论文检索

Deep Learning · Generative Models and Autoencoders

Jing Jia, Sifan Liu, Bowen Song, Wei Yuan, Liyue Shen, Guanyang Wang

We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model architectures, conditional and unconditional sampling, and even other generative models such as VAEs and Normalizing Flows. To explain it, we combine experiments and theory and propose a \textit{symmetry conjecture} that the learned score function is approximately affine antisymmetric (odd symmetry up to a constant shift), supported by empirical evidence. This negative correlation leads to substantially more reliable uncertainty quantification with up to $90\%$ narrower confidence intervals. We demonstrate these gains on tasks including estimating pixel-wise statistics and evaluating diffusion inverse solvers. We also provide extensions with randomized quasi-Monte Carlo noise designs for uncertainty quantification, and explore additional applications of the antithetic noise design to improve image editing and generation diversity. Our framework is training-free, model-agnostic, and adds no runtime overhead. Code is available at https://github.com/jjia131/Antithetic-Noise-in-Diffusion-Models-page.

Applications · Neuroscience, Cognitive Science

Max Wolff, Thomas Klein, Evgenia Rusak, Felix Wichmann, Wieland Brendel

Despite their impressive performance on computer vision benchmarks, Deep Neural Networks (DNNs) still fall short of adequately modeling human visual behavior, as measured by error consistency and shape bias. Recent work hypothesized that behavioral alignment can be drastically improved through generative - rather than discriminative - classifiers, with far-reaching implications for models of human vision. Here, we instead show that the increased alignment of generative models can be largely explained by a seemingly innocuous resizing operation in the generative model which effectively acts as a low-pass filter. In a series of controlled experiments, we show that removing high-frequency spatial information from discriminative models like CLIP drastically increases their behavioral alignment. Simply blurring images at test-time - rather than training on blurred images - achieves a new state-of-the-art score on the model-vs-human benchmark, halving the current alignment gap between DNNs and human observers. Furthermore, low-pass filters are likely optimal, which we demonstrate by directly optimizing filters for alignment. To contextualize the performance of optimal filters, we compute the frontier of all possible pareto-optimal solutions to the benchmark, which was formerly unknown. We explain our findings by observing that the frequency spectrum of optimal Gaussian filters roughly matches the spectrum of band-pass filters implemented by the human visual system. We show that the contrast sensitivity function, describing the inverse of the contrast threshold required for humans to detect a sinusoidal grating as a function of spatiotemporal frequency, is approximated well by Gaussian filters of a specific width.

Reinforcement Learning · Everything Else

Qili Shen, Kairui Feng, Ang He, Xuanhong Chen, Dake Zhang

Recent work increasingly adopts AI for Science (AI4S) models to replace expensive PDE solvers as simulation environments for reinforcement learning (RL), enabling faster training in complex physical control tasks. However, using approximate simulators introduces modeling errors that affect the learned policy. In this paper, we introduce a unified $\varepsilon$-$N$ framework that quantifies the minimal computational cost $N^*(\varepsilon)$ required for an AI4S model to ensure that tabular RL can estimate the value function with unbiasedness, with probability at least $1 - \delta$. This characterization allows us to connect surrogate accuracy, grid resolution, and RL policy quality under a shared probabilistic language. We analyze how the discretization level $K$ of AI4S and RL space governs both PDE surrogate error and RL lattice approximation error, and we employ spectral theory and Sobolev estimates to derive optimal grid strategies that minimize total cost while preserving learning fidelity. Our theory reveals that different systems, such as ODE- and PDE-governed environments, require different allocations of effort between physical simulation and RL optimization. Overall, our framework offers a principled foundation for designing efficient, scalable, and cost-aware AI4S-RL systems with provable learning guarantees.

