arXiv subjects

Yi-An Ma

Publications and source records attributed to Yi-An Ma.

At least 19 recordsLinked to original sources

arXiv2026

Reinforcement Learning without Ground-Truth Solutions can Improve LLMs

Reinforcement learning with verifiable rewards (RLVR) for training LLMs typically rely on ground-truth answers to assign rewards, limiting their applicability to tasks where the ground-truth solution is unknown. We introduce a \textbf{R}anking-\textbf{i}nduced \textbf{VER}ifiable framework (RiVER) that trains LLMs on score-based optimization tasks without ground-truth solutions, using deterministic execution feedback as continuous-valued supervision. When applying group-relative RL to such continuous rewards, we identify two key challenges: \emph{scale dominance}, where uncalibrated score magnitudes across test instances distort policy updates, and \emph{frequency dominance}, where repeatedly sampled suboptimal solutions can outweigh rare but stronger candidates. RiVER addresses these challenges with calibrated reward shaping that uses instance-wise comparisons and emphasizes top-ranked solvers while retaining bounded feedback for other valid solutions. We train on 12 AtCoder Heuristic Contest tasks and evaluate on Algorithm Engineering Benchmark (ALE-Bench), LiveCodeBench, and USACO. RiVER advances Qwen3-8B and GLM-Z1-9B-0414 by 8.9\% and 9.4\% in ALE rating rank. More importantly, despite training exclusively on score-based tasks without any ground-truth solutions, RiVER also improves the backbones across exact-solution benchmarks such as LiveCodeBench and USACO by an absolute average improvement of 2.4\% and 3.5\%. By contrast, baselines trained with raw execution scores improve ALE rating but fail to transfer to exact-solution benchmarks. These results suggest that score-based optimization tasks, combined with proper reward calibration, can serve as effective training environments for general coding ability without ground-truth solutions.

cs.LG↗

arXiv2026

Stochastic Gradient Variational Inference with Price's Gradient Estimator from Bures-Wasserstein to Parameter Space

For approximating a target distribution given only its unnormalized log-density, stochastic gradient-based variational inference (VI) algorithms are a popular approach. For example, Wasserstein VI (WVI) and black-box VI (BBVI) perform gradient descent in measure space (Bures-Wasserstein space) and parameter space, respectively. Previously, for the Gaussian variational family, convergence guarantees for WVI have shown superiority over existing results for black-box VI with the reparametrization gradient, suggesting the measure space approach might provide some unique benefits. In this work, however, we close this gap by obtaining identical state-of-the-art iteration complexity guarantees for both. In particular, we identify that WVI's superiority stems from the specific gradient estimator it uses, which BBVI can also leverage with minor modifications. The estimator in question is usually associated with Price's theorem and utilizes second-order information (Hessians) of the target log-density. We will refer to this as Price's gradient. On the flip side, WVI can be made more widely applicable by using the reparametrization gradient, which requires only gradients of the log-density. We empirically demonstrate that the use of Price's gradient is the major source of performance improvement.

stat.ML↗

arXiv2026

LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning

Reinforcement learning has become a central paradigm for improving LLM reasoning, but most existing methods optimize policies over discrete token sequences. This creates a mismatch between the optimization space and the structure of reasoning: many important decisions are semantic, global, and trajectory-level rather than local token choices. Continuous latent-space RL offers a promising alternative by allowing policies to explore higher-level reasoning representations. However, simply moving to latent space is not sufficient. The resulting policy must model a complex, multi-modal distribution over valid reasoning trajectories. We therefore propose Latent Diffusion Reasoning with Reinforcement Learning (LaDi-RL), where a diffusion model generates latent reasoning trajectories through iterative denoising. This formulation enables structured exploration and expressive distribution modeling, but also introduces a fundamental credit-assignment challenge: the policy acts in latent space, while rewards are observed only after the latent is decoded into text. A naive rollout strategy therefore entangles latent reasoning quality with text decoding quality, making it unclear whether an incorrect answer results from a poor latent trajectory or from an imperfect textual realization. To address this, we introduce hierarchical latent-text rollouts. We sample multiple text completions for each latent trajectory and aggregate their rewards to obtain a decoder-marginalized estimate of latent utility. This provides a cleaner and lower-variance reward signal for optimizing the diffusion policy. Empirically, LaDi-RL outperforms token-level RL by 9.4% on code generation and 5.7% on math reasoning in pass@1, and even surpasses the base model's pass@k performance.

