论文检索

Deep Learning · Robustness

Shixin Li, Zewei Li, Xiaojing Ma, Xiaofan Bai, Pingyi Hu, Dongmei Zhang, Bin Zhu

Adversarial examples crafted on one model often exhibit poor transferability to others, hindering their effectiveness in black-box settings. This limitation arises from two key factors: (i) \emph{decision-boundary variation} across models and (ii) \emph{representation drift} in feature space. We address these challenges through a new perspective that frames transferability for \emph{untargeted attacks} as a \emph{consensus-robust optimization} problem: adversarial perturbations should remain effective across a neighborhood of plausible target models. To model this uncertainty, we introduce two complementary perturbation channels: a \emph{parameter channel}, capturing boundary shifts via weight perturbations, and a \emph{representation channel}, addressing feature drift via stochastic blending of clean and adversarial activations. We then propose \emph{CORTA} (COnsensus--Robust Transfer Attack), a lightweight attack instantiated from this robust formulation using two first-order strategies: (i) sensitivity regularization based on the squared Frobenius norm of logits’ Jacobian with respect to weights, and (ii) Monte Carlo sampling for blended feature representations. Our theoretical analysis provides a certified lower bound linking these approximations to the robust objective. Extensive experiments on CIFAR-100 and ImageNet show that CORTA significantly outperforms state-of-the-art transfer-based methods---including ensemble approaches---across CNN and Vision Transformer targets. Notably, CORTA achieves a \emph{19.1 percentage-point gain in transfer success rate over the best prior method} while using only a single surrogate model.

Theory · Learning Theory

Hongjian Wang, Aaditya Ramdas

We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unknown variance in a tight manner: the deviation captured by the first-order $1/\sqrt{n}$ term asymptotically matches the matrix Bernstein inequality exactly, including constants, the latter requiring knowledge of the variance. Our first inequality holds for the sample mean of independent matrices, and our second inequality holds for a mean estimator under martingale dependence at stopping times.

Optimization

Liuyuan Jiang, Quan Xiao, Lisha Chen, Tianyi Chen

Bilevel optimization, a hierarchical optimization paradigm, has gained significant attention in a wide range of practical applications, notably in the fine-tuning of generative models. However, due to the nested problem structure, most existing algorithms require either the Hessian vector calculation or the nested loop updates, which are computationally inefficient in large language model (LLM) fine-tuning. In this paper, building upon the fully first-order penalty-based approach, we propose an efficient value function-free (\textsf{PBGD-Free}) algorithm that eliminates the loop of solving the lower-level problem and admits fully single-loop updates. Inspired by the landscape analysis of representation learning-based LLM fine-tuning problem, we propose a relaxed flatness condition for the upper-level function and prove the convergence of the proposed value-function-free algorithm. We test the performance of the proposed algorithm in various applications and demonstrate its superior computational efficiency over the state-of-the-art bilevel methods.

Optimization · Neural Network Optimization

Kyo Kuroki, Yasuyuki Okoshi, Thiem Van Chu, Kazushi Kawamura, Masato Motomura

This paper proposes a novel matrix quantization method, Binary Quadratic Quan- tization (BQQ). In contrast to conventional first-order quantization approaches— such as uniform quantization and binary coding quantization—that approximate real-valued matrices via linear combinations of binary bases, BQQ leverages the expressive power of binary quadratic expressions while maintaining an extremely compact data format. We validate our approach with two experiments: a matrix compression benchmark and post-training quantization (PTQ) on pretrained Vision Transformer-based models. Experimental results demonstrate that BQQ consistently achieves a superior trade-off between memory efficiency and reconstruction error than conventional methods for compressing diverse matrix data. It also delivers strong PTQ performance, even though we neither target state-of-the-art PTQ accuracy under tight memory constraints nor rely on PTQ-specific binary matrix optimization. For example, our proposed method outperforms the state-of- the-art PTQ method by up to 2.2% and 59.1% on the ImageNet dataset under the calibration-based and data-free scenarios, respectively, with quantization equivalent to 2 bits. These findings highlight the surprising effectiveness of binary quadratic expressions for efficient matrix approximation and neural network compression.