Optimization · Large Scale, Parallel and Distributed

Yuanbin Zou, Junyu Huang, Jianxin Wang, Qilong Feng

In this paper, we study coreset construction for LASSO regression, where a coreset is a small, weighted subset of the data that approximates the original problem with provable guarantees. For unregularized regression problems, sensitivity sampling is a successful and widely applied technique for constructing coresets. However, extending these methods to LASSO typically requires coreset size to scale with O(\mathcal{G}d), where d is the VC dimension and \mathcal{G} is the total sensitivity, following existing generalization bounds. A key challenge in improving upon this general bound lies in the difficulty of capturing the sparse and localized structure of the function space induced by the \ell_1 penalty in LASSO objective. To address this, we first provide an empirical process-based method of sensitivity sampling for LASSO, localizing the procedure by decomposing the functional space into separate components, which leads to tighter estimation error. By carefully leveraging the geometric properties of these localized spaces, we establish tight empirical process bounds on the required coreset size. These techniques enable us to achieve a coreset of size \tilde{O}(\epsilon^{-2}d\cdot(\log^3 d\cdot\min\{1,\log d/\lambda^2\}+\log(1/\delta))), which ensures a (1\pm\epsilon)-approximation for any \epsilon,\delta\in(0,1) and \lambda > 0. Furthermore, we give a lower bound showing that any algorithm achieving a (1+\epsilon)-approximation must select at least $Omega(\frac{d\log{d}}{\epsilon^2}) rows in the regime where \lambda=O(d^{-1/2}). Empirical experiments show that our proposed algorithm is at least 4 times faster than the existing LASSO solver and more than 9 times faster on half of the datasets, while ensuring high solution quality and sparsity.

Theory · Learning Theory

Xuyang Chen, Fengzhuo Zhang, Keyu Yan, Lin Zhao

Actor–critic (AC) algorithms underpin many of today’s most successful reinforcement learning (RL) applications, yet their finite-time convergence in realistic settings remains largely underexplored. Existing analyses often rely on oversimplified formulations and are largely confined to linear function approximation. In practice, however, nonlinear approximations with deep neural networks dominate AC implementations, leaving a substantial gap between theory and practice. In this work, we provide the first finite-time analysis of single-timescale AC with deep neural network approximation in continuous state-action spaces. In particular, we consider the challenging time-average reward setting, where one needs to simultaneously control three highly-coupled error terms including the reward error, the critic error, and the actor error. Our novel analysis is able to establish convergence to a stationary point at a rate $\widetilde{\mathcal{O}}(T^{-1/2})$, where $T$ denotes the total number of iterations, thereby providing theoretical grounding for widely used deep AC methods. We substantiate these theoretical guarantees with experiments that confirm the proven convergence rate and further demonstrate strong performance on MuJoCo benchmarks.

Social Aspects · Fairness, Equity, Justice and Safety

Jindong Yang, Han Fang, Weiming Zhang, Nenghai Yu, Kejiang Chen

Inversion-based watermarking is a promising approach to authenticate diffusion-generated images, yet practical use is bottlenecked by inversion that is both slow and error-prone. While the primary challenge in the watermarking setting is robustness against external distortions, existing approaches over-optimize internal truncation error, and because that error scales with the sampler step size, they are inherently confined to high-NFE (number of function evaluations) regimes that cannot meet the dual demands of speed and robustness. In this work, we have two key observations: (i) the inversion trajectory has markedly lower curvature than the forward generation path does, making it highly compressible and amenable to low-NFE approximation; and (ii) in inversion for watermark verification, the trade-off between speed and truncation error is less critical, since external distortions dominate the error. A faster inverter provides a dual benefit: it is not only more efficient, but it also enables end-to-end adversarial training to directly target robustness, a task that is computationally prohibitive for the original, lengthy inversion trajectories. Building on this, we propose **FARI** (**F**ast **A**symmetric **R**obust **I**nversion), a one-step inversion framework paired with lightweight adversarial LoRA fine-tuning of the denoiser for watermark extraction. While consolidation slightly increases internal error, FARI delivers large gains in both speed and robustness: with ~20 minutes of fine-tuning on a single NVIDIA RTX A6000 GPU, it surpasses 50-step DDIM inversion on watermark-verification robustness while dramatically reducing inference time.

