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Deep Learning · Large Language Models

Seungdong Yoa, Ye Seul Sim, Suhee Yoon, Sanghyu Yoon, Dongmin Kim, Soonyoung Lee, Bumsoo Kim, Junhyun Lee

Multi-agent debate has shown promise for improving the reasoning of large language models, yet recent theory suggests its benefits are highly regime-dependent. While interaction can amplify informative signals under corrective conditions, symmetric debate dynamics are neutral in expectation, often making majority voting preferable. We reconcile these views by arguing that debate is effective only when invoked at the right time and with appropriate structure. Based on this insight, we propose LASE, a leader-centric multi-agent debate framework that selectively engages interaction only in non-neutral regimes. LASE introduces an asymmetric leader–supporter architecture that enables directed information flow and selective signal amplification, while defaulting to simple aggregation otherwise. Experiments across diverse reasoning benchmarks show that LASE achieves multi-agent-level performance with near single-agent token cost, substantially improving efficiency over static debate and voting baselines.

Theory · Learning Theory

Futoshi Futami, Masahiro Fujisawa

Despite their remarkable success, a rigorous theoretical understanding of how latent variables (LVs) govern the generalization performance of Variational Autoencoders (VAEs) remains largely elusive. Existing theoretical analyses are confined to supervised learning or models with discrete latent spaces, leaving their role in standard VAEs with continuous LVs poorly understood. This paper establishes the first information-theoretic analysis for VAEs by adapting a theoretical framework from supervised learning---the leave-one-out conditional mutual information framework---to the unsupervised, continuous latent space of these models. Our analysis reveals that their generalization error is bounded solely by the information complexity of the encoder and LVs, independent of the decoder. The versatility of our framework is demonstrated through its extension to both hierarchical VAEs, for which we provide layer-wise bounds, and data generation, where we link our information-theoretic principles to a novel bound on the 2-Wasserstein distance between true and generated distributions.

Reinforcement Learning · Batch/Offline

Tobias Schmähling, Matthias Burkhardt, Tobias Windisch

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

Deep Learning · Generative Models and Autoencoders

Gabriel Moreira, Manuel Marques, Joao Costeira, Chenyan Xiong

We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for control. We characterize them as the singular functions of a conditional expectation operator and show that they can be learned via a self-supervised objective. Once recovered, this basis enables the projection of arbitrary guidance signals, such as labels, CLIP embeddings, or masks, directly onto the sampling trajectory. This approach allows for stable, high-fidelity control without retraining or denoiser backpropagation during sampling. Empirically, we improve conditional accuracy on CIFAR-10 by 37 percentage points over the strongest training-free baseline while offering $4\times$ faster sampling. Moreover, the same representations that support label and CLIP guidance also enable spatial control, such as mask-based guidance, without auxiliary models. Finally, our framework reveals a phase transition in the generative process, pinpointing the optimal time window for effective guidance.

Andrew Ilyas, Amin Saberi, Grigorios Velegkas

Data plays an invaluable role in large-scale ML training pipelines. Multiple factors, including the need to incentivize the creation of high-quality data and efforts to compensate creative data work, have led to increased interest in data {\em pricing}. Data pricing mechanisms seek to establish a market where data providers are compensated based (in part) on the value of their data to the data buyer, e.g., frontier AI labs. However, assessing the exact value that each provider's data adds to the data buyer's objective requires repeated re-training, which is infeasible in practice. Our work studies {\em data pricing under compute constraints}. In our setting, data buyers cannot make data acquisition decisions optimally due to limited compute. Inspired by existing practice in the field of data selection, we propose a model for this problem called ``pricing with an attribution oracle,'' and provide a theoretical and empirical analysis of compute-efficient acquisition and pricing.