cs.LG↗

arXiv2026

Functional-level Uncertainty Quantification for Calibrated Fine-tuning on LLMs

Accurate uncertainty quantification in large language models (LLMs) is essential for reliable confidence estimation, yet fine-tuned LLMs often become overconfident under limited adaptation data. Existing uncertainty methods for PEFT-based LLMs are largely post hoc, estimating uncertainty after fine-tuning rather than improving how adapters specialize to task-specific input-output relationships. We propose Functional-Level Uncertainty Quantification for Calibrated Fine-Tuning (UQ4CT), which calibrates uncertainty over the functional space induced by prompt-dependent mixtures of LoRA experts. UQ4CT implements this perspective through a mixture-of-experts fine-tuning framework, where a calibration loss aligns functional-level confidence with predictive correctness during training. Across four multiple-choice benchmarks and two open-ended generative QA tasks, UQ4CT reduces Expected Calibration Error (ECE) by over $25\%$ while preserving high accuracy. Under distribution shift, UQ4CT maintains superior calibration and competitive accuracy, demonstrating improved reliability and generalization for fine-tuned LLMs.

cs.LG↗

arXiv2026

LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning

Large Language Models (LLMs) demonstrate their reasoning ability through chain-of-thought (CoT) generation. However, LLM's autoregressive decoding may limit the ability to revisit and refine earlier tokens in a holistic manner, which can also lead to inefficient exploration for diverse solutions. In this paper, we propose LaDiR} (Latent Diffusion Reasoner), a novel reasoning framework that unifies the expressiveness of continuous latent representation with the iterative refinement capabilities of latent diffusion models for an existing LLM. We first construct a structured latent reasoning space using a Variational Autoencoder (VAE) that encodes text reasoning steps into blocks of thought tokens, preserving semantic information and interpretability while offering compact but expressive representations. Subsequently, we utilize a latent diffusion model that learns to denoise a block of latent thought tokens with a blockwise bidirectional attention mask, enabling longer horizon and iterative refinement with adaptive test-time compute. This design, combined with explicit diversity guidance during diffusion inference, enables the generation of multiple diverse reasoning trajectories that explore distinct regions of the latent space, rather than producing repetitive solutions as often occurs in standard autoregressive sampling. We conduct evaluations on a suite of mathematical reasoning, code generation and puzzle planning benchmarks. Empirical results show that LaDiR consistently improves accuracy, diversity, and interpretability over existing autoregressive, diffusion-based, and latent reasoning methods, revealing a new paradigm for text reasoning with latent diffusion.

cs.LG↗

arXiv2026

Zephyrus: An Agentic Framework for Weather Science

Foundation models for weather science are pre-trained on vast amounts of structured numerical data and outperform traditional weather forecasting systems. However, these models lack language-based reasoning capabilities, limiting their utility in interactive scientific workflows. Large language models (LLMs) excel at understanding and generating text but cannot reason about high-dimensional meteorological datasets. We bridge this gap by building the first agentic framework for weather science. Our framework includes a Python code-based environment for agents (ZephyrusWorld) to interact with weather data, featuring tools including a WeatherBench 2 dataset indexer, geolocator for geocoding from natural language, weather forecasting, climate simulation capabilities, and a climatology module for querying precomputed climatological statistics (e.g., means, extremes, and quantiles) across multiple timescales. We design Zephyrus, a multi-turn LLM-based weather agent that iteratively analyzes weather datasets, observes results, and refines its approach through conversational feedback loops. We accompany the agent with a new benchmark, ZephyrusBench, with a scalable data generation pipeline that constructs diverse question-answer pairs across weather-related tasks, from basic lookups to advanced forecasting, extreme event detection, and counterfactual reasoning. Experiments on this benchmark demonstrate the strong performance of Zephyrus agents over text-only baselines, outperforming them by up to 44 percentage points in correctness. However, the hard tasks are still difficult even with frontier LLMs, highlighting the challenging nature of our benchmark and suggesting room for future development. Our codebase and benchmark are available at https://github.com/Rose-STL-Lab/Zephyrus.

