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Optimization · Non-Convex

Marien Renaud, Julien Hermant, Deliang Wei, Yu Sun

Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization by denoising (RED), often focus on designing sophisticated image priors to improve reconstruction quality, while leaving convergence acceleration to heuristics. To bridge the gap, we propose Restarted Inertia with Score-based Priors (RISP) as a principled extension of RED. RISP incorporates a restarting inertia for fast convergence, while still allowing score-based image priors for high-quality reconstruction. We prove that RISP attains a faster stationary-point convergence rate than RED, without requiring the convexity of the image prior. We further derive and analyze the associated continuous-time dynamical system, offering insight into the connection between RISP and the heavy-ball ordinary differential equation (ODE). Experiments across a range of imaging inverse problems demonstrate that RISP enables fast convergence while achieving high-quality reconstructions.

Optimization · Learning for Optimization

Yu Wang, Yang Li, Jiale Ma, Junchi Yan, Yi Chang

One central challenge in Neural Combinatorial Optimization (NCO) is handling hard constraints efficiently. Beyond the two classic paradigms, i.e., Local Construction (LC), which sequentially builds feasible solutions but scales poorly, and Global Prediction (GP), which produces one-shot heatmaps yet struggles with constraint conflicts, the recently proposed Adaptive Expansion (AE) shares the advantages of both by progressively growing partial solutions with instance-wise global awareness. However, existing realizations bolt AE onto external GP predictors, so their solution quality is bounded by the backbone and their inference cost scales with repeated global calls. In this paper, we fundamentally rethink adaptive expansion and make it native to a generative model, acting as its intrinsic decoding principle rather than an external wrapper. We propose NEXCO, a CO-specific masked diffusion framework that turns adaptive expansion into the model’s own iterative unmasking process. Specifically, it involves a solution-expansion training procedure with a time-agnostic GNN denoiser, which learns diffusion trajectories between fully masked solutions and ground-truth solutions. With the trained time-agnostic denoiser, we introduce a novel solution expansion scheme at the solving stage, enabling adaptive control over the intermediate solution states. It is achieved by constructing candidate sets according to confidence scores and applying feasibility projection to expand the solution while respecting constraints. In this way, ``adaptive" is not an afterthought but the decoding itself: intermediate diffusion states are meaningful partial solutions and progress is instance-adaptive rather than schedule-bound. Extensive experiments on representative CO problems show that NEXCO achieves approximately 50\% improvement in solution quality and up to $4\times$ faster inference compared to prior state-of-the-art solvers.

Reinforcement Learning · Online

Zhihao Lin

Gaussian policies have dominated continuous control in deep reinforcement learning (RL), yet they suffer from a fundamental mismatch: their unbounded support requires ad-hoc squashing functions that distort the geometry of bounded action spaces. While von Mises-Fisher (vMF) distributions offer a theoretically grounded alternative on the sphere, their reliance on Bessel functions and rejection sampling hinders practical adoption. We propose \textbf{Geometric Action Control (GAC)}, a novel action generation paradigm that preserves the geometric benefits of spherical distributions while \textit{simplifying computation}. GAC decomposes action generation into a direction vector and a learnable concentration parameter, enabling efficient interpolation between deterministic actions and uniform spherical noise. This design reduces parameter count from \(2d\) to \(d+1\), and avoids the \(O(dk)\) complexity of vMF rejection sampling, achieving simple \(O(d)\) operations. Empirically, GAC consistently matches or exceeds state-of-the-art methods across six MuJoCo benchmarks, achieving 37.6\% improvement over SAC on Ant-v4 and up to 112\% on complex DMControl tasks, demonstrating strong performance across diverse benchmarks. Our ablation studies reveal that both \textbf{spherical normalization} and \textbf{adaptive concentration control} are essential to GAC's success. These findings suggest that robust and efficient continuous control does not require complex distributions, but a principled respect for the geometry of action spaces. Code and pretrained models are available in supplementary materials.

Optimization · Learning for Optimization

Hongyang Jia, Qingchun Hou, Bojun Du, Xiao Cai, Ning Zhang, Chongqing Kang

Learning compact and reliable convex hulls from data is a fundamental yet challenging problem with broad applications in classification, constraint learning, and decision optimization. We propose Projection Convex Hull (PCH), a scalable framework for learning polyhedral trust regions in high-dimensional spaces. Starting from an exact MINLP formulation, we derive an unconstrained surrogate objective and show that, under suitable weight assignments, the optimal hyperplanes of the MINLP are recovered as stationary points of the surrogate. Building on this theoretical foundation, PCH adaptively constructs and refines hyperplanes by subregion partition, strategic weight assignment, and gradient-based updates, yielding convex hulls that tightly enclose the positive class while excluding negatives. The learned polyhedra can serve as geometric trust regions to enhance selective classification and constraint learning. Extensive experiments on synthetic and real-world datasets demonstrate that PCH achieves strong performance in accuracy, scalability, and model compactness, outperforming classical geometric algorithms and recent optimization-based approaches, especially in high-dimensional and large-scale settings. These results confirm the value of PCH as a theoretically grounded and practically effective framework for trust-region learning. Codes are available at https://github.com/IDO-Lab/trust-region-pch.