Applications · Everything Else

Mustafa Chasmai, Wuao Liu, Subhransu Maji, Grant Horn

Can we determine someone’s geographic location solely from the sounds they hear? Are acoustic signals enough to localize within a country, state, or even city? In this work, we tackle the challenge of global-scale audio geolocation, with a particular focus on wildlife and natural sounds. We posit that bioacoustic signals contain informative geolocation cues because of well-defined geographic ranges of species. To test this hypothesis, we benchmark image geolocation and soundscape mapping methods, design oracles and species-centric baselines, and propose a hybrid approach that combines species range prediction with retrieval-based geolocation. We further ask whether geolocation improves with species-diverse recordings and spatiotemporal aggregation across neighboring samples. Finally, we extend our study to multimodal geolocation with case studies from movies that combine both audio and visual content. Our results highlight the potential of incorporating bioacoustic signals into geospatial tasks, motivating future work on species recognition and audio geolocation.

Applications · Neuroscience, Cognitive Science

Ganchao Wei, Daniela de Albuquerque, Miles Martinez, Shiyang Pan, John Pearson

While neuroscience experiments have repeatedly demonstrated the involvement of large populations of neurons in even simple behaviors, these studies have just as often reported that the collective dynamics of neural activity are approximately low-dimensional. As a result, methods for identifying low-dimensional latent representations of time series data have become increasingly prominent in neuroscience. However, most existing methods either ignore temporal structure or model time evolution using latent dynamical systems approaches. In the first case, dynamics may be distorted or even scrambled in the latent space, while in the second, many possible latent dynamics may give rise to the same data. Here, we address these challenges using a novel flow-matching approach in which data are generated by a pair of flow fields, one governing time evolution, the other a mapping between data and a low-dimensional latent space. Importantly, the dimension-reducing flow is trained to minimize distortions of the temporal dynamics, learning an identifiable low-dimensional representation that preserves temporal relations in the original data. Additionally, we constrain our latent spaces to have low-dimensional support in a soft, parameterized manner, taking inspiration from ideas on nested dropout. Across both neural and behavioral data, we show that this dual flow approach produces both more interpretable dynamics and higher-quality reconstructions than competing models, including in noise-dominated data sets where conventional approaches fail.

Optimization · Everything Else

Zhong Li, Hongliang Lu, Tao Wei, Wenyu Liu, Yuxuan Chen, Yuan LAN, Fan Zhang, Zaiwen Wen

Optimization modeling underpins decision-making in logistics, manufacturing, energy, and finance, yet translating natural-language requirements into correct optimization formulations and solver-executable code remains labor-intensive. Although large language models (LLMs) have been explored for this task, evaluation is still dominated by toy-sized or synthetic benchmarks, masking the difficulty of industrial problems with $10^{3}$--$10^{6}$ (or more) variables and constraints. A key bottleneck is the lack of benchmarks that align natural-language specifications with reference formulations/solver code grounded in real optimization models. To fill in this gap, we introduce MIPLIB-NL, built via a structure-aware reverse construction methodology from real mixed-integer linear programs in MIPLIB~2017. Our pipeline (i) recovers compact, reusable model structure from flat solver formulations, (ii) reverse-generates natural-language specifications explicitly tied to this recovered structure under a unified model--data separation format, and (iii) performs iterative semantic validation through expert review and human--LLM interaction with independent reconstruction checks. This yields 223 one-to-one reconstructions that preserve the mathematical content of the original instances while enabling realistic natural-language-to-optimization evaluation. Experiments show substantial performance degradation on MIPLIB-NL for systems that perform strongly on existing benchmarks, exposing failure modes invisible at toy scale.

