arXiv subjects

Sen Na

Publications and source records attributed to Sen Na.

At least 19 recordsLinked to original sources

arXiv2026

Online Covariance Estimation for Averaged Stochastic Gradient Descent on Riemannian Manifolds

We study online inference for averaged Riemannian stochastic gradient descent (RSGD) when the unknown parameter lies on a manifold. Although the averaged RSGD iterate is asymptotically normal, practical inference requires estimating the unknown covariance operator in its limiting distribution. Existing online batch-means methods cannot be applied directly because a general Riemannian manifold lacks an addition operation, and the tangent space containing the Riemannian gradient varies across iterations. Through vector transport, we construct overlapping and non-overlapping covariance estimators that adaptively combine information from successive batches while accounting for the changing tangent spaces. The proposed estimators are online, require neither Riemannian Hessian computations nor a prespecified terminal sample size, and attain the same convergence rates as their Euclidean counterparts (Zhu et al., 2023). Together with asymptotic normality, these estimators enable online statistical inference for RSGD on manifolds. We illustrate the proposed framework through a detailed study of streaming principal component analysis on Grassmann manifolds.

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arXiv2026

LatentPress: Context Compression Beyond Text and Vision

Compressed context is usually carried as human-readable text or as rendered images that must be decoded, even when its consumer is a language model. We introduce LatentPress, which writes conversational histories and long documents into a third representation: continuous memory tokens that a frozen decoder reads directly through its input-embedding interface, with no text reconstruction at inference. A small reader-matched writer compresses $4$-$16\times$ while training only an adapter (4.2M-26.2M parameters, $\sim\!0.1\%$ of the decoder). On LongMemEval, LatentPress reaches $0.504$ accuracy at $7.70\times$ compression versus $0.490$ for uncompressed evidence, outperforming text summaries (0.184) and OCR-based compression (0.426 to 0.312). On LongBench-QA, in-domain writers match or exceed raw-context reading at $4$-$8\times$ compression, while $16\times$ trails raw. Writing takes 43ms per conversation, roughly an order of magnitude faster than text summarization or OCR reconstruction, and reading is $5$-$9\times$ faster than raw context or cached OCR. We validate the interface under two transfer settings, zero-shot from UltraChat to LongMemEval memory QA and from LongMemEval-derived QA to unseen LongBench document domains, establishing direct soft tokens as a practical machine-facing context interface beyond text and vision. The implementation of the experiments could be found at: https://github.com/HJSang/LatentPress.

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arXiv2026

SHARPO: Segment-Level Credit Assignment for Agentic Reinforcement Learning

Agentic reinforcement learning (RL) trains a large language model (LLM) to act over long, multi-step interactions. However, a single localized error can cause task failure, while trajectory-level rewards provide limited guidance for assigning credit to individual decisions. To address this limitation, we introduce Segment-level Hindsight Advantage Reweighting for Policy Optimization (SHARPO), a credit-assignment mechanism that refines Group Relative Policy Optimization (GRPO) at the level of environment-facing segments. Inspired by the existing on-policy self-distillation (OPSD) method, SHARPO computes teacher-student log-probability gaps within each segment and uses the resulting signal to compute a bounded multiplier on the GRPO advantage. This multiplier is shared by all tokens within the segment, allowing credit to vary across different segments. With Qwen2.5-7B-Instruct, SHARPO outperforms existing baselines on the ALFWorld and WebShop benchmarks, including GRPO, SDAR, RLSD, and StepOPSD.

