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Theory · Learning Theory

Thomas Boudou, Batiste Le Bars, Nirupam Gupta, Aurélien Bellet

Robust distributed learning algorithms aim to maintain reliable performance despite the presence of misbehaving workers. Such misbehaviors are commonly modeled as *Byzantine failures*, allowing arbitrarily corrupted communication, or as *data poisoning*, a weaker form of corruption restricted to local training data. While prior work shows similar optimization guarantees for both models, an important question remains: *How do these threat models impact generalization?* We show, for the first time, a fundamental gap in generalization guarantees between the two threat models: Byzantine failures yield strictly worse rates than those achievable under data poisoning. Our findings leverage a tight algorithmic stability analysis of robust distributed learning. Specifically, we prove that: *(i)* under data poisoning, the uniform algorithmic stability of an algorithm with optimal optimization guarantees degrades by an additive factor of $\varTheta ( \frac{f}{n-f} )$, with $f$ out of $n$ workers misbehaving; whereas *(ii)* under Byzantine failures, the degradation is in $\Omega \big( \sqrt{ \frac{f}{n-2f}} \big)$.

Deep Learning · Everything Else

Yongding Tian, Zaid Al-Ars, Maksim Kitsak, H Peter Hofstee

Empirical studies have shown that continuous low-loss paths can be constructed between independently trained neural network models. This phenomenon, known as mode connectivity, refers to the existence of such paths between distinct modes-i.e., well-trained solutions in parameter space. However, existing empirical methods do not reliably connect independently trained modes and have been evaluated mainly on a narrow set of architectures (e.g., basic CNNs, VGG, and ResNet), leaving their effectiveness on newer models unclear. In this work, we propose a new empirical algorithm for connecting independently trained modes that generalizes beyond traditional architectures and supports a broader range of networks, including MobileNet, ShuffleNet, EfficientNet, RegNet, Deep Layer Aggregation (DLA), and Compact Convolutional Transformers (CCT). In addition to broader applicability, the proposed method yields more consistent connectivity paths across independently trained mode pairs and supports connecting modes obtained with different training hyperparameters.

Deep Learning · Theory

Yijin Zhou, Yutang Ge, Wenyuan XIE, Linqian Zeng, Xiaowen Dong, Yuguang Wang

Transformers excel in natural language processing and computer vision tasks. However, they still face challenges in generalizing to Out-of-Distribution (OOD) datasets, i.e. data whose distribution differs from that seen during training. OOD detection aims to distinguish outliers while preserving in-distribution (ID) data performance. This paper introduces the OOD detection Probably Approximately Correct (PAC) Theory for transformers, which establishes the conditions for data distribution and model configurations for the OOD detection learnability of transformers. It shows that outliers can be accurately represented and distinguished with sufficient data under conditions. The theoretical implications highlight the trade-off between theoretical principles and practical training paradigms. By examining this trade-off, we naturally derived the rationale for leveraging auxiliary outliers to enhance OOD detection. Our theory suggests that by penalizing the misclassification of outliers within the loss function and strategically generating soft synthetic outliers, one can robustly bolster the reliability of transformer networks. This approach yields a novel algorithm that ensures learnability and refines the decision boundaries between inliers and outliers. In practice, the algorithm consistently achieves state-of-the-art (SOTA) performance across various data formats.

Applications · Health / Medicine

Danush Kumar Venkatesh, Adam Schmidt, Muhammad Abdullah Jamal, Omid Mohareri

Surgical video datasets are essential for scene understanding, enabling procedural modeling and intra-operative support. However, these datasets are often heavily imbalanced, with rare actions and tools under-represented, which limits the robustness of downstream models. We address this challenge with *SurgiFlowVid*, a sparse and controllable video diffusion framework for generating surgical videos of under-represented classes. Our approach introduces a dual-prediction diffusion module that jointly denoises RGB frames and optical flow, providing temporal inductive biases to improve motion modeling from limited samples. In addition, a sparse visual encoder conditions the generation process on lightweight signals (e.g., sparse segmentation masks or RGB frames), enabling controllability without dense annotations. We validate our approach on three surgical datasets across tasks including action recognition, tool presence detection, and laparoscope motion prediction. Synthetic data generated by our method yields consistent gains of $10$–$20$% over competitive baselines, establishing *SurgiFlowVid* as a promising strategy to mitigate data imbalance and advance surgical video understanding methods.