Computer Vision · Everything Else

Bin Ren, Runyi Yang, Qi Ma, Xu Zheng, Mengyuan Liu, Danda Pani Paudel, Luc Van Gool, Rita Cucchiara, Nicu Sebe

All-in-one image restoration (IR) aims to recover high-quality images from diverse degradations, which in real-world settings are often mixed and unknown. Unlike single-task IR, this problem requires a model to approximate a family of heterogeneous inverse functions, making it fundamentally more challenging and practically important. Although recent focus has shifted toward large multimodal models, their robustness still depends on faithful low-level inputs, and the principles that govern effective restoration remain underexplored. We revisit attention mechanisms through the lens of all-in-one IR and identify two overlooked bottlenecks in widely adopted Restormer-style backbones: (i) the value path remains purely linear, restricting outputs to the span of inputs and weakening expressivity, and (ii) the absence of an explicit global slot prevents attention from encoding degradation context. To address these issues, we propose two minimal, backbone-agnostic primitives: a nonlinear value transform that upgrades attention from a selector to a selector–transformer, and a global spatial token that provides an explicit degradation-aware slot. Together, these additions improve restoration across synthetic, mixed, underwater, and medical benchmarks, with negligible overhead and consistent performance gains. Analyses with foundation model embeddings, spectral statistics, and separability measures further clarify their roles, positioning our study as a step toward rethinking attention primitives for robust all-in-one IR.

Powei Chang, Jinpeng Zhang, Bowen Chen, Chenyu Wang, Chenlu Guo, Yixing Zhang, Yukang Gao, JianXiang Xiang, Yue Gao, Chaoqun Sun 等

Information-based data selection for instruction tuning is compelling: maximizing the log-determinant of the Fisher information yields a monotone submodular objective, enabling greedy algorithms to achieve a $(1-1/e)$ approximation under a cardinality budget. In practice, however, we identify alleviating gradient conflicts, misalignment between per-sample gradients, is a key factor that slows down the decay of marginal log-determinant information gains, thereby preventing significant loss of information. We formalize this via an $\varepsilon$-decomposition that quantifies the deviation from ideal submodularity as a function of conflict statistics, yielding data-dependent approximation factors that tighten as conflicts diminish. Guided by this analysis, we propose SPICE, a conflict-aware selector that maximizes information while penalizing misalignment, and that supports early stopping and proxy models for efficiency. Empirically, SPICE selects subsets with higher log-determinant information than original criteria, and these informational gains translate into performance improvements: across 8 benchmarks with LLaMA2-7B and Qwen2-7B, SPICE uses only 10% of the data, yet matches or exceeds 6 methods including full-data tuning. This achieves performance improvements with substantially lower training cost. Code is available at https://github.com/Chang-pw/SPICE#.

Deep Learning · Graph Neural Networks

Marco Pacini, Mircea Petrache, Bruno Lepri, Shubhendu Trivedi, Robin Walters

Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional hidden spaces, or they target specialized architectures, often confined to the invariant setting. This work develops a more general account. For invariant networks, we establish a universality theorem under separation constraints, showing that the addition of a fully connected readout layer secures approximation within the class of separation-constrained continuous functions. For equivariant networks, where results are even scarcer, we demonstrate that standard separability notions are inadequate and introduce the sharper criterion of *entry-wise separability*. We show that with sufficient depth or with the addition of appropriate readout layers, equivariant networks attain universality within the entry-wise separable regime. Together with prior results showing the failure of universality for shallow models, our findings identify depth and readout layers as a decisive mechanism for universality, additionally offering a unified perspective that subsumes and extends earlier specialized results.

Deep Learning · Theory

Penghao Yu, Haotian Jiang, Zeyu Bao, Ruoxi Yu, Qianxiao Li

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of transformers, with particular emphasis on the role of the number of attention heads. Our analysis begins with the introduction of a generalized $D$-retrieval task, which we prove to be dense in the space of continuous functions, thereby providing the basis for our theoretical framework. We then establish both upper and lower bounds on the parameter complexity required for $\epsilon$-approximation. Specifically, we show that transformers with sufficiently many heads admit efficient approximation, whereas with too few heads, the number of parameters must scale at least as $O(1/\epsilon^{cT})$, for some constant $c$ and sequence length $T$. To the best of our knowledge, this constitutes the first rigorous lower bound of this type in a nonlinear and practically relevant setting. We further examine the single-head case and demonstrate that an embedding dimension of order $O(T)$ allows complete memorization of the input, resulting in the approximation entirely achieved by the feed-forward block. Finally, we validate our theoretical findings with experiments on both synthetic data and real-world tasks, illustrating the practical relevance of our results.