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arXiv2026

An Adaptive, Parallel, and Inexact Newton Method for Large-scale Nonlinear Optimal Control

We design adaptive overlapping temporal decomposition (AOTD), a parallel sequential quadratic programming (SQP) method for long-horizon nonlinear optimal control problems (OCPs). As designed, AOTD is the first overlapping temporal decomposition (OTD) algorithm that adapts the overlap size online, eliminating the need to fix a suitable overlap a priori. Specifically, at each iteration, it partitions the long horizon into overlapping nonlinear subproblems, performs one SQP step on each in parallel, and adaptively selects both the overlap size and the accuracy to which the resulting local KKT systems are solved. Two conditions govern the accepted step: an adaptive residual condition bounding the distance from the concatenated inexact direction to the exact Newton direction of the full problem, and a descent condition on the adaptive penalty parameters that certifies descent for a carefully chosen exact augmented Lagrangian. The residual condition is solver independent and accommodates both deterministic iterative solvers and randomized sketching solvers. Under standard regularity assumptions, we prove that the KKT residual converges to zero from any initialization and establish a local linear rate for sequences converging to a strict local minimizer. We validate AOTD on a power-system frequency regulation OCP and a Burgers PDE OCP, attaining a reduction in estimated FLOPs of approximately $2.5\times$ to the best fixed-overlap variant while converging across multiple horizon lengths with a single parameter setting.

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arXiv2026

REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models

Deep ReLU networks are piecewise-affine mappings that partition the input space into cells, each characterized by a distinct activation pattern. This structure motivates fitting a local linear model within each cell to preserve predictive accuracy while improving interpretability. The challenge is to identify regimes that are stable, data-adaptive, and easy to explain. We propose REALM, a mixture of linear models whose regimes are induced by neural activation patterns. Because the number of activation cells in a deep neural network (DNN) can grow rapidly with depth, we first distill a deep teacher into a wide, shallow student network (WSSN), then binarize and cluster its hidden-layer activations to define the regimes and fit a linear model within each regime. Since the regimes are discovered from internal structure, the router does not carry the predictive burden. To make regime assignment interpretable, we train a multiclass logistic regression, the explanatory gate, to reproduce the regime assignments. The two-level structure is interpretable at both stages in terms of raw tabular or learned convolutional features: the gate identifies features that determine regime assignments, while the linear models identify features that drive predictions within each regime. We analyze an idealized setting that illustrates a trade-off between partition complexity and stability: as the number of regimes grows, finer partitions can improve approximation but may reduce regime-assignment stability. Experiments on tabular and image datasets show that REALM achieves competitive predictive performance relative to other DNN-guided mixture surrogates and inherently interpretable models while producing stable regime-level explanations.

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arXiv2026

TR-SSQP: A Trust-Region Method for Constrained Stochastic Optimization under Heavy-Tailed Noise

We consider stochastic nonlinear optimization problems with deterministic equality constraints. While unconstrained stochastic optimization is well understood, the interplay between optimality and feasibility in the constrained setting poses significant challenges. Moreover, existing theoretical guarantees for constrained stochastic methods predominantly rely on bounded-variance assumptions, leaving the heavy-tailed noise regime largely unexplored. To address this gap, we propose a novel trust-region method within the stochastic sequential quadratic programming framework, termed TR-SSQP. Our method employs a normal-tangential decomposition in the step computation to balance optimality and feasibility. In addition, we incorporate a normalization mechanism in the design of the trust-region radius, together with Polyak momentum for gradient estimation, ensuring stable updates without gradient clipping. When the trust-region radius and the momentum parameter decay at appropriate rates, we establish global almost-sure convergence of the method. To the best of our knowledge, this is the first asymptotic convergence result for constrained stochastic optimization under heavy-tailed noise. We demonstrate the promising performance of the proposed method through extensive numerical experiments, including comparisons among its variants and with existing constrained stochastic optimization methods.

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arXiv2026

Overlapping Schwarz Scheme for Linear-Quadratic Programs in Continuous Time

We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz decomposition based on the Pontryagin Minimum Principle, partitioning the temporal domain into overlapping intervals and independently solving Hamiltonian systems in continuous time. We demonstrate that the convergence is ensured by appropriately updating the boundary conditions of the individual Hamiltonian dynamics. The cornerstone of our analysis is to prove that the exponential decay of sensitivity (EDS) exhibited in discrete-time OCPs carries over to the continuous-time setting. Unlike the discretize-then-optimize approach, our method can flexibly incorporate different numerical integration methods for solving the resulting Hamiltonian two-point boundary-value subproblems, including adaptive-time integrators. A numerical experiment on a linear-quadratic OCP illustrates the practicality of our approach in broad scientific applications.