Steve Hanneke, Amin Karbasi, Anay Mehrotra, Grigorios Velegkas

We investigate language generation in the limit (Kleinberg & Mullainathan, 2024; Li et al., 2025) in variants where the generator receives some feedback based on its “actions.” We study two such variants. In the first, which is inspired by Littlestone’s model of online learning, the generator observes whether it made a mistake at each iteration. In the second, introduced by Charikar & Pabbaraju (2025a), the generator can query whether a string belongs to the target language. Our main result is a characterization of collections that are generable with mistake feedback. Using similar techniques, we also characterize when generation is possible in the query model with set-based generators; set-based generators have been studied in several works (Charikar & Pabbaraju, 2025a; Kalavasis et al., 2025; Kleinberg & Wei, 2025a; Li et al., 2025). Beyond the characterizations themselves, we derive several implications. First, our results imply new closure properties for generation with mistake and query feedback. Second, our results show that, under feedback, generation is robust to noise: it remains possible with arbitrary contamination in the adversary’s examples and with finite contamination in the feedback. Third, our techniques also yield new sufficient and necessary conditions for generation without feedback among other implications.

Applications · Computer Vision

Zihao Zhu, Wenyuan Zhao, Nuo Chen, Chao Tian, Zhiwen Fan

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images; however, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To fill this gap, we present ***Trust3R***, a trust-aware 3D reconstruction framework that pairs a lightweight gated residual mean refinement with evidential learning to predict pointmap evidence under a Normal-Inverse-Wishart prior and yield a closed-form multivariate Student-t predictive distribution. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks, and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk--coverage and sparsification, and generally improves geometric accuracy. Trust3R consistently improves uncertainty ranking across benchmarks (e.g. on ScanNet++: 25\% lower AURC and 41\% lower AUSE), enabling uncertainty-aware weighting for downstream alignment and fusion.

General Machine Learning · Representation Learning

Lixuan Guo, Yifei Wang, Tiansheng Wen, Aosong Feng, Stefanie Jegelka, Chenyu You

Multi-vector retrieval (MVR) models, exemplified by ColBERT, have established new benchmarks in retrieval accuracy by preserving fine-grained token-level interactions. However, this granularity imposes prohibitive storage and retrieval efficiency bottlenecks: to manage the immense memory footprint and computational overhead of billion-scale token vectors, state-of-the-art systems are forced to rely on aggressive dimension reduction and complex clustering (e.g., K-means). This compromise introduces two critical limitations: excessive indexing latency of clustering large-scale corpora and semantic information loss inherent to compression. In this paper, we propose Single-Stage Sparse Retrieval (SSR), a paradigm shift that replaces expensive clustering with efficient sparse coding. Instead of compressing features into low-dimensional dense vectors, we utilize Sparse Autoencoder (SAE) to project token embeddings into a high-dimensional but highly sparse representation. This transformation enables us to bypass vector clustering entirely and leverage inverted indexing for precise, high-throughput retrieval. Extensive experiments on the BEIR benchmark demonstrate that SSR achieves a "trifecta" of improvements: it reduces indexing time by 15× compared to ColBERTv2, halves retrieval latency, and simultaneously improves retrieval performance over leading baselines.

Deep Learning · Theory

Jerry Yao-Chieh Hu, Xiwen Zhang, Ali ElSheikh, Weimin Wu, Han Liu

Structured \underline{S}tate-\underline{S}pace \underline{D}uality (SSD) [Dao \& Gu, ICML 2024] is an equivalence between a simple Structured \underline{S}tate-\underline{S}pace \underline{M}odel (SSM) and a masked attention mechanism. In particular, a state-space model with a scalar-times-identity state matrix is equivalent to a masked self-attention with a $1$-semiseparable causal mask. Consequently, the same sequence transformation (model) has two algorithmic realizations: as a linear-time $O(T)$ recurrence or as a quadratic-time $O(T^2)$ attention. In this note, we formalize and generalize this duality: (i) we extend SSD from the scalar‑identity case to general diagonal SSMs (diagonal state matrices); (ii) we show that these diagonal SSMs match the scalar case's training complexity lower bounds while supporting richer dynamics; (iii) we establish a necessary and sufficient condition under which an SSM is equivalent to $1$-semiseparable masked attention; and (iv) we show that such duality fails to extend to standard softmax attention due to rank explosion. Together, these results tighten bridge between recurrent SSMs and Transformers, and widen the design space for expressive yet efficient sequence models.

