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Deep Learning · Self-Supervised Learning

Jiaxin Sun, Yuhua Qian, Yang Wang

Standard contrastive learning minimizes geometric distance between positive pairs, implicitly assuming that strict compactness optimizes discrimination. However, this topology-agnostic confusion neglects intrinsic data structures and topological complexity, leading to class confusion—particularly when aggressive augmentations induce semantic drift. To address this, we propose Topology-Aware Contrastive Learning, a framework that shifts the objective from geometric singularity to topological connectivity. Leveraging Persistent Homology, we explicitly regulate the connectivity of the latent space, ensuring positive pairs maintain an α–β that balances intra-class cohesion with separability. Theoretically, we formally define the topology-agnostic confusion phenomenon, prove that excessive compactness strictly lower-bounds the probability of confusion and derive a generalization bound demonstrating that richer topological connectivity tightens downstream risk. Furthermore, we establish a measure-theoretic framework to mitigating the sensitivity of our method against varying augmentation strengths. Empirical results on benchmarks confirm that our approach enhances representation quality and reduces reliance on specific augmentation strategies compared to standard baselines. Our code will be made publicly available upon acceptance.

Ruiqi Wu, Xuanhua He, Meng Cheng, Tianyu Yang, Yong Zhang, Zhuoliang Kang, Xunliang Cai, Xiaoming Wei, Chunle Guo, Chongyi Li 等

We propose **Infinite-World**, a robust interactive world model capable of maintaining coherent visual memory over **1000+ frames** in complex real-world environments. While existing world models can be efficiently optimized on synthetic data with perfect ground-truth, they lack an effective training paradigm for real-world videos due to noisy pose estimations and the scarcity of viewpoint revisits. To bridge this gap, we first introduce a **Hierarchical Pose-free Memory Compressor (HPMC)** that recursively distills historical latents into a fixed-budget representation. By jointly optimizing the compressor with the generative backbone, HPMC enables the model to autonomously anchor generations in the distant past with bounded computational cost, eliminating the need for explicit geometric priors. Second, we propose an **Uncertainty-aware Action Abstraction** module that discretizes continuous motion into a tri-state logic. This strategy maximizes the utilization of raw video data while shielding the deterministic action space from being corrupted by noisy trajectories, ensuring robust action-response learning. Furthermore, guided by insights from a pilot toy study, we employ a **Revisit-Dense Finetuning Strategy** using a compact, 30-minute dataset to efficiently activate the model’s long-range loop-closure capabilities. Extensive experiments, including objective metrics and user studies, demonstrate that Infinite-World achieves superior performance in visual quality, action controllability, and spatial consistency. Our code and data will be released.

Deep Learning · Self-Supervised Learning

Yaoqi Liu, Jin Wang, Chunchen Wang, Hui Wang, Chuan Shi

In recent years, wireless signal recognition (WSR), which leverages artificial intelligence (AI) to identify properties of passively received radio signals, has garnered significant attention due to its broad applications, such as spectrum management. Existing WSR methods typically learn directly from received signals, which are distorted by physical wireless channel effects such as fading, and current denoising diffusion models lack de-channeling capabilities, which leads to performance degradation. Therefore, we propose PWC-Diff, a novel framework that integrates prior Physical Wireless Channels into the denoising Diffusion process. The framework employs a dedicated architecture named FusedFormer, which contains a fusion module and a self-attention module that jointly capture the temporal and spectral characteristics of the signals throughout the diffusion trajectory. By leveraging prior wireless channels, PWC-Diff learns to progressively “de-channel” the received signal and recover a representation closer to the transmitted signal. Extensive experiments on several datasets across three WSR tasks have achieved state-of-the-art (SOTA) performance, which demonstrates the rationality of our theory, and ablation experiments further illustrate the effectiveness of our proposed PWC-Diff.

Applications · Chemistry, Physics, and Earth Sciences

Yitian Wang, Zhao Yang, Angxiao Yue, Wentao Guo, Yaning Cui, Hongteng Xu

Modeling peptide cyclization is critical for the virtual screening of candidate peptides with desirable physical and pharmaceutical properties. This task is challenging because a cyclic peptide often exhibits diverse, ring-shaped conformations, which cannot be well captured by deterministic prediction models derived from linear peptide folding. In this study, we propose MuCO (Multi-stage Conformation Optimization), a generative peptide cyclization method that models the distribution of cyclic peptide conformations conditioned on the corresponding linear peptide. In principle, MuCO decouples the peptide cyclization task into three stages: topology-aware backbone design, generative side-chain packing, and physics-aware all-atom optimization, thereby generating and optimizing conformations of cyclic peptides in a coarse-to-fine manner. This multi-stage framework enables an efficient parallel sampling strategy for conformation generation and allows for rapid exploration of diverse, low-energy conformations. Experiments on the large-scale CPSea dataset demonstrate that MuCO significantly outperforms state-of-the-art methods in consistently in physical stability, structural diversity, secondary structure recovery, and computational efficiency, making it a promising computational tool for exploring and designing cyclic peptides.