Deep Learning · Large Language Models

Wenhao Yu, Shaohang Wei, Jiahong Liu, Yifan Li, Minda Hu, Aiwei Liu, Hao Zhang, Irwin King

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects intrinsic uncertainty induced by the pre-training prior. Ignoring entropy can misidentify noisy or easily replaceable tokens as learning-critical, while ignoring probability fails to reflect target-specific alignment. RankTuner introduces a probability--entropy calibration signal, the **Relative Rank Indicator**, by comparing the rank of the ground-truth token with its expected rank under the predictiondiction distribution. The inverse indicator is used as a token-wise **Relative Scale** to reweight the fine-tuning objective, focusing updates on truly under-learned tokens without over-penalizing intrinsically uncertain positions. Experiments on multiple backbones show consistent improvements on mathematical reasoning benchmarks, transfer gains on out-of-distribution reasoning, and pre code generation performance over probability- or entropy-only reweighting baselines.

General Machine Learning · Representation Learning

Hao Chen, Lin Liu, Yuguang Wang

Causal representation learning (CRL) has garnered increasing interests from the causal inference and artificial intelligence community, due to its capability of disentangling potentially complex data-generating mechanism into causally interpretable latent features, by leveraging the heterogeneity of modern datasets. In this paper, we further contribute to the CRL literature, by focusing on the stylized linear structural causal model over the latent features and assuming a linear mixing function that maps latent features to the observed data or measurements. Existing linear CRL methods often rely on stringent assumptions, such as accessibility to single-node interventional data or restrictive distributional constraints on latent features and exogenous measurement noise. However, these prerequisites can be challenging to satisfy in certain scenarios. In this work, we propose a novel linear CRL algorithm that, unlike most existing linear CRL methods, operates under weaker assumptions about environment heterogeneity and data-generating distributions while still recovering latent causal features up to an equivalence class. We further validate our new algorithm via synthetic experiments and an interpretability analysis of large language models (LLMs), demonstrating both its superiority over competing methods in finite samples and its potential in integrating causality into AI. Source code is available at \href{https://anonymous.4open.science/r/creator-883D/}{the anonymous link}.

Applications · Computer Vision

Linli Yao, Yuancheng Wei, Yaojie Zhang, Lei Li, Xinlong Chen, Feifan Song, Ziyue Wang, Kun Ouyang, Yuanxin Liu, Lingpeng Kong 等

This paper proposes Omni Dense Captioning, a novel task designed to generate continuous, fine-grained, and structured audio-visual narratives with explicit timestamps. To ensure dense semantic coverage, we introduce a six-dimensional structural schema to create "script-like" captions, enabling readers to vividly imagine the video content scene-by-scene, akin to a cinematographic screenplay. To facilitate research, we construct OmniDCBench, a high-quality human-annotated benchmark, and propose SodaM, a unified metric that evaluates time-aware detailed descriptions while mitigating scene boundary ambiguity. Furthermore, we construct a training dataset OmniDenseCap-40K and present Omni-Captioner-7B, a strong baseline trained via SFT and GRPO with task-specific rewards. Extensive experiments demonstrate that Omni-Captioner-7B achieves state-of-the-art performance, surpassing Gemini-2.5-Pro, while its generated dense descriptions significantly boost downstream capabilities in audio-visual reasoning (DailyOmni and WorldSense) and temporal grounding (Charades-STA). All datasets, models, and code will be made publicly available.

Deep Learning · Algorithms

Chenhao Ye, Rongguang Ye, Yuchao Zhang, Ming Tang

Backpropagation (BP) remains the dominant training paradigm for deep neural networks, yet its reliance on global gradient propagation fundamentally induces update locking problem, enforcing strong inter-layer dependencies in parameter updates. To address this limitation, we propose Depth-progressive Monotonic Learning (DMoL), a training scheme that assigns layer-wise local belief objectives and incrementally refines them across network depth, enabling unlocked parameter updates. As a result, DMoL supports dynamic modification of network depth during training, adapting to available compute and device resources while maintaining stable optimization. We provide theoretical guarantees that layer-wise local belief objectives improve monotonically with increasing depth and converge exponentially. Empirically, DMoL consistently matches or outperforms BP across diverse tasks, yielding a 4.3\% accuracy gain on CIFAR-100, mitigating over-smoothing in deep graph neural networks (+37.5\% on Cora), and reducing the final loss by over 35\% in diffusion model training, highlighting its robustness and flexibility as an alternative to BP. The code is publicly available at: https://anonymous.4open.science/r/DMoL.