Deep Learning · Large Language Models

Haozhen Zhang, Haodong Yue, Tao Feng, Quanyu Long, Jianzhu Bao, Bowen Jin, Weizhi Zhang, Xiao Li, Jiaxuan You, Chengwei Qin 等

Memory is increasingly central to Large Language Model (LLM) agents operating beyond a single context window, yet most existing systems rely on offline, query-agnostic memory construction that can be inefficient and may discard query-critical information. Although runtime memory utilization is a natural alternative, prior work often incurs substantial overhead and offers limited explicit control over the performance-cost trade-off. In this work, we present \textbf{BudgetMem}, a runtime agent memory framework for explicit, query-aware performance–cost control. BudgetMem structures memory processing as a set of memory modules, each offered in three budget tiers (i.e., \textsc{Low}/\textsc{Mid}/\textsc{High}). A lightweight router performs budget-tier routing across modules to balance task performance and memory construction cost, which is implemented as a compact neural policy trained with reinforcement learning. Using BudgetMem as a unified testbed, we study three complementary strategies for realizing budget tiers: implementation (method complexity), reasoning (inference behavior), and capacity (module model size). Across LoCoMo, LongMemEval, and HotpotQA, BudgetMem surpasses strong baselines when performance is prioritized (i.e., high-budget setting), and delivers better accuracy–cost frontiers under tighter budgets. Moreover, our analysis disentangles the strengths and weaknesses of different tiering strategies, clarifying when each axis delivers the most favorable trade-offs under varying budget regimes.

Probabilistic Methods · Gaussian Processes

Wenyuan Zhao, Rui Tuo, Chao Tian

Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse inducing kernel approximations based on a dyadic ordered template basis, incurring only ${O}(\log M)$ complexity dependence on the number of inducing points. Our approach constructs compact and expressive kernel representations from sparsely activated bases, enabling efficient tensorized GPU computation and seamless integration with modern large-scale models. SIKA-GP can be naturally embedded into Bayesian neural networks (BNNs) with sparse activations, yielding significant speedups in both training and inference without sacrificing predictive performance. The method naturally extends to deep feature learning, addressing the scalability challenges introduced by deep architectures and high-dimensional feature representations. Empirical results on vision and transformer-based language benchmarks demonstrate that our approach consistently delivers fast and accurate GP models, providing a principled path toward scalable kernel learning.

Deep Learning · Graph Neural Networks

Chendi Qian, Christopher Morris, Stefanie Jegelka, Christian Sohler

There has been a growing interest in using neural networks, especially message-passing neural networks (MPNNs), to solve hard combinatorial optimization problems heuristically. However, existing learning-based approaches for hard combinatorial optimization tasks often rely on supervised training data, reinforcement learning, or gradient estimators, leading to significant computational overhead, unstable training, or a lack of provable performance guarantees. In contrast, classical approximation algorithms offer such performance guarantees under worst-case inputs but are non-differentiable and unable to adaptively exploit structural regularities in natural input distributions. We address this dichotomy with the fundamental example of Uniform Facility Location (UniFL), a variant of the combinatorial facility location problem with applications in clustering, data summarization, logistics and supply chain design. We develop a fully differentiable MPNN model that embeds approximation-algorithmic principles while avoiding the need for solver supervision or discrete relaxations. Our approach admits provable approximation and size generalization guarantees to much larger instances than seen during training. Empirically, we show that our approach outperforms standard non-learned approximation algorithms in terms of solution quality, closing the gap with computationally intensive integer linear programming approaches. Overall, this work provides a step toward bridging learning-based methods and approximation algorithms for discrete optimization.