Santiago Gonzalez, Alireza Amiribavandpour, Peter Ye, Edward Zhang, Ruslans Aleksejevs, Todor Antić, Polina Baron, Sujeet Bhalerao, Shubhrajit Bhattacharya, Zachary Burton 等

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic evaluation Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first benchmark to systematically measure alignment with human experts on undergraduate-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix ($7$ judges $\times$ $5$ solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude 4.5 Opus exhibit significant positive bias (up to $+0.28$ mean score inflation), effectively "hallucinating rigor" in flawed proofs. Furthermore, we uncover a critical reasoning disparity: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 raw score), specialized reasoning models like o3-deep-research collapse in discrete domains, dropping to 42.1\% accuracy in Graph Theory. We release QEDBench as a public benchmark for evaluating and improving AI judges.

General Machine Learning · Representation Learning

Mathieu Simon, Pascal Frossard, Christophe De Vleeschouwer

This paper explores unsupervised disentangled representation learning from a functional perspective. We define latent concepts as factors that influence observations through locally orthogonal directions, formalized as an orthogonality constraint on the Jacobian of the generative mapping. We prove that this condition yields identifiability of general nonlinear generative models, without requiring statistical independence or causal assumptions, provided the latent domain admits all combinations of factor values. Experiments with orthogonality-regularized normalizing flows empirically confirm the theory, demonstrate reliable recovery of ground-truth factors, and shed light on the success of VAEs. These findings challenge the prevailing impossibility claims for unsupervised disentanglement and provide a principled alternative foundation.

Applications · Health / Medicine

Shuntian Zheng, Jiaqi Li, Xiaoman Lu, Shuai He, Yu Guan

Millimeter-wave (mmWave) enables privacy-preserving, illumination-robust human pose estimation (HPE), with each mmWave frame represented as a range--angle--Doppler tensor, providing spatial magnitude for localization and Doppler signatures for motion-related cues. However, existing mmWave-based HPE methods either underutilize or naïvely fuse Doppler signatures with spatial magnitude, disregarding their distinct physical semantics. As a result, non-human Doppler signatures can be misinterpreted as human motion cues, leading to jittery trajectories. We propose \textbf{PULSE}, which converts Doppler signatures into confidence-aware motion prompts and injects them into spatial magnitude reasoning through constrained interactions. By screening Doppler prompts before they influence prediction, PULSE first suppresses spurious spectral motion cues and then uses the screened prompts to stabilize prediction. Across three datasets spanning single- and multi-person settings, PULSE consistently improves pose accuracy and temporal stability, indicating that controlled Doppler prompting is a practical direction for stable mmWave HPE. Codes are available in supplementary materials.

Deep Learning · Self-Supervised Learning

Julie Mordacq, Vicky Kalogeiton, Steve Oudot

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning meaningful representations from unlabeled data. However, the standard protocol for evaluating these representations, linear probing, is computationally expensive, sensitive to hyperparameters, and provides limited insight into the geometric structure of the representation space. In this work, motivated by connections between neural network generalization and intrinsic dimensionality (ID) we propose IdEst, a method for estimating the ID of SSL representations via the Minimum Spanning Tree dimension estimator ($\mathrm{dim}_\mathrm{MST}$). Across diverse datasets, architectures, and SSL pretraining objectives, we show that IdEst strongly correlates withdownstream linear probe performances. Furthermore, we demonstrate that IdEst enables efficient hyperparameter selection, significantly reducing the computational cost compared to supervised alternatives. Our results highlight intrinsic dimensionality as a principled geometric proxy for assessing and optimizing SSL representations, complementing standard supervised probing protocols.