cs.AI↗

arXiv2026

Divide and Learn: Multi-Objective Combinatorial Optimization at Scale

Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning problem over a decomposed decision space, solving position-wise bandit subproblems via adaptive expert-guided sequential construction. This formulation admits regret bounds of $O(d\sqrt{T \log T})$ depending on subproblem dimensionality $d$ rather than combinatorial space size. On standard benchmarks, our method achieves 80--98\% of specialized solvers performance while achieving two to three orders of magnitude improvement in sample and computational efficiency over Bayesian optimization methods. On real-world hardware-software co-design for AI accelerators with expensive simulations, we outperform competing methods under fixed evaluation budgets. The advantage grows with problem scale and objective count, establishing bandit optimization over decomposed decision spaces as a principled alternative to surrogate modeling or offline training for multi-objective optimization.

cs.LG↗

arXiv2025

Purifying Approximate Differential Privacy with Randomized Post-processing

We propose a framework to convert $(\varepsilon, δ)$-approximate Differential Privacy (DP) mechanisms into $(\varepsilon', 0)$-pure DP mechanisms under certain conditions, a process we call ``purification.'' This algorithmic technique leverages randomized post-processing with calibrated noise to eliminate the $δ$ parameter while achieving near-optimal privacy-utility tradeoff for pure DP. It enables a new design strategy for pure DP algorithms: first run an approximate DP algorithm with certain conditions, and then purify. This approach allows one to leverage techniques such as strong composition and propose-test-release that require $δ>0$ in designing pure-DP methods with $δ=0$. We apply this framework in various settings, including Differentially Private Empirical Risk Minimization (DP-ERM), stability-based release, and query release tasks. To the best of our knowledge, this is the first work with a statistically and computationally efficient reduction from approximate DP to pure DP. Finally, we illustrate the use of this reduction for proving lower bounds under approximate DP constraints with explicit dependence in $δ$, avoiding the sophisticated fingerprinting code construction.

cs.CR↗

arXiv2025

Beyond Length: Quantifying Long-Range Information for Long-Context LLM Pretraining Data

Long-context language models unlock advanced capabilities in reasoning, code generation, and document summarization by leveraging dependencies across extended spans of text. However, a significant portion of readily available long-text data lacks meaningful long-distance dependencies; most spans can be predicted using only local context. Training on such data is inefficient, making careful data selection crucial. Therefore, we introduce LongFilter, a framework for curating training data tailored to long-context pretraining. LongFilter measures the information gain provided by extended context by contrasting model predictions under long-context versus short-context settings, thereby identifying samples where long-range dependencies are essential. Experiments with LLaMA-3-8B, extending its context length from 8K to 64K, show that LongFilter efficiently selects high-quality data and yields substantial improvements on benchmarks such as HELMET, LongBench, and RULER.

cs.CL↗

arXiv2025

Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inference

We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at a rate that is nearly independent of explicit dimension dependence. Specifically, for a $d$-dimensional strongly log-concave and log-smooth target, the number of iterations for BBVI with a sub-Gaussian family to obtain a solution $ε$-close to the global optimum has a dimension dependence of $\mathrm{O}(\log d)$. This is a significant improvement over the $\mathrm{O}(d)$ dependence of full-rank location-scale families. For heavy-tailed families, we prove a weaker $\mathrm{O}(d^{2/k})$ dependence, where $k$ is the number of finite moments of the family. Additionally, if the Hessian of the target log-density is constant, the complexity is free of any explicit dimension dependence. We also prove that our bound on the gradient variance, which is key to our result, cannot be improved using only spectral bounds on the Hessian of the target log-density.