Reinforcement Learning · Multi-agent

yueheng li, Guangming Xie, Zongqing Lu

Due to practical constraints such as partial observability and limited communication, Centralized Training with Decentralized Execution (CTDE) has become the dominant paradigm in cooperative Multi-Agent Reinforcement Learning (MARL). However, existing CTDE methods often underutilize centralized training or lack theoretical guarantees. We propose Multi-Agent Guided Policy Optimization (MAGPO), a novel framework that better leverages centralized training by integrating centralized guidance with decentralized execution. MAGPO uses an autoregressive joint policy for scalable, coordinated exploration and explicitly aligns it with decentralized policies to ensure deployability under partial observability. We provide theoretical guarantees of monotonic policy improvement and empirically evaluate MAGPO on 43 tasks across 6 diverse environments. Results show that MAGPO consistently outperforms strong CTDE baselines and matches or surpasses fully centralized approaches, offering a principled and practical solution for decentralized multi-agent learning.

Optimization · Global Optimization

Luca Di Carlo, Chase Goddard, David J Schwab

Modern neural networks exhibit a striking property: basins of attraction in the loss landscape are often connected by low-loss paths, yet optimization dynamics generally remain confined to a single convex basin and rarely explore intermediate points. We resolve this paradox by identifying entropic barriers arising from the interplay between curvature variations along these paths and noise in optimization dynamics. Empirically, we find that curvature systematically rises away from minima, producing effective forces that bias noisy dynamics back toward the endpoints — even when the loss remains nearly flat. These barriers persist longer than energetic barriers, shaping the late-time localization of solutions in parameter space. Our results highlight the role of curvature-induced entropic forces in governing both connectivity and confinement in deep learning landscapes.

General Machine Learning · Everything Else

Yan Sun, Qixin ZHANG, Zhiyuan Yu, Xikun Zhang, Li Shen, Dacheng Tao

The rapid scaling of large language models(LLMs) has made inference efficiency a primary bottleneck in the practical deployment. To address this, semi-structured sparsity offers a promising solution by strategically retaining $N$ elements out of every $M$ weights, thereby enabling hardware-friendly acceleration and reduced memory. However, existing (N:M)-compatible approaches typically fall into two categories: rule-based layerwise greedy search, which suffers from considerable errors, and gradient-driven combinatorial learning, which incurs prohibitive training costs. To tackle these challenges, we propose a novel linear-space probabilistic framework named MaskPro, which aims to learn a prior categorical distribution for every $M$ consecutive weights and subsequently leverages this distribution to generate the (N:M)-sparsity throughout an $N$-way sampling without replacement. Furthermore, to mitigate the training instability induced by the high variance of policy gradients in the super large combinatorial space, we propose a novel update method by introducing a moving average tracker of loss residuals instead of vanilla loss. Finally, we conduct comprehensive theoretical analysis and extensive experiments to validate the superior performance of MaskPro, as well as its excellent scalability in memory efficiency and exceptional robustness to data samples.

General Machine Learning · Everything Else

Martin Zach, Youssef Haouchat, Michael Unser

We propose a statistical benchmark for diffusion-posterior-sampling (DPS) algorithms in linear inverse problems. Our test signals are discretized Lévy processes whose posteriors admit efficient Gibbs methods. These Gibbs methods provide gold-standard posterior samples for direct, distribution-level comparisons with DPS algorithms. They can also sample the denoising posteriors in the reverse diffusion, which enables the arbitrary-precision Monte Carlo estimation of various objects that may be needed in the DPS algorithms, such as the expectation or the covariance of the denoising posteriors. In turn, this can be used to isolate algorithmic errors from the errors due to learned components. We instantiate the benchmark with the minimum-mean-squared-error optimality gap and posterior-coverage tests and evaluate popular algorithms on the inverse problems of denoising, deconvolution, imputation, and reconstruction from partial Fourier measurements. We release the benchmark code at https://github.com/zacmar/dps-benchmark and invite the community to contribute and report results.