Data-centric AI · Data-centric AI methods and tools

Jundong Xu, Hao Fei, Yuhui Zhang, Liangming Pan, Qijun Huang, Qian Liu, Preslav Nakov, Min-Yen Kan, William Yang Wang, Mong-Li Lee 等

Multimodal symbolic logical reasoning, which aims to deduce new facts from multimodal input via formal logic, is critical in high-stakes applications such as autonomous driving and medical diagnosis, as its rigorous, deterministic reasoning helps prevent serious consequences. To evaluate such capabilities of current state-of-the-art vision language models (VLMs), we introduce the first benchmark MuSLR for multimodal symbolic logical reasoning grounded in formal logical rules. MuSLR comprises 1,093 instances across 7 domains, including 35 atomic symbolic logic and 976 logical combinations, with reasoning depths ranging from 2 to 9. We evaluate 7 state-of-the-art VLMs on MuSLR and find that they all struggle with multimodal symbolic reasoning, with the best model, GPT-4.1, achieving only 46.8%. Thus, we propose LogiCAM, a modular framework that applies formal logical rules to multimodal inputs, boosting GPT-4.1’s Chain-of-Thought performance by 14.13%, and delivering even larger gains on complex logics such as first-order logic. We also conduct a comprehensive error analysis, showing that around 70% of failures stem from logical misalignment between modalities, offering key insights to guide future improvements.

Social Aspects

Ali Shirali, Arash Nasr-Esfahany, Abdullah Alomar, Parsa Mirtaheri, Rediet Abebe, Ariel Procaccia

Alignment with human preferences is commonly framed using a universal reward function, even though human preferences are inherently heterogeneous. We formalize this heterogeneity by introducing user types and examine the limits of the homogeneity assumption. We show that aligning to heterogeneous preferences with a single policy is best achieved using the average reward across user types. However, this requires additional information about annotators. We examine improvements under different information settings, focusing on direct alignment methods. We find that minimal information can yield first-order improvements, while full feedback from each user type leads to consistent learning of the optimal policy. Surprisingly, however, no sample-efficient consistent direct loss exists in this latter setting. These results reveal a fundamental tension between consistency and sample efficiency in direct policy alignment.

Reinforcement Learning · Deep RL

Haoru Tan, Xiuzhe Wu, Sitong Wu, Shaofeng Zhang, Yanfeng Chen, Xingwu Sun, Jeanne Shen, Xiaojuan Qi

Reinforcement fine-tuning (RFT) is essential for enhancing the reasoning and generalization capabilities of large language models, but its success heavily relies on the quality of the training data. While data selection has been extensively studied in supervised learning, its role in reinforcement learning, particularly during the RFT stage, remains largely underexplored. In this work, we introduce RFT-Inf, the first influence estimator designed for data in reinforcement learning. RFT-Inf quantifies the importance of each training example by measuring how its removal affects the final training reward, offering a direct estimate of its contribution to model learning. To ensure scalability, we propose a first-order approximation of the RFT-Inf score by backtracking through the optimization process and applying temporal differentiation to the sample-wise influence term, along with a first-order Taylor approximation to adjacent time steps. This yields a lightweight, gradient-based estimator that evaluates the alignment between an individual sample’s gradient and the average gradient direction of all training samples, where a higher degree of alignment implies greater training utility. Extensive experiments demonstrate that RFT-Inf consistently improves reward performance and accelerates convergence in reinforcement fine-tuning.

Optimization

Xuchen Gong, Tian Li

One of the major bottlenecks for deploying popular first-order differentially private (DP) machine learning algorithms (e.g., DP-SGD) lies in their high computation and memory cost, despite the existence of optimized implementations. Zeroth-order methods have promise in mitigating the overhead, as they leverage function evaluations to approximate the gradients, hence significantly easier to privatize. While recent works have explored zeroth-order approaches in both private and non-private settings, they still suffer from relatively low utilities compared with DP-SGD, and have only been evaluated in limited application domains. In this work, we propose to leverage public information to guide and improve gradient approximation of private zeroth-order algorithms. We explore a suite of \underline{p}ublic-data-\underline{a}ssisted \underline{z}eroth-\underline{o}rder optimizers (PAZO) with minimal overhead. We provide theoretical analyses of the PAZO framework under an assumption of the similarity between public and private data. Empirically, we demonstrate that PAZO achieves superior privacy/utility tradeoffs across vision and text tasks in both pre-training and fine-tuning settings, outperforming the best first-order baselines (with public data) especially in highly private regimes, while offering up to $16\times$ runtime speedup.