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arXiv2026

Inference for Newton Methods with Accelerated Sketch-and-Project via Random Scaling

We study an online sketched Newton method that approximates the Newton direction at each step via a state-of-the-art sketching solver, called the generalized accelerated sketch-and-project solver (GAS), thereby mitigating the computational bottleneck of classical second-order methods. The GAS solver improves upon vanilla, unaccelerated sketch-and-project solvers by achieving accelerated convergence through Nesterov momentum updates, and accommodates a flexible projection metric whose proper choice further reduces computational cost. Building on this design, we establish asymptotic normality of the averaged sketched Newton iterates and characterize their limiting covariance matrix. The resulting covariance recovers that of the unaccelerated sketched Newton method under a specific choice of acceleration parameters, converges more rapidly (in the number of sketching steps) to the minimax-optimal covariance in general, and is smaller than that of the last iterate produced by the accelerated method. Finally, we strengthen these results by establishing a functional central limit theorem for the Newton iterates, which allows us to bypass explicit covariance estimation and develop an online inference procedure based on random scaling. Specifically, we construct a pivotal test statistic by appropriately rescaling the averaged iterates, so that its limiting distribution is free of any unknown parameters, enabling asymptotically valid online inference. Numerical experiments demonstrate superior performance of the proposed inference procedure.

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arXiv2026

TRIAGE: Role-Typed Credit Assignment for Agentic Reinforcement Learning

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that the Bayes-optimal role-measurable correction is the L2 projection of the per-segment advantage residual onto the role variable, and that TRIAGE's fixed role constants approximate this projection, reducing advantage estimation error whenever the judge is reliable; we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional $10.4\%$ and $14.8\%$ relative to GRPO.

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arXiv2026

TREK: Distill to Explore, Reinforce to Refine

Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-$r$ proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.

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arXiv2026

Kwai Keye-VL-2.0 Technical Report

We introduce Kwai Keye-VL-2.0-30B-A3B, an open-source Mixture-of-Experts (MoE) multimodal foundation model designed to advance long-video understanding and agentic intelligence. To address the challenges of ultra-long contexts, information redundancy, and prohibitive computational costs inherent in hour-level videos, Keye-VL-2.0 is the first to adapt DeepSeek Sparse Attention (DSA) to GQA-based multimodal architectures, enabling lossless 256K context processing while capturing critical frames and long-range temporal dependencies. This architecture is underpinned by a highly optimized training and inference infrastructure, including scalable video I/O, heterogeneous ViT-LM parallelism, and custom DSA kernels that significantly maximize throughput and minimize computational overhead. Furthermore, to overcome the algorithmic dilemma of catastrophic forgetting during multi-task alignment, we introduce Cross-Modal Multi-Teacher On-Policy Distillation (MOPD) paired with Context-RL and Video-RL. By distilling dense token-level teacher feedback from on-policy rollouts back into the MoE backbone, which activates only 3B parameters, Keye-VL-2.0 natively empowers advanced agent collaboration across Code, Tool, and Search scenarios with multimodal self-correction. Extensive evaluations across video understanding, temporal grounding, reasoning, STEM, and agent benchmarks demonstrate that Keye-VL-2.0-30B-A3B achieves state-of-the-art performance among models of similar scale, particularly excelling in fine-grained temporal localization on TimeLens and long-video comprehension on Video-MME-v2 and LongVideoBench. We release our model checkpoints to accelerate community progress toward scalable and robust multimodal agentic applications.