General Machine Learning · Everything Else

Hadi Pouransari, David Grangier, C Thomas, Michael Kirchhof, Oncel Tuzel

The impressive performance gains of modern language models currently rely on scaling parameters: larger models store more world knowledge and reason better. Yet compressing all world knowledge into parameters is unnecessary, as only a fraction is used per prompt, and impractical for edge devices with limited inference-time memory and compute. We address this shortcoming by a memory-augmented architecture and a pretraining strategy aligned with existing hardware paradigms. We introduce small language models that access large hierarchical parametric memory banks encoding world knowledge. Our pretraining learns to store long-tail world knowledge in the memory parameters, while the small language model acts as an anchor capturing common knowledge and general reasoning abilities. Through trillion-token-scale experiments, we show significant gains: a 160M-parameters model augmented with an 18M-parameters memory fetched from a 4.6B memory bank obtains comparable performance to a regular model with more than 2x the parameters. We study the optimal type and size of parametric memories in transformers, scaling them to over 21B parameters. We find that our proposed hierarchical feed-forward memories work robustly across transformer architectures, whether added during pretraining or post-hoc.

General Machine Learning · Everything Else

Qian Shao, Qiyuan Chen, Jiahe Chen, Zepeng Li, Qianqian Tang, Hongxia Xu, JIAN Wu

Long-tailed semi-supervised learning is hampered by a vicious cycle of confirmation bias, where skewed pseudo-labeling progressively marginalizes tail classes. This challenge is compounded in real-world scenarios by a class distribution mismatch between labeled and unlabeled data, rendering the bias unpredictable and difficult to mitigate. While existing methods adapt Logit Adjustment (LA) using dynamic estimates of the unlabeled distribution, we argue their effectiveness is undermined by two critical limitations stemming from LA's core design, *i.e.*, its class-wise and overall adjustment mechanisms. First, their reliance on simple frequency counting overestimates the prevalence of head classes due to sample redundancy, leading to harmful over-suppression. Second, and more critically, they overlook the interplay between the above two types of adjustment, treating the overall adjustment strength as a fixed hyperparameter. This is a significant oversight, as we empirically find that the optimal strength is highly sensitive to the estimated distribution. To address these limitations, we propose Co-Calibrated Logit Adjustment (CoLA), a framework that co-designs the class-wise and overall LA components. Specifically, CoLA refines the class-wise adjustment by estimating each class's effective sample size via the effective rank of its representations. Subsequently, it formulates the overall adjustment strength as a learnable parameter, which is optimized through a meta-learning procedure on a proxy validation set constructed to mirror the refined distribution. Supported by a theoretical generalization bound, our extensive experiments show that CoLA outperforms existing baselines on $4$ public benchmarks across standard long-tail setups.

General Machine Learning · Probabilistic Methods

Leo Zhang, Peter Potaptchik, Jiajun He, Yuanqi Du, Arnaud Doucet, Francisco Vargas, Hai-Dang Dau, Saifuddin Syed

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target distributions. Parallel Tempering (PT) enhances MCMC's sample efficiency through annealing and parallel computation, propagating samples from tractable reference distributions to intractable targets via state swapping across interpolating distributions. The effectiveness of PT is limited by the often minimal overlap between adjacent distributions in challenging problems, which requires increasing the computational resources to compensate. We introduce a framework that accelerates PT by leveraging neural samplers---including normalising flows, diffusion models, and controlled diffusions---to reduce the required overlap. Our approach utilises neural samplers in parallel, circumventing the computational burden of neural samplers while preserving the asymptotic consistency of classical PT. We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality, reduces the computational cost compared to classical PT, and enables efficient free energy/normalising constant estimation.

General Machine Learning · Probabilistic Methods

Madhav Kanda, Shubham Dipak Ugare, Sasa Misailovic

Probabilistic programming offers a powerful framework for modeling uncertainty, yet statistical model discovery in this domain entails navigating an immense search space under strict domain‐specific constraints. When small language models are tasked with generating probabilistic programs, they frequently produce outputs that suffer from both syntactic, and semantic errors, such as flawed inference constructs. Motivated by probabilistic programmers’ domain expertise and debugging strategies, we introduce RefineStat, a language model–driven framework that enforces semantic constraints ensuring synthesized programs contain valid distributions, well‐formed parameters, and then applies diagnostic‐aware refinement by resampling prior or likelihood components whenever reliability checks fail. We evaluate RefineStat on multiple probabilistic-programming code-generation tasks using smaller language models (SLMs) and find that it produces programs that are both syntactically sound and statistically reliable, often matching or surpassing those from closed-source large language models (e.g., OpenAI o3).