Theory · Learning Theory

Zihao Tang, Boyuan Wang, Chuan Wen, Jiaye Teng

Conformal prediction is widely adopted in uncertainty quantification, due to its post-hoc, distribution-free, and model-agnostic properties. In the realm of modern deep learning, researchers have proposed Feature Conformal Prediction (FCP), which deploys conformal prediction in a feature space, yielding reduced band lengths. However, the practical utility of FCP is limited due to the time-consuming non-linear operations required to transform confidence bands from feature space to output space. In this paper, we present Fast Feature Conformal Prediction (FFCP), a method that accelerates FCP by leveraging a first-order Taylor expansion to approximate these non-linear operations. The proposed FFCP introduces a novel non-conformity score that is both effective and efficient for real-world applications. Empirical validations showcase that FFCP performs comparably with FCP (both outperforming the vanilla version) while achieving a significant reduction in computational time by approximately 50x in both regression and classification tasks.

Deep Learning · Algorithms

Manchao Bao, Shengjiang Fang, Tao Yue, Xuemei Hu

Long-distance depth imaging holds great promise for applications such as autonomous driving and robotics. Direct time-of-flight (dToF) imaging offers high-precision, long-distance depth sensing, yet demands ultra-short pulse light sources and high-resolution time-to-digital converters. In contrast, indirect time-of-flight (iToF) imaging often suffers from phase wrapping and low signal-to-noise ratio (SNR) as the sensing distance increases. In this paper, we introduce a novel ToF imaging paradigm, termed Burst-Encodable Time-of-Flight (BE-ToF), which facilitates high-fidelity, long-distance depth imaging. Specifically, the BE-ToF system emits light pulses in burst mode and estimates the phase delay of the reflected signal over the entire burst period, thereby effectively avoiding the phase wrapping inherent to conventional iToF systems. Moreover, to address the low SNR caused by light attenuation over increasing distances, we propose an end-to-end learnable framework that jointly optimizes the coding functions and the depth reconstruction network. A specialized double well function and first-order difference term are incorporated into the framework to ensure the hardware implementability of the coding functions. The proposed approach is rigorously validated through comprehensive simulations and real-world prototype experiments, demonstrating its effectiveness and practical applicability. The code is available at: https://github.com/ComputationalPerceptionLab/BE-ToF.

Optimization · Optimization and Learning under Uncertainty

Abhishek Sinha, Rahul Vaze

We study Online Convex Optimization with adversarial constraints (COCO). At each round a learner selects an action from a convex decision set and then an adversary reveals a convex cost and a convex constraint function. The goal of the learner is to select a sequence of actions to minimize both regret and the cumulative constraint violation (CCV) over a horizon of length $T$. The best-known policy for this problem achieves $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV. In this paper, we improve this by trading off regret to achieve substantially smaller CCV. This trade-off is especially important in safety-critical applications, where satisfying the safety constraints is non-negotiable. Specifically, for any bounded convex cost and constraint functions, we propose an online policy that achieves $\tilde{O}(\sqrt{dT}+ T^\beta)$ regret and $\tilde{O}(dT^{1-\beta})$ CCV, where $d$ is the dimension of the decision set and $\beta \in [0,1]$ is a tunable parameter. We begin with a special case, called the $\textsf{Constrained Expert}$ problem, where the decision set is a probability simplex and the cost and constraint functions are linear. Leveraging a new adaptive small-loss regret bound, we propose a computationally efficient policy for the $\textsf{Constrained Expert}$ problem, that attains $O(\sqrt{T\ln N}+T^{\beta})$ regret and $\tilde{O}(T^{1-\beta} \ln N)$ CCV for $N$ number of experts. The original problem is then reduced to the $\textsf{Constrained Expert}$ problem via a covering argument. Finally, with an additional $M$-smoothness assumption, we propose a computationally efficient first-order policy attaining $O(\sqrt{MT}+T^{\beta})$ regret and $\tilde{O}(MT^{1-\beta})$ CCV.

Applications · Neuroscience, Cognitive Science

Shuhan Zhang, Zhi Wang, Rui Gao, Shuang Li

Modeling human decision-making is central to applications such as recommendation, preference learning, and human-AI alignment. While many classic models assume context-independent choice behavior, a large body of behavioral research shows that preferences are often influenced by the composition of the choice set itself---a phenomenon known as the context effect or Halo effect. These effects can manifest as pairwise (first-order) or even higher-order interactions among the available alternatives. Recent models that attempt to capture such effects either focus on the featureless setting or, in the feature-based setting, rely on restrictive interaction structures or entangle interactions across all orders, which limits interpretability. In this work, we propose DeepHalo, a neural modeling framework that incorporates features while enabling explicit control over interaction order and principled interpretation of context effects. Our model enables systematic identification of interaction effects by order and serves as a universal approximator of context-dependent choice functions when specialized to a featureless setting. Experiments on synthetic and real-world datasets demonstrate strong predictive performance while providing greater transparency into the drivers of choice.