Deep Learning · Large Language Models

Aiwei Liu, Minghua He, Shaoxun Zeng, Sijun Zhang, Linhao Zhang, Chuhan Wu, Wei Jia, Yuan Liu, Zhou Xiao, Jie Zhou

Autoregressive (AR) generation is the standard decoding paradigm for Large Language Models (LLMs), but its token-by-token nature limits parallelism at inference time. Diffusion Language Models (DLLMs) offer parallel decoding by recovering multiple masked tokens per step; however, in practice they often fail to translate this parallelism into speed gains over optimized AR engines (e.g., vLLM). A key reason is that many DLLMs rely on bidirectional attention, which breaks standard prefix KV caching. We propose WeDLM, a diffusion decoding framework built entirely on standard causal attention to make parallel generation prefix-cache friendly. The core idea is to let each masked position condition on all observed tokens while keeping a causal mask, achieved by Topological Reordering that moves observed tokens to the physical prefix while preserving their logical positions. Building on this, we introduce a streaming decoding procedure that continuously commits confident tokens into a growing left-to-right prefix, avoiding the stop-and-wait behavior common in block diffusion methods. Experiments show that WeDLM preserves the quality of strong AR backbones while delivering substantial speedups, approaching 3× on challenging reasoning benchmarks and up to 10× in low-entropy generation regimes; critically, our comparisons are against AR baselines served by vLLM under matched deployment settings.

Applications · Computer Vision

Hangwei Zhang, Armando Fortes, Tianyi Wei, Xingang Pan

Bokeh rendering and depth estimation share a fundamental optical connection, yet existing methods fail to fully exploit this reciprocity. Conventional bokeh pipelines rely heavily on noisy depth maps that inevitably introduce visual artifacts. Conversely, existing monocular depth models typically follow two flawed paradigms. Generative diffusion-based frameworks often lack consistent metric scale. Meanwhile, feed-forward metric depth models frequently fail in textureless or distant regions where defocus blur can provide geometric information. We propose BokehDepth, a two-stage framework that treats synthetic defocus as a supervision-free geometric signal. In the first stage, a physically grounded generative model produces calibrated bokeh stacks from a single sharp input without requiring prior depth input. Subsequently, a lightweight defocus-aware aggregation module integrates these stacks into the encoder of a depth estimation framework. This mechanism allows the model to extract consistent geometric features from the defocus dimension while keeping the decoder architecture unchanged. Experiments demonstrate that BokehDepth achieves superior visual bokeh fidelity compared to depth-dependent rendering baselines and consistently enhances the metric accuracy of state-of-the-art monocular depth models.

Deep Learning · Everything Else

Ke Xiao, Qiyuan Wang, Christos Anagnostopoulos, Zhuoran Tan, Wenhao Li

Driven by the imperative to leverage privacy-sensitive data scattered across decentralized devices, federated fine-tuning has emerged as a vital paradigm for adapting large language models without compromising data privacy. Yet, its practical efficacy is bottlenecked by severe client resource heterogeneity. Existing truncation-based methods typically couple the transmitted rank with the trainable rank, which (i) under-utilizes bandwidth on communication-rich but compute-limited clients and (ii) exacerbates truncation-induced gradient drift. To address this, we propose FedHera, a resource-decoupled framework that explicitly differentiates information reception from gradient optimization. FedHera employs a spectrum-preserving allocation strategy to maximize the transfer of global knowledge (via high-rank singular values) within bandwidth limits, irrespective of training constraints. Furthermore, we introduce a prefix-gating mechanism that utilizes the downloaded high-capacity basis as a frozen reference to guide local updates, thereby minimizing the optimization gap caused by aggressive truncation. Extensive experiments under different heterogeneous settings show that FedHera improves stability and accuracy over state-of-the-art baselines.

Yanbang Wang, Jon Kleinberg, Yanhong Wu

Negative sampling is an important yet challenging component in self-supervised graph representation learning, particularly for recommendation systems where user-item interactions are modeled as bipartite graphs. Existing methods often rely on heuristics or human-specified principles to design negative sampling distributions. This potentially overlooks the usage of an underlying ``true'' negative distribution, which we might be able to access as an oracle despite not knowing its exact form. In this work, we shift the focus from manually designing negative sampling distributions to a more principled method that approximates and leverages the underlying true distribution from the ground up. We expand this idea in the analysis of two scenarios: (1) when the observed graph is an unbiased sample from the true distribution, and (2) when the observed graph is biased with partially observable positive edges. The analysis result is the derivation of a sampling strategy as the numerical approximation of a well-established learning objective. Our theoretical findings are also empirically validated, and our new sampling methods achieve state-of-the-art performance on real-world datasets.