stat.ML↗

arXiv2025

Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has focused on scenarios where feasibility constraints are not given explicitly. Overlooking these constraints can lead to spurious solutions that are unrealistic in practice. To deal with such unknown constraints, we propose to perform optimization within the data manifold using diffusion models. To constrain the optimization process to the data manifold, we reformulate the original optimization problem as a sampling problem from the product of the Boltzmann distribution defined by the objective function and the data distribution learned by the diffusion model. Depending on the differentiability of the objective function, we propose two different sampling methods. For differentiable objectives, we propose a two-stage framework that begins with a guided diffusion process for warm-up, followed by a Langevin dynamics stage for further correction. For non-differentiable objectives, we propose an iterative importance sampling strategy using the diffusion model as the proposal distribution. Comprehensive experiments on a synthetic dataset, six real-world black-box optimization datasets, and a multi-objective molecule optimization dataset show that our method achieves better or comparable performance with previous state-of-the-art baselines.

cs.LG↗

arXiv2025

Learnable Mixed Nash Equilibria are Collectively Rational

We extend the study of learning in games to dynamics that exhibit non-asymptotic stability. We do so through the notion of uniform stability, which is concerned with equilibria of individually utility-seeking dynamics. Perhaps surprisingly, it turns out to be closely connected to economic properties of collective rationality. Up to strategic equivalence, if a mixed equilibrium is uniformly stable, then it is weakly Pareto optimal; there is no way for all players to improve by jointly deviating from the equilibrium. This is a form of collective rationality that rules out the types of behaviors in the prisoner's dilemma or the tragedy of the commons. Moreover, we show that uniform stability determines the last-iterate convergence behavior for the family of incremental smoothed best-response dynamics, used to model individual and corporate behaviors in the markets. Unlike dynamics around strict equilibria, which can stabilize to socially-inefficient solutions, individually utility-seeking behaviors near mixed Nash equilibria lead to collective rationality.

cs.GT↗

arXiv2025

SimulRAG: Simulator-based RAG for Grounding LLMs in Long-form Scientific QA

Large Language Models (LLMs) show promise in generating long-form scientific explanations that synthesize evidence and connect multiple factors. However, in long-form scientific question answering, LLMs often hallucinate, producing unsupported or inconsistent claims. Retrieval-Augmented Generation (RAG) improves trustworthiness by grounding generation in external sources; scientific simulators are valuable because they can validate quantitative hypotheses and capture evolving dynamics. Yet simulation-based RAG is non-trivial due to two challenges: how to retrieve from scientific simulators, and how to efficiently verify and update long-form answers. To overcome these challenges, we propose SimulRAG, a simulator-based RAG framework with a generalized retrieval interface that translates between text and simulator parameters/outputs. SimulRAG further introduces claim-level generation with uncertainty estimation and simulator boundary assessment (UE+SBA) to selectively verify and update claims. Unlike tool-first or holistic answer revision, it first elicits diverse answers without retrieval and then grounds uncertain, simulator-verifiable atomic claims with simulator evidence. We also release a long-form scientific QA benchmark spanning climate science, epidemiology, and urban planning, with ground truth verified by simulations and human annotators. Experiments show SimulRAG improves informativeness by 30.4% and factuality by 16.3% over the strongest adapted RAG baselines, while UE+SBA enhances claim-level efficiency and quality.

cs.CL↗

arXiv2025

Discovering Latent Causal Graphs from Spatiotemporal Data

Many important phenomena in scientific fields like climate, neuroscience, and epidemiology are naturally represented as spatiotemporal gridded data with complex interactions. Inferring causal relationships from these data is a challenging problem compounded by the high dimensionality of such data and the correlations between spatially proximate points. We present SPACY (SPAtiotemporal Causal discoverY), a novel framework based on variational inference, designed to model latent time series and their causal relationships from spatiotemporal data. SPACY alleviates the high-dimensional challenge by discovering causal structures in the latent space. To aggregate spatially proximate, correlated grid points, we use spatial factors, parametrized by spatial kernel functions, to map observational time series to latent representations. Theoretically, we generalize the problem to a continuous spatial domain and establish identifiability when the observations arise from a nonlinear, invertible function of the product of latent series and spatial factors. Using this approach, we avoid assumptions that are often unverifiable, including those about instantaneous effects or sufficient variability. Empirically, SPACY outperforms state-of-the-art baselines on synthetic data, even in challenging settings where existing methods struggle, while remaining scalable for large grids. SPACY also identifies key known phenomena from real-world climate data. An implementation of SPACY is available at https://github.com/Rose-STL-Lab/SPACY/