General Machine Learning · Transfer, Multitask and Meta-learning

Nilushika Udayangani Hewa Dehigahawattage, Nandakishor Desai, Marimuthu Palaniswami

While traditional time-series classifiers assume full sequences at inference, practical constraints (latency and cost) often limit inputs to partial prefixes. The absence of class-discriminative patterns in partial data can significantly hinder a classifier’s ability to generalize. This work uses knowledge distillation (KD) to equip partial time series classifiers with the generalization ability of their full-sequence counterparts. In KD, high-capacity teacher transfers supervision to aid student learning on the target task. Matching with teacher features has shown promise in closing the generalization gap due to limited parameter capacity. However, when the generalization gap arises from training-data differences (full versus partial), the teacher’s full-context features can be an overwhelming target signal for the student’s short-context features. To provide progressive, diverse, and collective teacher supervision, we propose Generative Diffusion Prior Distillation (GDPD), a novel KD framework that treats short-context student features as degraded observations of the target full-context features. Inspired by the iterative restoration capability of diffusion models, we learn a diffusion-based generative prior over teacher features. Leveraging this prior, we posterior-sample target teacher representations that could best explain the missing long-range information in the student features and optimize the student features to be minimally degraded relative to these targets. GDPD provides each student feature with a distribution of task-relevant long-context knowledge, which benefits learning on the partial classification task. Extensive experiments across earliness settings, datasets, and architectures demonstrate GDPD’s effectiveness for full-to-partial distillation.

General Machine Learning · Transfer, Multitask and Meta-learning

Bangguo Ye, Yuanwei Zhang, Xiaoqun Zhang

Fine-tuning large pre-trained models under resource constraints remains challenging due to the massive number of parameters involved. Existing parameter-efficient tuning methods, such as low-rank adaptation (LoRA) and its variants, rely heavily on matrix factorization and often struggle in extremely low-parameter regimes. In this work, we propose TRAC, a novel fine-tuning framework that leverages Tensor-Train decomposition with Across-layer Compression. Specifically, TRAC represents each adaptation module as a compact sequence of tensor-train cores and allows certain cores to be frozen or shared across layers, thereby exploiting the inherent similarity and redundancy among layer weight matrices. To retain layer-specific flexibility, lightweight controllers are introduced, enabling shared tensor cores to adaptively modulate representations. We evaluate TRAC on diverse architectures, including Qwen, LLaMA, GPT, BERT, and ViT, across benchmarks covering text classification, text generation, and image classification. Experimental results demonstrate that TRAC achieves performance comparable to or better than LoRA and its variants, while substantially reducing trainable parameters and storage requirements.

Applications · Language, Speech and Dialog

Shengyin Sun, Yiming Li, Xing Li, Yingzhao Lian, Weizhe Lin, Huiling Zhen, Zhiyuan Yang, Xianzhi Yu, Chen Chen, Mingxuan Yuan 等

Test-time scaling has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs) by allocating additional computational resources during inference. However, this paradigm is inherently inefficient due to the generation of different reasoning traces, leading to significant computational overhead. Speculative decoding offers a promising avenue for mitigating this inefficiency, yet its efficacy in the structured and repetition-rich context remains unexplored. To bridge this gap, we introduce the first comprehensive benchmark designed to evaluate speculative decoding methods in LLM test-time scaling. Our benchmark provides consistent experimental protocols across representative test-time scaling paradigms (e.g., Best-of-N sampling and multi-round thinking), enabling a fair comparison of three major categories of speculative decoding: model-based, training-based, and N-gram-based methods. Extensive experiments reveal that simple N-gram-based methods effectively capture repetitive patterns, demonstrating unique potential in accelerating test-time scaling. This phenomenon demonstrates the value of integrating N-gram-based methods with model-based or training-based approaches to benefit both repetitive and diverse reasoning in test-time scaling. We hope this benchmark spurs further research on speculative decoding for test-time scaling, enabling faster and more practical reasoning in LLMs through better handling of repetitive and diverse reasoning paths. Code available at .