Deep Learning · Generative Models and Autoencoders

Minyoung Kim

The famous Schr\"{o}dinger bridge (SB) has gained renewed attention in the generative machine learning field these days for its successful applications in various areas including unsupervised image-to-image translation and particle crowd modeling. Recently, a promising algorithm dubbed GSBM was proposed to solve the generalized SB (GSB) problem, an extension of SB to deal with additional path constraints. Therein the SB is formulated as a minimal kinetic energy conditional flow matching problem, and an additional task-specific stage cost is introduced as the conditional stochastic optimal control (CondSOC) problem. The GSB is a new emerging problem with considerable room for research contributions, and we introduce a novel Gaussian process pinned marginal path posterior inference as a meaningful contribution in this area. Our main motivation is that the stage cost in GSBM, typically representing task-specific obstacles in the particle paths and other congestion penalties, can be potentially noisy and uncertain. Whereas the current GSBM approach regards this stage cost as a noise-free deterministic quantity in the CondSOC optimization, we instead model it as a stochastic quantity. Specifically, we impose a Gaussian process (GP) prior on the pinned marginal path, view the CondSOC objective as a (noisy) likelihood function, and infer the posterior path via sparse variational free-energy GP approximate inference. The main benefit is more flexible marginal path modeling that takes into account the uncertainty in the stage cost such as more realistic noisy observations. On some image-to-image translation and crowd navigation problems under noisy scenarios, we show that our proposed GP-based method yields more robust solutions than the original GSBM.

Deep Learning · Generative Models and Autoencoders

Min Cheng, Fatemeh Doudi, Dileep Kalathil, Mohammad Ghavamzadeh, Panganamala Kumar

Reinforcement learning (RL) algorithms have been used recently to align diffusion models with downstream objectives such as aesthetic quality and text-image consistency by fine-tuning them to maximize a single reward function under a fixed KL regularization. However, this approach is inherently restrictive in practice, where alignment must balance multiple, often conflicting objectives. Moreover, user preferences vary across prompts, individuals, and deployment contexts, with varying tolerances for deviation from a pre-trained base model. We address the problem of inference-time multi-preference alignment: given a set of basis reward functions and a reference KL regularization strength, can we design a fine-tuning procedure so that, at inference time, it can generate images aligned with any user-specified linear combination of rewards and regularization, without requiring additional fine-tuning? We propose Diffusion Blend, a novel approach to solve inference-time multi-preference alignment by blending backward diffusion processes associated with fine-tuned models, and we instantiate this approach with three algorithms: DB-MPA for multi-reward alignment, DB-KLA for KL regularization control, and DB-MPA-LS for approximating DB-MPA without additional inference cost. Extensive experiments show that Diffusion Blend algorithms consistently outperform relevant baselines and closely match or exceed the performance of individually fine-tuned models, enabling efficient, user-driven alignment at inference-time.

Reinforcement Learning · Batch/Offline

Qiyang Li, Sergey Levine

We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching policy with respect to a parameterized Q-function. Effective optimization requires exploiting the first-order information of the critic, but it is challenging to do so for flow or diffusion policies because direct gradient-based optimization via backpropagation through their multi-step denoising process is numerically unstable. Existing methods work around this either by only using the value and discarding the gradient information, or by relying on approximations that sacrifice policy expressivity or bias the learned policy. QAM sidesteps both of these challenges by leveraging adjoint matching, a recently proposed technique in generative modeling, which transforms the critic's action gradient to form a step-wise objective function that is free from unstable backpropagation, while providing an unbiased, expressive policy at the optimum. Combined with temporal-difference backup for critic learning, QAM consistently outperforms prior approaches on hard, sparse reward tasks in both offline and offline-to-online RL.