Deep Learning · Large Language Models

Senkang Hu, Yong Dai, Yuzhi Zhao, Yihang Tao, Yu Guo, Zhengru Fang, Sam Kwong, Yuguang Fang

Agentic reasoning enables large reasoning models (LRMs) to dynamically acquire external knowledge, but yet optimizing the retrieval process remains challenging due to the lack of dense, principled reward signals. In this paper, we introduce *InfoReasoner*, a unified framework that incentivizes effective information seeking via a *synthetic semantic information gain reward*. Theoretically, we redefine information gain as uncertainty reduction over the model's belief states, establishing guarantees, including non-negativity, telescoping additivity, and channel monotonicity. Practically, to enable scalable optimization without manual retrieval annotations, we propose an output-aware intrinsic estimator that computes information gain directly from the model's output distributions using *semantic clustering via bidirectional textual entailment*. This intrinsic reward guides the policy to maximize epistemic progress, enabling efficient training via Group Relative Policy Optimxization (GRPO). Experiments across seven question-answering benchmarks demonstrate that InfoReasoner consistently outperforms strong retrieval-augmented baselines, achieving up to 5.4% average accuracy improvement. Our work provides a theoretically grounded and scalable path toward agentic reasoning with retrieval.

Aiwei Liu, Minghua He, Shaoxun Zeng, Sijun Zhang, Linhao Zhang, Chuhan Wu, Wei Jia, Yuan Liu, Zhou Xiao, Jie Zhou

Autoregressive (AR) generation is the standard decoding paradigm for Large Language Models (LLMs), but its token-by-token nature limits parallelism at inference time. Diffusion Language Models (DLLMs) offer parallel decoding by recovering multiple masked tokens per step; however, in practice they often fail to translate this parallelism into speed gains over optimized AR engines (e.g., vLLM). A key reason is that many DLLMs rely on bidirectional attention, which breaks standard prefix KV caching. We propose WeDLM, a diffusion decoding framework built entirely on standard causal attention to make parallel generation prefix-cache friendly. The core idea is to let each masked position condition on all observed tokens while keeping a causal mask, achieved by Topological Reordering that moves observed tokens to the physical prefix while preserving their logical positions. Building on this, we introduce a streaming decoding procedure that continuously commits confident tokens into a growing left-to-right prefix, avoiding the stop-and-wait behavior common in block diffusion methods. Experiments show that WeDLM preserves the quality of strong AR backbones while delivering substantial speedups, approaching 3× on challenging reasoning benchmarks and up to 10× in low-entropy generation regimes; critically, our comparisons are against AR baselines served by vLLM under matched deployment settings.

Theory · Learning Theory

Yuma Ichikawa, Shuhei Kashiwamura, Ayaka Sakata

Quantized neural network training optimizes a discrete, non-differentiable objective. The straight-through estimator (STE) enables backpropagation through surrogate gradients and is widely used. While previous studies have primarily focused on the properties of surrogate gradients and their convergence, the influence of quantization hyperparameters, such as bit width and quantization range, on learning dynamics remains largely unexplored. We theoretically show that in the high-dimensional limit, STE dynamics converge to a deterministic ordinary differential equation. This reveals that STE training exhibits a plateau followed by a sharp drop in generalization error, with plateau length depending on the quantization range. A fixed-point analysis quantifies the asymptotic deviation from the unquantized linear model. We also extend analytical techniques for stochastic gradient descent to nonlinear transformations of weights and inputs.

Deep Learning · Generative Models and Autoencoders

Ky Dan Nguyen, Hoang Lam Tran, Anh-Dung Dinh, Daochang Liu, Weidong Cai, Xiuying Wang, Chang Xu

Autoregressive (AR) models based on next-scale prediction are rapidly emerging as a powerful tool for image generation, but they face a critical weakness: information inconsistencies between patches across timesteps introduced by progressive resolution scaling. These inconsistencies scatter guidance signals, causing them to drift away from conditioning information and leaving behind ambiguous, unfaithful features. We tackle this challenge with Information-Grounding Guidance (IGG), a novel mechanism that anchors guidance to semantically important regions through attention. By adaptively reinforcing informative patches during sampling, IGG ensures that guidance and content remain tightly aligned. Across both class-conditioned and text-to-image generation tasks, IGG delivers sharper, more coherent, and semantically grounded images, setting a new benchmark for AR-based methods.