Probabilistic Methods · Bayesian Models and Methods

Junxi Xiao, Qinliang Su, Zexin Yuan

Mean-field variational inference (VI), despite its scalability, is limited by the independence assumption, making it unsuitable for scenarios with correlated data instances. Existing structured VI methods either focus on correlations among latent dimensions which lack scalability for modeling instance-level correlations, or are restricted to simple first-order dependencies, limiting their expressiveness. In this paper, we propose High-order Tree-structured Variational Inference (HoT-VI), that explicitly models $k$-order instance-level correlations among latent variables. By expressing the global posterior through overlapping $k$-dimensional local marginals, our method enables efficient parameterized sampling via a sequential procedure. To ensure the validity of these marginals, we introduce a conditional correlation parameterization method that guarantees positive definiteness of their correlation matrices. We further extend our method with a tree-structured backbone to capture more flexible dependency patterns. Extensive experiments on time-series and graph-structured datasets demonstrate that modeling higher-order correlations leads to significantly improved posterior approximations and better performance across various downstream tasks.

Deep Learning · Generative Models and Autoencoders

Yinuo Ren, Haoxuan Chen, Yuchen Zhu, Wei Guo, Yongxin Chen, Grant Rotskoff, Molei Tao, Lexing Ying

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as $\tau$-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, $\tau$-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the $\theta$-Trapezoidal method in KL divergence. Empirical evaluations on GSM8K-level math-reasoning, GPT-2-level text, and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints, with consistent performance gains across models ranging from 200M to 8B. Our code is available at https://github.com/yuchen-zhu-zyc/DiscreteFastSolver

Optimization

Qichao Cao, Shangzhi Zeng, Jin Zhang

Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient algorithms for optimistic bilevel optimization, the study of methods for solving Pessimistic Bilevel Optimization (PBO) remains relatively less explored, especially the design of fully first-order, single-loop gradient-based algorithms. This paper aims to bridge this research gap. We first propose a novel smooth approximation to the PBO problem, using penalization and regularization techniques. Building upon this approximation, we then propose SiPBA (Single-loop Pessimistic Bilevel Algorithm), a new gradient-based method specifically designed for PBO which avoids second-order derivative information or inner-loop iterations for subproblem solving. We provide theoretical validation for the proposed smooth approximation scheme and establish theoretical convergence for the algorithm SiPBA. Numerical experiments on synthetic examples and practical applications demonstrate the effectiveness and efficiency of SiPBA.

Shrinivas Ramasubramanian, Benjamin Freed, Alexandre Capone, Jeff Schneider

Model-based reinforcement learning (MBRL) hinges on a learned dynamics model whose errors can compound along imagined rollouts. We study how encouraging \emph{flatness} in the model’s training loss affects downstream control, and show that steering optimization toward flatter minima yields a better policy. Concretely, we integrate \emph{Sharpness-Aware Minimization} (SAM) into world-model training as a drop-in objective, leaving the planner and policy components unchanged. On the theory side, we derive PAC-Bayesian bounds that link first-order sharpness to the value-estimation gap and the performance gap between model-optimal and true-optimal policies, implying that flatter minima tighten both. Empirically, SAM reduces measured sharpness and value-prediction error and improves returns across HumanoidBench, Atari-100k, and high-DoF DeepMind Control tasks. Augmenting existing MBRL algorithms with SAM increases mean return, with especially large gains in settings with high dimensional state–action space. We further observe positive transfer across algorithms and input modalities, including a transformer-based world-model. These results position flat-minima training as a simple, general mechanism for more robust MBRL without architectural changes.