cs.CV↗

arXiv2026

Inference of Online Newton Methods with Nesterov's Accelerated Sketching

Reliable decision-making with streaming data requires principled uncertainty quantification of online methods. While first-order methods enable efficient iterate updates, their inference procedures still require updating proper (covariance) matrices, incurring $O(d^2)$ time and memory complexity, and are sensitive to ill-conditioning and noise heterogeneity of the problem. This costly inference task offers an opportunity for more robust second-order methods, which are, however, bottlenecked by solving Newton systems with $O(d^3)$ complexity. In this paper, we address this gap by studying an online Newton method with Hessian averaging, where the Newton direction at each step is approximately computed using a sketch-and-project solver with Nesterov's acceleration, matching $O(d^2)$ complexity of first-order methods. For the proposed method, we quantify its uncertainty arising from both random data and randomized computation. Under standard smoothness and moment conditions, we establish global almost-sure convergence, prove asymptotic normality of the last iterate with a limiting covariance characterized by a Lyapunov equation, and develop a fully online covariance estimator with non-asymptotic convergence guarantees. We also connect the resulting uncertainty quantification to that of exact and sketched Newton methods without Nesterov's acceleration. Extensive experiments on regression models demonstrate the superiority of the proposed method for online inference.

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arXiv2026

Parallel Sequential Quadratic Programming with Overlapping Graph Decomposition and Exact Augmented Lagrangian

In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and depend on the variables of adjacent nodes. This graph-structured formulation encompasses various specific instances, such as dynamic optimization, PDE-constrained optimization, multi-stage stochastic optimization, and general network optimization. By leveraging the sequential quadratic programming (SQP) framework, we propose a globally convergent overlapping graph decomposition method to solve large-scale gsNLPs under standard mild regularity conditions on the graph topology. In each iteration, we perform an overlapping graph decomposition to compute an approximate Newton direction in a parallel environment. Then, we select a suitable stepsize and update the primal-dual iterate by performing a backtracking line search on an exact augmented Lagrangian merit function. Built on the exponential decay of sensitivity of gsNLPs, we show that the approximate Newton direction is a descent direction of the augmented Lagrangian, which leads to global convergence with local linear convergence rate. In particular, global convergence is achieved for sufficiently large overlaps, and the local linear convergence rate improves exponentially in terms of the overlap size. Our results match existing state-of-the-art guarantees established for dynamic programs (which simply correspond to linear graphs). We validate the theory on two PDE-constrained problems: a semilinear elliptic problem and a boundary heating problem.

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arXiv2026

Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition

Most first-order optimizers treat matrix-valued parameters as vectors, ignoring the intrinsic geometry of hidden-layer weights in neural networks. Muon addresses this mismatch by updating along the polar factor of a momentum matrix, but its theoretical understanding has lagged behind practice. In particular, practical implementations incorporate Nesterov momentum, compute the polar factor only approximately, and operate with stochastic gradients that may be heavy-tailed. We close this gap by developing a convergence theory for Muon with Nesterov momentum and inexact polar decomposition in non-convex matrix optimization under heavy-tailed noise. Our analysis builds on a unified framework for inexact polar decomposition that captures practical iterative approximations such as Newton-Schulz and quantifies how their errors propagate through the optimization dynamics. Under this framework, we establish an optimal iteration and sample complexity of $O \left(\varepsilon^{\frac{-(3α-2)}{(α-1)}} \right)$ for finding an $\varepsilon$-stationary point, where $α\in(1,2]$ denotes the heavy-tail index. For the inexact-polar setting with $σ_1=0$, we also provide guarantees that do not require prior knowledge of $α$. We analyze a randomized low-rank polar decomposition that is substantially more efficient than full-space methods while remaining compatible with our theory. Numerical experiments further demonstrate the effectiveness of the proposed inexact and randomized variants.