General Machine Learning · Representation Learning

Zhenyao Ma, Yue Liang, Dongxu Li

Inspired by behavioral science, we propose Behavior Learning (BL), a novel general-purpose machine learning framework that learns interpretable and identifiable optimization structures from data, ranging from single optimization problems to hierarchical compositions. It unifies predictive performance, intrinsic interpretability, and identifiability, with broad applicability to scientific domains involving optimization. BL parameterizes a compositional utility function built from intrinsically interpretable modular blocks, which induces a data distribution for prediction and generation. Each block represents and can be written in symbolic form as a utility maximization problem (UMP), a foundational paradigm in behavioral science and a universal framework of optimization. BL supports architectures ranging from a single UMP to hierarchical compositions, the latter modeling hierarchical optimization structures that offer both expressiveness and structural transparency. Its smooth and monotone variant (IBL) guarantees identifiability under mild conditions. Theoretically, we establish the universal approximation property of both BL and IBL, and analyze the M-estimation properties of IBL. Empirically, BL demonstrates strong predictive performance, intrinsic interpretability and scalability to high-dimensional data. Code: https://github.com/MoonYLiang/Behavior-Learning; installable via pip install blnetwork.

Deep Learning · Everything Else

Saanjali S. Maharaj, Prasanth Nair

Modern neural architectures are fundamentally constrained by their reliance on fixed activation functions, limiting their ability to adapt representations to task-specific structure and efficiently capture high-order interactions. We introduce deep low-rank separated neural networks (LRNNs), a novel architecture generalizing MLPs that achieves enhanced expressivity by learning adaptive, factorized activation functions. LRNNs generalize the core principles underpinning continuous low-rank function decomposition to the setting of deep learning, constructing complex, high-dimensional neuron activations through a multiplicative composition of simpler, learnable univariate transformations. This product structure inherently captures multiplicative interactions and allows each LRNN neuron to learn highly flexible, data-dependent activation functions. We provide a detailed theoretical analysis that establishes the universal approximation property of LRNNs and reveals why they are capable of excellent empirical performance. Specifically, we show that LRNNs can mitigate the curse of dimensionality for functions with low-rank structure. Moreover, the learnable product-structured activations enable LRNNs to adaptively control their spectral bias, crucial for signal representation tasks. These theoretical insights are validated through extensive experiments where LRNNs achieve state-of-the-art performance across diverse domains including image and audio representation, numerical solution of PDEs, sparse-view CT reconstruction, and supervised learning tasks. Our results demonstrate that LRNNs provide a powerful and versatile building block with a distinct inductive bias for learning compact yet expressive representations.

Applications · Physics

Vladimir Fanaskov, Vladislav Trifonov, Alexander Rudikov, Ekaterina Muravleva, Ivan Oseledets

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of the problem. A practical way to apply such a scheme is to compute subspaces for a selected set of parameters in the computationally demanding offline stage and in the online stage approximate subspace for unknown parameters by interpolation. For realistic problems the space of parameters is high dimensional, which renders classical interpolation strategies infeasible or unreliable. We propose to relax the interpolation problem to regression, introduce several loss functions suitable for subspace data, and use a neural network as an approximation to high-dimensional target function. To further simplify a learning problem we introduce redundancy: in place of predicting subspace of a given dimension we predict larger subspace. We show theoretically that this strategy decreases the complexity of the mapping for elliptic eigenproblems with constant coefficients and makes the mapping smoother for general smooth function on the Grassmann manifold. Empirical results also show that accuracy significantly improves when larger-than-required subspaces are predicted. With the set of numerical illustrations we demonstrate that subspace regression can be useful for a range of tasks including parametric eigenproblems, deflation techniques, relaxation methods, optimal control and solution of parametric partial differential equations.