Deep Learning · Algorithms

Reza Shirkavand, Peiran Yu, Qi He, Heng Huang

Fine-tuning pre-trained Large Language Models (LLMs) for downstream tasks using First-Order (FO) optimizers presents significant computational challenges. Parameter-Efficient Fine-Tuning~(PEFT) methods have been proposed to address these challenges by freezing most model parameters and training only a small subset. While PEFT is efficient, it may not outperform full fine-tuning when high task-specific performance is required. Zeroth-Order (ZO) methods offer an alternative for fine-tuning the entire pre-trained model by approximating gradients using only the forward pass, thus eliminating the computational burden of back-propagation, % in first-order methods, but they converge painfully slowly and are very sensitive to the choice of task prompts. We bridge these worlds with Bilevel‑ZOFO, a penalty‑based bilevel formulation that treats adapter parameters as a lower‑level learner coupled to an upper‑level ZO optimizer of the full backbone. This double-loop optimization strategy only requires the gradient of the PEFT model and the forward pass of the base model. We provide theoretical convergence guarantees for Bilevel ZOFO. Empirically, we demonstrate that Bilevel-ZOFO significantly outperforms existing ZO methods, achieves 2–4$\times$ faster training, and reduces sensitivity to prompts. Bilevel-ZOFO also outperforms FO PEFT methods while maintaining similar memory efficiency. Additionally, we show its strong potential for meta learning.

Optimization

Jincheng Cao, Ruichen Jiang, Erfan Yazdandoost Hamedani, Aryan Mokhtari

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper- and lower-level objectives are smooth but potentially nonconvex. Due to the absence of additional structural assumptions for the lower-level objective—such as convexity or the Polyak–Łojasiewicz (PL) condition—guaranteeing global optimality is generally intractable. Instead, we introduce a suitable notion of stationarity for this class of problems and aim to design a first-order algorithm that finds such stationary points in polynomial time. Intuitively, stationarity in this setting means the upper-level objective cannot be substantially improved locally without causing a larger deterioration in the lower-level objective. To this end, we show that a simple and implementable variant of the dynamic barrier gradient descent (DBGD) framework can effectively solve the considered nonconvex simple bilevel problems up to stationarity. Specifically, to reach an $(\epsilon_f, \epsilon_g)$-stationary point—where $\epsilon_f$ and $\epsilon_g$ denote the target stationarity accuracies for the upper- and lower-level objectives, respectively—the considered method achieves a complexity of $\mathcal{O}(\max(\epsilon_f^{-\frac{3+p}{1+p}}, \epsilon_g^{-\frac{3+p}{2}}))$, where $p \geq 0$ is an arbitrary constant balancing the terms. To the best of our knowledge, this is the first complexity result for a discrete-time algorithm that guarantees joint stationarity for both levels in general nonconvex simple bilevel problems.

Theory · Reinforcement Learning and Planning

James Chapman, Kedar Karhadkar, Guido Montufar

Deep reinforcement learning (DRL) has achieved remarkable success across multiple domains, including competitive games, natural language processing, and robotics. Despite these advancements, policies trained via DRL often struggle to generalize to evaluation environments with different parameters. This challenge is typically addressed by training with multiple contexts and/or by leveraging additional structure in the problem. However, obtaining sufficient training data across diverse contexts can be impractical in real-world applications. In this work, we consider contextual Markov decision processes (CMDPs) with transition and reward functions that exhibit regularity in context parameters. We introduce the context-enhanced Bellman equation (CEBE) to improve generalization when training on a single context. We prove both analytically and empirically that the CEBE yields a first-order approximation to the Q function trained across multiple contexts. We then derive context sample enhancement (CSE) as an efficient data augmentation method for approximating the CEBE in deterministic control environments. We numerically validate the performance of CSE in simulation environments, showcasing its potential to improve generalization in DRL.

Theory · Everything Else

Bochen Lyu, Xiaojing Zhang, Fangyi Zheng, He Wang, Zheng Wang, Zhanxing Zhu

This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has been a promising approach for studying the discrete optimization methods. Despite the crucial role of momentum in gradient-based optimization methods, the gap between the original dynamics and the continuous time approximations due to the discretization error has not been comprehensively bridged yet. In this work, we study the HB momentum method in continuous time while putting more focus on the discretization error to provide additional theoretical tools to this area. In particular, we design a first-order piece-wise continuous differential equation, where we add a number of counter terms to account for the discretization error explicitly. As a result, we provide a continuous time model for the HB momentum method that allows the control of discretization error to arbitrary order of the learning rate. As an application, we leverage it to find a new implicit regularization of the directional smoothness and investigate the implicit bias of HB for diagonal linear networks, indicating how our results can be used in deep learning. Our theoretical findings are further supported by numerical experiments.