Drew Prinster, Clara Fannjiang, Ji Won Park, Kyunghyun Cho, Anqi Liu, Suchi Saria, Samuel Stanton

An agent must try new behaviors to explore and improve. In high-stakes environments, an agent that violates safety constraints may cause harm and must be taken offline, curtailing any future interaction. Imitating old behavior is safe, but excessive conservatism discourages exploration. How much behavior change is too much? We show how to use any safe reference policy as a probabilistic regulator for any optimized but untested policy. Conformal calibration on data from the safe policy determines how aggressively the new policy can act, while provably enforcing the user's declared risk tolerance. Unlike conservative optimization methods, we do not assume the user has identified the correct model class nor tuned any hyperparameters. Unlike previous conformal methods, our theory provides finite-sample guarantees even for non-monotonic bounded constraint functions. Our experiments on applications ranging from natural language question answering to biomolecular engineering show that safe exploration is not only possible from the first moment of deployment, but can also improve performance.

Deep Learning · Theory

Rui Dai, SHURAN ZHENG

Recent research has established empirical scaling laws to predict model performance on multi-domain data mixtures. However, a theoretical understanding of these model loss behaviors remains limited. In this work, we propose a unified framework to explain the underlying mechanics of data mixing. Our approach extends theoretical perspectives originally developed for standard neural scaling laws (e.g., Kaplan and Chinchilla) to the multi-domain setting. Based on the distributional assumption that domains overlap on fundamental skills while diverging on specialized skills, we identify two key factors that decide the domain loss of models trained on different data mixtures: Capacity Competition, where the allocation of finite model capacity couples domain losses globally, and Noise Reduction, where optimal weights shift toward harder-to-learn domains to minimize variance. Experiments demonstrate that our framework fits the loss landscape with lower Mean Relative Error than existing empirical baselines and accurately predicts optimal training mixtures. Crucially, our model achieves these results using significantly fewer parameters.

Deep Learning · Theory

Tianze Jiang, Blake Bordelon, Cengiz Pehlevan, Boris Hanin

Mixture-of-Experts (MoE) layers have emerged as an important tool in scaling up modern neural networks by decoupling total trainable parameters from activated parameters in the forward pass for each token. However, sparse MoEs add complexity to training due to (i) new trainable parameters (router weights) that, like all other parameter groups, require hyperparameter (HP) tuning; (ii) new architecture scale dimensions (number of and size of experts) that must be chosen and potentially taken large. To make HP selection cheap and reliable, we propose a new parameterization for transformer models with MoE layers when scaling model width, depth, number of experts, *and* expert (hidden) size. Our parameterization is justified by a novel dynamical mean-field theory (DMFT) analysis. When varying different model dimensions trained at a fixed token budget, we find empirically that our parameterization enables reliable HP transfer across models from 51M to 2B total parameters. We further take HPs identified from sweeping small models on a short token horizon to train larger models on longer horizons and report performant model behaviors.

Optimization · Stochastic

Maria-Eleni Sfyraki, Jun-Kun Wang

Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers such as Lion and Muon have gained quite significant popularity in deep learning. In this work, building on recent initiatives, we provide a unifying perspective by interpreting these seemingly disparate methods through the lens of Stochastic Frank-Wolfe. Specifically, we show that Lion and Muon with weight decay can be viewed as special instances of a Stochastic Frank-Wolfe, and we establish their convergence guarantees in terms of the Frank-Wolfe gap, a standard stationarity measure in non-convex optimization for Frank-Wolfe methods. We further find that convergence to this gap implies convergence to a KKT point of the original problem under a norm constraint for Lion and Muon. Moreover, motivated by recent empirical findings that stochastic gradients in modern machine learning tasks often exhibit heavy-tailed distributions, we extend Stochastic Frank-Wolfe to settings with heavy-tailed noise by developing two robust variants with strong theoretical guarantees that hold for general compact convex sets without the need for a large batch size, filling the gap in the literature on Stochastic Frank-Wolfe for non-convex optimization. Our contributions in the later part of this work, in turn, yield new variants of Lion and Muon, that better accommodate heavy-tailed gradient noise, thereby enhancing their practical scope.