Deep Learning · Self-Supervised Learning

Achleshwar Luthra, Yash Salunkhe, Tomer Galanti

Frozen self-supervised representations often transfer well with only a few labels across many semantic tasks. We argue that a single geometric quantity, *directional* CDNV (decision-axis variance), sits at the core of two favorable behaviors: strong few-shot transfer within a task, and low interference across many tasks. We show that both emerge when variability *along* class-separating directions is small. First, we prove sharp non-asymptotic multiclass generalization bounds for downstream classification whose leading term is the directional CDNV. The bounds include finite-shot corrections that cleanly separate intrinsic decision-axis variability from centroid-estimation error. Second, we link decision-axis collapse to multitask geometry: for independent balanced labelings, small directional CDNV across tasks forces the corresponding decision axes to be nearly orthogonal, helping a single representation support many tasks with minimal interference. Empirically, across SSL objectives, directional CDNV collapses during pretraining even when classical CDNV remains large, and our bounds closely track few-shot error at practical shot sizes. Additionally, on synthetic multitask data, we verify that SSL learns representations whose induced decision axes are nearly orthogonal.

Social Aspects · Alignment

Wonduk Seo, Wonseok Choi, Junseo Koh, Juhyeon Lee, Hyunjin An, Minhyeong Yu, Jian Park, Qingshan Zhou, Seunghyun lee, Yi Bu

Large Language Models (LLMs) increasingly support culturally sensitive decision making, yet often exhibit misalignment due to skewed pretraining data and the absence of structured value representations. Existing methods can steer outputs, but often lack demographic grounding and treat values as independent, unstructured signals, reducing consistency and interpretability. We propose OG-MAR, an Ontology-Guided Multi-Agent Reasoning framework. OG-MAR summarizes respondent-specific values from the World Values Survey (WVS) and constructs a global cultural ontology by eliciting relations over a fixed taxonomy via competency questions. At inference time, it retrieves ontology-consistent relations and demographically similar profiles to instantiate multiple value-persona agents, whose outputs are synthesized by a judgment agent that enforces ontology consistency and demographic proximity. Experiments on regional social-survey benchmarks across four LLM backbones show that OG-MAR improves cultural alignment and robustness over competitive baselines, while producing more transparent reasoning traces.

Deep Learning · Self-Supervised Learning

Ziwei Li, Shuzi Niu, Tao Yuan, Huiyuan Li

The performance of sparse direct solvers is fundamentally governed by fill-in, i.e. new nonzero entries arising from the LU factorization of a sparse matrix, as they dictate memory footprint and subsequent computation time. For decades, a variety of graph-theoretic algorithms have aimed to minimize fill-in, a problem known to be both NP-hard and critically important. While recent deep learning methods, optimizing surrogate fill-in objectives, show empirical promise and can outperform classical algorithms on certain matrices, they offer limited interpretability into the underlying mechanism of fill-in generation. To address this, we propose a novel reordering approach, Causal Triplet Structure Learning (CTS), which is grounded in the Fill-Path Theorem and reduces arbitrary-length fill-paths to length-two candidate triplets, identifies the causal structures that trigger fill-in, and intervenes to block their formation. Empirically, we design a multigrid-style GAT with KAN activations to learn vertex embeddings and introduce a causal triplet loss that discourages such structures during training. Experiments on the SuiteSparse Matrix Collection demonstrate that our method reduces fill-in by 6$\times$, leading to 12$\times$ speedup in factorization time compared to state-of-the-art methods on Chemical Process Simulation and Computational Fluid Dynamics matrices.

Applications · Chemistry, Physics, and Earth Sciences

Yi Zhang, Peng Wang, Difan Zou

Diffusion models show growing promise for generative modeling of physical systems, but enforcing partial differential equation (PDE) constraints directly is infeasible during the stochastic denoising process. Current methods apply constraints to the expected clean sample, incurring a Jensen’s Gap that forces a trade-off between PDE satisfaction and generative accuracy. To bridge this gap, we propose Physics-Informed Distillation of Diffusion Models (PIDDM), a simple yet effective post-hoc distillation strategy that enforces PDE constraints after training. PIDDM enables fast single-step generation while improving both physical consistency and sample quality, supporting forward/inverse problems and reconstruction from partial observations. Extensive experiments across PDE benchmarks show PIDDM outperforms recent baselines, such as PIDM, DiffusionPDE, and ECI-sampling, in both accuracy and constraint satisfaction, with lower computation and minimal hyperparameter tuning, offering a more efficient pathway to physics-informed diffusion models.