cs.LG↗

arXiv2025

Learning to Steer Learners in Games

We consider the problem of learning to exploit learning algorithms through repeated interactions in games. Specifically, we focus on the case of repeated two player, finite-action games, in which an optimizer aims to steer a no-regret learner to a Stackelberg equilibrium without knowledge of its payoffs. We first show that this is impossible if the optimizer only knows that the learner is using an algorithm from the general class of no-regret algorithms. This suggests that the optimizer requires more information about the learner's objectives or algorithm to successfully exploit them. Building on this intuition, we reduce the problem for the optimizer to that of recovering the learner's payoff structure. We demonstrate the effectiveness of this approach if the learner's algorithm is drawn from a smaller class by analyzing two examples: one where the learner uses an ascent algorithm, and another where the learner uses stochastic mirror ascent with known regularizer and step sizes.

cs.GT↗

arXiv2025

Demystifying SGD with Doubly Stochastic Gradients

Optimization objectives in the form of a sum of intractable expectations are rising in importance (e.g., diffusion models, variational autoencoders, and many more), a setting also known as "finite sum with infinite data." For these problems, a popular strategy is to employ SGD with doubly stochastic gradients (doubly SGD): the expectations are estimated using the gradient estimator of each component, while the sum is estimated by subsampling over these estimators. Despite its popularity, little is known about the convergence properties of doubly SGD, except under strong assumptions such as bounded variance. In this work, we establish the convergence of doubly SGD with independent minibatching and random reshuffling under general conditions, which encompasses dependent component gradient estimators. In particular, for dependent estimators, our analysis allows fined-grained analysis of the effect correlations. As a result, under a per-iteration computational budget of $b \times m$, where $b$ is the minibatch size and $m$ is the number of Monte Carlo samples, our analysis suggests where one should invest most of the budget in general. Furthermore, we prove that random reshuffling (RR) improves the complexity dependence on the subsampling noise.

stat.ML↗

arXiv2025

A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery

Real-world data often violates the equal-variance assumption (homoscedasticity), making it essential to account for heteroscedastic noise in causal discovery. In this work, we explore heteroscedastic symmetric noise models (HSNMs), where the effect $Y$ is modeled as $Y = f(X) + σ(X)N$, with $X$ as the cause and $N$ as independent noise following a symmetric distribution. We introduce a novel criterion for identifying HSNMs based on the skewness of the score (i.e., the gradient of the log density) of the data distribution. This criterion establishes a computationally tractable measurement that is zero in the causal direction but nonzero in the anticausal direction, enabling the causal direction discovery. We extend this skewness-based criterion to the multivariate setting and propose SkewScore, an algorithm that handles heteroscedastic noise without requiring the extraction of exogenous noise. We also conduct a case study on the robustness of SkewScore in a bivariate model with a latent confounder, providing theoretical insights into its performance. Empirical studies further validate the effectiveness of the proposed method.

cs.LG↗

arXiv2025

Diffusion-BBO: Diffusion-Based Inverse Modeling for Online Black-Box Optimization

Online black-box optimization (BBO) aims to optimize an objective function by iteratively querying a black-box oracle in a sample-efficient way. While prior studies focus on forward approaches such as Gaussian Processes (GPs) to learn a surrogate model for the unknown objective function, they struggle with steering clear of out-of-distribution and invalid designs in scientific discovery tasks. Recently, inverse modeling approaches that map the objective space to the design space with conditional diffusion models have demonstrated impressive capability in learning the data manifold. However, these approaches proceed in an offline fashion with pre-collected data. How to design inverse approaches for online BBO to actively query new data and improve the sample efficiency remains an open question. In this work, we propose Diffusion-BBO, a sample-efficient online BBO framework leveraging the conditional diffusion model as the inverse surrogate model. Diffusion-BBO employs a novel acquisition function Uncertainty-aware Exploration (UaE) to propose scores in the objective space for conditional sampling. We theoretically prove that Diffusion-BBO with UaE achieves a near-optimal solution for online BBO. We also empirically demonstrate that Diffusion-BBO with UaE outperforms existing online BBO baselines across 6 scientific discovery tasks.

cs.LG↗