep neural networks remain highly susceptible to adversarial attacks, where small, subtle perturbations to input images may induce misclassification. We propose a novel optimization-based purification framework that directly removes these perturbations by maximizing a Bayesian-inspired objective combining a pretrained diffusion prior with a likelihood term tailored to the adversarial perturbation space. Our method iteratively refines a given input through gradient-based updates of a combined score-based loss to guide the purification process. Unlike existing optimization-based defenses that treat adversarial noise as generic corruption, our approach explicitly integrates the adversarial landscape into the objective. Experiments performed on CIFAR-10 and CIFAR-100 demonstrate strong robust accuracy against a range of common adversarial attacks. Our work offers a principled test-time defense grounded in probabilistic inference using score-based generative models. Our code can be found at \url{https://github.com/rooshenasgroup/aaopt}.

General Machine Learning · Everything Else

Xinpeng Lv, Yunxin Mao, Haoxuan Li, KE LIANG, Jinxuan Yang, Wanrong Huang, Haoang Chi, Huan Chen, Long Lan, Cyuanlong 等

Strategic classification (SC) explores how individuals or entities modify their features strategically to achieve favorable classification outcomes. However, existing SC methods, which are largely based on linear models or shallow neural networks, face significant limitations in terms of scalability and capacity when applied to real-world datasets with significantly increasing scale, especially in financial services and the internet sector. In this paper, we investigate how to leverage large language models to design a more scalable and efficient SC framework, especially in the case of growing individuals engaged with decision-making processes. Specifically, we introduce GLIM, a gradient-free SC method grounded in in-context learning. During the feed-forward process of self-attention, GLIM implicitly simulates the typical bi-level optimization process of SC, including both the feature manipulation and decision rule optimization. Without fine-tuning the LLMs, our proposed GLIM enjoys the advantage of cost-effective adaptation in dynamic strategic environments. Theoretically, we prove GLIM can support pre-trained LLMs to adapt to a broad range of strategic manipulations. We validate our approach through experiments with a collection of pre-trained LLMs on real-world and synthetic datasets in financial and internet domains, demonstrating that our GLIM exhibits both robustness and efficiency, and offering an effective solution for large-scale SC tasks.

Optimization · Discrete Optimization

Ruixiao Yang, Chuchu Fan

The Time-Dependent Traveling Salesman Problem (TDTSP) extends classical TSP with dynamic edge weights that vary with departure time, reflecting real-world scenarios like transportation networks, where travel times fluctuate due to congestion patterns. TDTSP violates symmetry, triangle inequality, and cyclic invariance properties of classical TSP, creating unique computational challenges. In this paper, we propose a neural model that extends MatNet from static asymmetric TSP to time-dependent settings through an adjacency tensor that captures temporal variations, followed by a time-aware decoder. Our architecture addresses the unique challenge where asymmetry and triangle inequality violations change dynamically with time. Beyond architectural innovations, our research reveals a critical evaluation insight: many practical TDTSP instances maintain the same optimal solution regardless of time-dependent edge weights. This exposes a fundamental limitation in current evaluation practices for TDTSP that rely solely on average travel time metrics across all instances. Such metrics fail to effectively distinguish between methods that genuinely capture temporal dynamics and those that merely perform well on static routing problems. Instead, we present extensive experiments on real-world datasets, evaluating our approach on both entire datasets and specifically filtered instances where temporal dependencies alter the optimal solution. Results show that our method achieves state-of-the-art average optimality gap on full instances and significant travel time reduction on instances for which time-aware routing saves time. These results demonstrate state-of-the-art ability to identify and exploit temporal dependencies while establishing new standards for evaluating routing problems with temporal dependencies.

Deep Learning · Theory

Xiaotian Zhang, Yue Shang, Entao Yang, Ge Zhang

Understanding neural network' (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches near-perfect level, offers a unique window to investigate the underlying mechanisms of NNs' generalizability. Here we propose an interpretation for grokking by framing it as a computational glass relaxation: viewing NNs as a physical system where parameters are the degrees of freedom and train loss is the system energy, we find memorization process resembles a rapid cooling of liquid into non-equilibrium glassy state at low temperature and the later generalization is like a slow relaxation towards a more stable configuration. This mapping enables us to sample NNs' Boltzmann entropy (states of density) landscape as a function of training loss and test accuracy. Our experiments in transformers on arithmetic tasks suggests that there is NO entropy barrier in the memorization-to-generalization transition of grokking, challenging previous theory that defines grokking as a first-order phase transition. We identify a high-entropy advantage under grokking, an extension of prior work linking entropy to generalizability but much more significant. Inspired by grokking's far-from-equilibrium nature, we develop a toy optimizer WanD based on Wang-landau molecular dynamics, which can eliminate grokking without any constraints and find high-norm generalizing solutions. This provides strictly-defined counterexamples to theory attributing grokking solely to weight norm evolution towards the Goldilocks zone and also suggests new potential ways for optimizer design.