General Machine Learning · Methodology

Inés Castilla Rieso

Topological Machine Learning provides strong discriminative power for classification tasks through the use of Topological Data Analysis, and more particularly, Persistent Homology. Although it has strong theoretical appeal, it remains underused by the broader Machine Learning community; criticism often targets the reliance on synthetic data and the absence of shared experimental standards, which makes reported results difficult to compare. Indeed, current empirical evaluations lack a consistent framework for assessing methods: the construction of topological signatures is often opaque, statistical significance testing to validate reported gains, computing times and robustness to perturbations-such as missing data or noise-are often omitted. We assert that **progress in Topological Machine Learning depends on establishing clear and consolidated experimental standards that support meaningful comparison across methods**, articulated through a transparent and reproducible empirical framework including data processing and performance evaluation. We review current practices, highlight their limitations, and propose a set of principles for conducting rigorous and comparable empirical evaluations. Adopting these standards will enable trustworthy studies, clarify the gains of new methods, and ultimately support the broader adoption of Topological Machine Learning by the Machine Learning community.

Justinas Zaliaduonis, Sergios Gatidis, Till Richter, Patrick Putzky

Contrastive learning has emerged as a powerful paradigm for self-supervised representation learning, yet the precise conditions under which it recovers meaningful latent structure remain incompletely understood. We develop a measure-theoretic framework that formalizes the diversity condition, a requirement on the sampling mechanism that is necessary for recovering the latent space up to orthogonal transformation. We prove that when this condition is violated, as commonly occurs in practical settings where augmentations preserve semantic content, the optimal encoder no longer preserves geometric structure and linear identifiability is lost. Crucially, we demonstrate that the contrastive loss alone is insufficient for latent space reconstruction: encoder inductive bias emerges as a critical component that compensates for violations of the diversity condition. Our experiments on synthetic datasets and CIFAR-10 confirm these theoretical predictions, showing that architectural constraints become essential precisely when sampling diversity is limited. These findings have direct implications for the design of data augmentation strategies and encoder architectures in self-supervised contrastive learning systems.

Applications · Language, Speech and Dialog

Ke Lei, Yu Zhang, Changhao Pan, Xueyi Pu, Wenxiang Guo, Ruiqi Li, Zhou Zhao

Real-time and accurate spatial audio generation is pivotal for delivering an immersive experience. However, existing spatial audio synthesis technologies are often encumbered by a tradeoff between generation quality and high inference latency, as well as difficulty in capturing precise spatial information from multimodal inputs. To address these challenges, we propose S3Audio, a unified streaming framework for high-fidelity spatial audio generation from panoramic videos and text prompts. S3Audio mainly makes the following contributions: 1) We introduce a causal autoregressive diffusion transformer architecture that enables streaming high-quality spatial audio generation. 2) We design a Spatial Video–Audio Contrastive (SVAC) learning strategy to align the video encoder with the acoustic domain, and further employ a multi-objective online direct preference optimization~(ODPO) scheme, resulting in strong spatial perception and robust multimodal spatial audio synthesis. 3) To alleviate the current scarcity of spatial audio datasets, we also develop an automated annotation pipeline for generating detailed spatial captions. Experimental results demonstrate that S3Audio achieves superior performance in both video-to-spatial and text-to-spatial audio generation tasks. Demos can be found at: \url{https://s3audio.github.io}

Applications · Computer Vision

Hao-Xuan Ma, Jin-Fei Qi, YiCheng Xiao, Han-Jia Ye

Multimodal large language models (MLLMs) have recently made strong progress in vision-language reasoning, yet their performance often degrades as generations grow longer. A key factor is that they frequently lose track of earlier visual evidence and intermediate constraints under a monolithic growing context. Inspired by how humans separately recall what they see and what they infer when solving complex tasks, we propose DLMR, a parameter-efficient mechanism that equips MLLMs with dual latent memories: a visual memory that compresses image evidence and a reasoning memory that tracks intermediate conclusions and constraints. A router then dynamically decides which memory and how much to reuse during inference, preserving visual grounding while maintaining coherent long-horizon reasoning. DLMR is trained in three stages from latent memory construction to selective router learning while keeping the base MLLM frozen, yielding substantial gains on both general and reasoning benchmarks with only a small number of additional trainable parameters. Further analyses reveal interpretable, state-dependent routing in which the visual and reasoning memories specialize as intended, and demonstrate that this design reduces redundant decoding and improves token efficiency over long generations.