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arXiv2026

Online Covariance Matrix Estimation in Sketched Newton Methods

Given the ubiquity of streaming data, online algorithms have been widely used for parameter estimation, with second-order methods particularly standing out for their efficiency and robustness. In this paper, we study an online sketched Newton method that leverages a randomized sketching technique to perform an approximate Newton step in each iteration, thereby eliminating the computational bottleneck of second-order methods. While existing studies have established the asymptotic normality of sketched Newton methods, a consistent estimator of the limiting covariance matrix remains an open problem. We propose a fully online covariance matrix estimator that is constructed entirely from the Newton iterates and requires no matrix factorization. Compared to covariance estimators for first-order online methods, our estimator for second-order methods is batch-free. We establish the consistency and convergence rate of our estimator, and coupled with asymptotic normality results, we can then perform online statistical inference for the model parameters based on sketched Newton methods. We also discuss the extension of our estimator to constrained problems, and demonstrate its superior performance on regression problems as well as benchmark problems in the CUTEst set.

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arXiv2026

High Probability Complexity Bounds of Trust-Region Stochastic Sequential Quadratic Programming with Heavy-Tailed Noise

In this paper, we consider nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method and establish its high-probability iteration complexity bounds for identifying first- and second-order $ε$-stationary points. In our algorithm, we assume that exact objective values, gradients, and Hessians are not directly accessible but can be estimated via zeroth-, first-, and second-order probabilistic oracles. Compared to existing complexity studies of SSQP methods that rely on a zeroth-order oracle with sub-exponential tail noise (i.e., light-tailed) and focus mostly on first-order stationarity, our analysis accommodates biased (also referred to as irreducible in the literature) and heavy-tailed noise in the zeroth-order oracle, and significantly extends the analysis to second-order stationarity. We show that under heavy-tailed noise conditions, our SSQP method achieves the same high-probability first-order iteration complexity bounds as in the light-tailed noise setting, while further exhibiting promising second-order iteration complexity bounds. Specifically, the method identifies a first-order $ε$-stationary point in $\mathcal{O}(ε^{-2})$ iterations and a second-order $ε$-stationary point in $\mathcal{O}(ε^{-3})$ iterations with high probability, provided that $ε$ is lower bounded by a constant determined by the bias magnitude (i.e., the irreducible noise) in the estimation. We validate our theoretical findings and evaluate practical performance of our method on CUTEst benchmark test set.

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arXiv2026

A Trust-Region Interior-Point Stochastic Sequential Quadratic Programming Method

In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality constraints. In this setting, exact evaluations of the objective function and its gradient are unavailable, but their stochastic estimates can be constructed. In particular, at each iteration our method builds stochastic oracles, which estimate the objective value and gradient to satisfy proper adaptive accuracy conditions with a fixed probability. To handle inequality constraints, we adopt an interior-point method (IPM), in which the barrier parameter follows a prescribed decaying sequence. Under standard assumptions, we establish global almost-sure convergence of the proposed method to first-order stationary points. We implement the method on a subset of problems from the CUTEst test set, as well as on logistic regression problems, to demonstrate its practical performance.

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arXiv2025

Online Inference of Constrained Optimization: Primal-Dual Optimality and Sequential Quadratic Programming

We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation, physics-informed models, safe reinforcement learning, and algorithmic fairness. We develop a stochastic sequential quadratic programming (SSQP) method to solve these problems, where the step direction is computed by sequentially performing a quadratic approximation of the objective and a linear approximation of the constraints. Despite having access to unbiased estimates of population gradients, a key challenge in constrained stochastic problems lies in dealing with the bias in the step direction. As such, we apply a momentum-style gradient moving-average technique within SSQP to debias the step. We show that our method achieves global almost-sure convergence and exhibits local asymptotic normality with an optimal primal-dual limiting covariance matrix in the sense of Hájek and Le Cam. In addition, we provide a plug-in covariance matrix estimator for practical inference. To our knowledge, the proposed SSQP method is the first fully online method that attains primal-dual asymptotic minimax optimality without relying on projection operators onto the constraint set, which are generally intractable for nonlinear problems. Through extensive experiments on benchmark nonlinear problems, as well as on constrained generalized linear models and portfolio allocation problems using both synthetic and real data, we demonstrate superior performance of our method, showing that the method and its asymptotic behavior not only solve constrained stochastic problems efficiently but also provide valid and practical online inference in real-world applications.

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