General Machine Learning · Transfer, Multitask and Meta-learning

Matthew Macfarlane, Clem Bonnet, Herke van Hoof, Levi Lelis

A central challenge in program induction has long been the trade-off between symbolic and neural approaches. Symbolic methods offer compositional generalisation and data efficiency, yet their scalability is constrained by formalisms such as domain-specific languages (DSLs), which are labor-intensive to create and may not transfer to new domains. In contrast, neural networks flexibly learn from data but fail to generalise systematically. We bridge this divide with the Neural Language Interpreter (NLI), an architecture that learns its own discrete, symbolic-like programming language end-to-end. NLI autonomously discovers a vocabulary of subsymbolic primitive operations and uses a novel differentiable neural executor to interpret variable-length sequences of these primitives. This allows NLI to represent programs that are not bound to a constant number of computation steps, enabling it to solve more complex problems than those seen during training. To make these discrete, compositional program structures amenable to gradient-based optimisation, we employ the Gumbel-Softmax relaxation, enabling the entire model to be trained end-to-end. Crucially, this same differentiability enables powerful test-time adaptation. At inference, NLI's program inductor provides an initial program guess. This guess is then refined via gradient descent through the neural executor, enabling efficient search for the neural program that best explains the given data. We demonstrate that NLI outperforms in-context learning, test-time training, and continuous latent program networks (LPNs) on tasks that require combinatorial generalisation and rapid adaptation to unseen tasks. Our results establish a new path toward models that combine the compositionality of discrete languages with the gradient-based search and end-to-end learning of neural networks.

General Machine Learning · Transfer, Multitask and Meta-learning

Zijun Wu, Yongchang Hao, Lili Mou

Large language models are typically controlled via prompts, which must be repeatedly re-processed for every new query and are difficult to reuse modularly. We introduce TokMem, a procedural memory framework that compiles each reusable task procedure into a single trainable memory token. Each token serves as both a procedure index and a generation control signal that steers generation, enabling targeted behaviors with constant-size overhead. TokMem keeps the backbone LLM frozen and stores procedural knowledge entirely in these dedicated units, so new procedures can be added continually without interfering with existing ones. We evaluate TokMem on two settings: atomic recall over 1,000 Super-Natural Instructions tasks and compositional recall on multi-step function-calling. Our results show that TokMem consistently outperforms retrieval-augmented prompting while avoiding repeated context overhead. Moreover, it matches or exceeds parameter-efficient fine-tuning with substantially fewer trainable parameters.

General Machine Learning · Transfer, Multitask and Meta-learning

Minsang Kim, Seung Baek

Knowledge Distillation (KD) can transfer the reasoning abilities of large models to smaller ones, which can reduce the costs to generate Chain-of-Thoughts for reasoning tasks. KD methods typically ask the student to mimic the teacher's distribution over the entire output. However, a student with limited capacity can be overwhelmed by such extensive supervision causing a distribution mismatch, especially in complex reasoning tasks. We propose Token-Selective Dual Knowledge Distillation (TSD-KD), a framework for student-centric distillation. TSD-KD focuses on distilling important tokens for reasoning and encourages the student to explain reasoning in its own words. TSD-KD combines indirect and direct distillation. Indirect distillation uses a weak form of feedback based on preference ranking. The student proposes candidate responses generated on its own; the teacher re-ranks those candidates as indirect feedback without enforcing its entire distribution. Direct distillation uses distribution matching; however, it selectively distills tokens based on the relative confidence between teacher and student. Finally, we add entropy regularization to maintain the student's confidence during distillation. Overall, our method provides the student with targeted and indirect feedback to support its own reasoning process and to facilitate self-improvement. The experiments show the state-of-the-art performance of TSD-KD on 10 challenging reasoning benchmarks, outperforming the baseline and runner-up in accuracy by up to 54.4% and 40.3%, respectively. Notably, a student trained by TSD-KD even outperformed its own teacher model in four cases by up to 20.3%. The source code is available at https://github.com/kmswin1/TSD-KD.

General Machine Learning · Representation Learning

Ziheng Chen, Zihan Su, Bernhard Schölkopf, Nicu Sebe

Hyperbolic Neural Networks (HNNs) have shown remarkable success in representing hierarchical and tree-like structures, yet most existing work relies on the Poincaré ball and hyperboloid models. While these models admit closed-form Riemannian operators, their constrained nature potentially leads to numerical instabilities, especially near model boundaries. In this work, we explore the Proper Velocity (PV) space, an unconstrained representation of hyperbolic space rooted in Einstein’s special relativity, as a stable alternative. We first establish the complete Riemannian toolkit of the PV space. Building on this foundation, we introduce Proper Velocity Neural Networks (PVNNs) with core layers including Multinomial Logistic Regression (MLR), Fully Connected (FC), convolutional, activation, and batch normalization layers. Extensive experiments across four tasks, namely numerical stability, image classification, graph node classification, and genomic sequence learning, demonstrate the stability and effectiveness of PVNNs. The code is available at https://github.com/NickyoyoSu/PVNN.

Reinforcement Learning · Batch/Offline

Qiyang Li, Sergey Levine

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