Deep Learning · Large Language Models

Patrick Putzky, Martin Genzel, Mattes Mollenhauer, Sebastian Schulze, Thomas Wollmann, Stefan Dietzel

Post-training compression is currently divided into two contrasting regimes. On the one hand, fast, data-free, and model-agnostic methods (e.g., NF4 or HQQ) offer maximum accessibility but suffer from functional collapse at extreme bit-rates below 4 bits. On the other hand, techniques leveraging calibration data or extensive recovery training achieve superior fidelity but impose high computational constraints and face uncertain robustness under data distribution shifts. We introduce EntQuant, the first framework to unite the advantages of these distinct paradigms. By matching the performance of data-dependent methods with the speed and universality of data-free techniques, EntQuant enables practical utility in the extreme compression regime. Our method decouples numerical precision from storage cost via entropy coding, compressing a 70B parameter model in less than 30 minutes. We demonstrate that EntQuant does not only achieve state-of-the-art results on standard evaluation sets and models, but also retains functional performance on more complex benchmarks with instruction-tuned models, all at modest inference overhead.

Theory · Online Learning and Bandits

Emmanuel Esposito, Andrew Jacobsen, Hao Qiu, Mengxiao Zhang

In this paper, we study dynamic regret in unconstrained online convex optimization (OCO) with movement costs. Specifically, we generalize the standard setting by allowing the movement cost coefficients $\lambda_t$ to vary arbitrarily over time. Our main contribution is a novel algorithm that establishes the first comparator-adaptive dynamic regret bound for this setting, guaranteeing $\widetilde{\mathcal{O}}(\sqrt{(1+P_T)(T+\sum_t \lambda_t)})$ regret, where $P_T$ is the path length of the comparator sequence over $T$ rounds. This recovers the optimal guarantees for both static and dynamic regret in standard OCO as a special case where $\lambda_t=0$ for all rounds. To demonstrate the versatility of our results, we consider two applications: *OCO with delayed feedback* and *OCO with time-varying memory*. We show that both problems can be translated into time-varying movement costs, establishing a *novel reduction* specifically for the delayed feedback setting that is of independent interest. A crucial observation is that the first-order dependence on movement costs in our regret bound plays a key role in enabling optimal comparator-adaptive dynamic regret guarantees in both settings.

Applications · Time Series

Valentina Kuskova, Dmitry Zaytsev, Michael Coppedge

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: function-valued causal influence. In such models, each directed relationship corresponds not to a single weight or coefficient, but to a state-dependent function whose effect varies across regimes, magnitudes, and contexts of the system. In this paper, we formalize function-valued causal influence in nonlinear multivariate time series and show that common scalar summaries, such as aggregated contribution magnitudes, constitute severe information bottlenecks. Using Neural Additive Vector Autoregression as a representative architecture, we demonstrate that edges with indistinguishable scalar causal scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. These differences explain persistent discrepancies between causal score magnitude, interpretability, and predictive relevance that cannot be resolved by significance testing alone. We present a general framework for extracting and visualizing causal response functions from neural autoregressive models using learned contribution tensors and local attribution methods. Through controlled synthetic systems and an applied case study of democratic development, we show how function-valued analysis reveals regime-specific and asymmetric causal structure that is systematically missed by coefficient-centric or score-centric approaches. Our results suggest that meaningful interpretation of nonlinear causal time-series models requires moving beyond scalar causal scores toward explicit analysis of causal response functions. This reframing clarifies the representational content of modern causal discovery methods and provides a foundation for more faithful interpretation of complex dynamical systems.

Deep Learning · Theory

Adam Shai, Loren Amdahl-Culleton, Casper Christensen, Henry R Bigelow, Fernando Rosas, Alexander Boyd, Eric Alt, Kyle Ray, Paul Riechers

Transformers pretrained via next token prediction learn to factor their world into parts, representing these factors in orthogonal subspaces of the residual stream. We formalize two representational hypotheses: (1) a representation in the product space of all factors, whose dimension grows exponentially with the number of parts, or (2) a factored representation in orthogonal subspaces, whose dimension grows linearly. Both track context-induced uncertainty over the latent parts, but the factored representation sacrifices fidelity when factors are not conditionally independent. We derive precise predictions about the geometric structure of activations for each, including the number of subspaces, their dimensionality, and the arrangement of context embeddings within them. We test between these hypotheses on transformers trained on synthetic processes with known latent structure. When factors are conditionally independent, models learn factored representations; when noise or dependencies break this structure, models gradually expand their effective dimensionality over training to recover fidelity. This provides a principled explanation for why transformers decompose the world into parts, and suggests that interpretable low dimensional structure may persist even in models trained on complex data.