Reinforcement Learning · Function Approximation

Xiaoqiang Lin, Arun Verma, Zhongxiang Dai, Daniela Rus, See-Kiong Ng, Bryan Kian Hsiang Low

The recent success in using human preferences to align large language models (LLMs) has significantly improved their performance in various downstream tasks, such as question answering, mathematical reasoning, and code generation. However, achieving effective LLM alignment depends on high-quality datasets of human preferences. Collecting these datasets requires human preference annotation, which is costly and resource-intensive, necessitating efficient active data selection methods. Existing methods either lack a strong theoretical foundation or depend on restrictive assumptions about the reward function, such as linear latent reward functions. To this end, we propose an algorithm, ActiveDPO, that uses a theoretically grounded data selection criterion for non-linear reward functions while directly leveraging the LLM itself to parameterize the reward model used for active data selection. As a result, ActiveDPO explicitly accounts for the LLM's influence on data selection, unlike methods that select data without considering the LLM that is being aligned, thereby leading to more effective and efficient data collection. Our extensive experiments demonstrate that ActiveDPO outperforms existing methods across various models and real-world preference datasets.

Reinforcement Learning · Batch/Offline

Qiushui Xu, Yuhao Huang, Yushu Jiang, Wenliang Zheng, Lei Song, Jinyu Wang, Jiang Bian

Accurate estimation of the Q-function is a central challenge in offline reinforcement learning. However, existing approaches often rely on a shared global Q-function, which is inadequate for capturing the compositional structure of tasks that consist of diverse subtasks. We propose In-context Compositional Q-Learning (ICQL), an offline RL framework that formulates Q-learning as a contextual inference problem and uses linear Transformers to adaptively infer local Q-functions from retrieved transitions without explicit subtask labels. Theoretically, we show that, under two assumptions---linear approximability of the local Q-function and accurate inference of weights from retrieved context---ICQL achieves a bounded approximation error for the Q-function and enables near-optimal policy extraction. Empirically, ICQL substantially improves performance in offline settings, achieving gains of up to 16.4\% on kitchen tasks and up to 8.8\% and 6.3\% on MuJoCo and Adroit tasks, respectively. These results highlight the underexplored potential of in-context learning for robust and compositional value estimation and establish ICQL as a principled and effective framework for offline RL.

General Machine Learning · Causality

Matthew Vowels, Mathieu Rochat, Sina Akbari

Artificial Neural Networks (ANNs), including fully-connected networks and transformers, are highly flexible and powerful function approximators, widely applied in fields like computer vision and natural language processing. However, their inability to inherently respect causal structures can limit their robustness, making them vulnerable to covariate shift and difficult to interpret/explain. This poses significant challenges for their reliability in real-world applications. In this paper, we introduce Causal Transformers (CaTs), a general model class designed to operate under predefined causal constraints, as specified by a Directed Acyclic Graph (DAG). CaTs retain the powerful function approximation abilities of traditional neural networks while adhering to the underlying structural constraints, improving robustness, reliability, and interpretability at inference time. This approach opens new avenues for deploying neural networks in more demanding, real-world scenarios where robustness and explainability is critical.

Optimization · Zero-order and Black-box Optimization

Zhe Li, Bicheng Ying, Zidong Liu, Chaosheng Dong, Haibo Yang

Zeroth-order (ZO) optimization enables dimension-free communication in federated learning (FL), making it attractive for fine-tuning of large language models (LLMs) due to significant communication savings. However, existing ZO-FL methods largely overlook curvature information, despite its well-established benefits for convergence acceleration. To address this, we propose **HiSo**, a Hessian-informed ZO federated optimization method that accelerates convergence by leveraging global diagonal Hessian approximations, while strictly preserving scalar-only communication **without transmitting any second-order information**. Theoretically, for non-convex functions, we show that HiSo can achieve an accelerated convergence rate that is independent of the Lipschitz constant $L$ and model dimension $d$ under some Hessian approximation assumptions, offering a plausible explanation for the observed phenomenon of ZO convergence being much faster than its worst-case $O(d)$-bound. Empirically, across diverse LLM fine-tuning benchmarks, HiSo delivers a 1$\sim$5× speedup in communication rounds over existing state-of-the-art ZO-FL baselines. This superior convergence not only cuts communication costs but also provides strong empirical evidence that Hessian information acts as an effective accelerator in federated ZO optimization settings.