Jiaqi Jin, Siwei Wang, Taichun Zhou, Dong Zhibin, Siqi Wang, Miaomiao Li, Xinwang Liu, En Zhu

In incomplete multi-view clustering, unbalanced missingness is prevalent, where different views exhibit significantly varying missing rates, causing severe observation bias. This imbalance poses two core challenges: models develop serious learning biases by over-relying on low-missing-rate views while neglecting high-missing-rate ones, and cross-view data recovery becomes extremely difficult due to sparse training samples in highly missing views, leading traditional generation methods into a "data starvation" dilemma. Existing methods either naively assume low-missing-rate views as high-quality or lack effective debiasing mechanisms, showing limited performance under imbalance. To address this, we propose the Causal-Invariant Meta-Learning Network (CIMLN). It employs a meta-learning paradigm to transfer knowledge across views, using complete samples as support sets to guide generation for highly missing views. Meanwhile, it incorporates a causal inference framework with counterfactual reasoning and adversarial intervention strategies to eliminate spurious dependencies on observation patterns, learning causally invariant clustering structures. These modules synergistically optimize to ensure generated representations possess both feature fidelity and clustering discriminability. Extensive experiments on benchmarks demonstrate the effectiveness of CIMLN.

Applications · Health / Medicine

Yifan Lin, Kevin Lin

High-dimensional genomics studies are frequently confounded by unmeasured biological processes that obscure disease-specific signals. While existing workflows can estimate these latent confounders, they fail to quantify how robust a discovery is to varying levels of hypothetical confounding. We introduce sensGAN, a deep-learning adversarial framework that systematically explores the confounding spectrum by learning "worst-case" latent variables that nullify the most gene associations under novel predictive-gain constraints. By identifying the minimum confounding strength required to explain away an observed effect, our method shifts the paradigm toward a formal, quantitative sensitivity analysis. In diverse simulations, sensGAN accurately recovers latent structures and outperforms existing methods in identifying confounder-sensitive genes. Applied to human Alzheimer's disease microglia, our framework prioritizes robust disease pathways while successfully isolating signals driven by unmeasured co-occurring neurodegenerative pathologies.

Deep Learning · Generative Models and Autoencoders

Zhiqi Li, Yuchen Sun, Duowen Chen, Jinjin He, Bo Zhu

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory consistency constraint, which is difficult to supervise and optimize over long time scales, with a principled linear surrogate that enables direct data supervision for long-horizon flow-map compositions. We derive this approximation from the semigroup formulation of flow-based models and show that, under mild regularity assumptions, it faithfully approximates the original consistency objective while being substantially easier to optimize. This formulation leads to a unified, JVP-free training framework that supports both $u$-prediction and $x_1$-prediction variants, avoiding explicit Jacobian computations and significantly reducing memory and computational overhead. Experiments on image synthesis, particle-based geometry generation, and functional generation demonstrate improved optimization stability and sample quality under fixed sampling budgets, together with approximately $50\%$ reductions in training time and memory consumption compared to existing one-step methods for image generation.

Theory · Learning Theory

Sophia Pi, Mingcheng Lu, Jerry Yao-Chieh Hu, Maojiang Su, Weimin Wu, Han Liu

We study flow-matching transformers when data lie on a low-dimensional manifold. Our key insight is a flow decomposition that splits motion along the manifold from motion off the manifold. The scheme works for first- and higher-order flow matching and ties model complexity to the intrinsic manifold dimension. Building on these, we establish tighter sample-complexity bounds for velocity approximation, velocity estimation, and distribution estimation. These bounds meet near-minimax rates for flow-matching transformers of any order. Our results show how flow-matching transformers escape the curse of dimensionality by utilizing intrinsic data structure.

Social Aspects · Accountability, Transparency, and Interpretability

Yining Jiao, Shankar Bhamidi, Carlton ZDANSKI, Julia Kimbell, Andrew Prince, Cameron Worden, Samuel Kirse, Christopher Rutter, Benjamin Shields, William Dunn 等

Understanding how anatomical shapes evolve in response to developmental covariates—and quantifying their spatially varying uncertainties—is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce \texttt{PRISM}, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. \texttt{PRISM} models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate \texttt{PRISM}'s strong performance across diverse tasks—from modeling shape evolution to anomaly detection—within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.