Momentum is a pillar of modern optimization, yet its benefits in reinforcement learning with verifiable rewards (RLVR) remain unclear. This paper studies a KL-regularized bandit formulation of RLVR and proves that, with exact policy gradients, larger EMA coefficients strictly accelerate convergence within a safe overshoot-free range. Its central insight is that stochastic sampling obscures this gain unless the coefficient scales with the learning rate so that $\eta/(1-\beta)$ stays constant, a principle validated in bandits and in LLM post-training on Qwen models.

Reinforcement learning with verifiable rewards suffers from coarse scalar supervision and moving-target instability in self-distillation. FSPO eliminates the persistent teacher model by storing sparse historical next-token distributions as fixed function-space targets, combining them with privileged disagreement correction and reliability-adaptive grounding. Across scientific reasoning and tool-use benchmarks, it achieves roughly 4% higher average accuracy than SDPO under a 5-hour budget while cutting peak memory from about 70 GB to 56 GB on Olmo3-7B-Instruct.

This paper claims the first global joint lower bound for zeroth-order nonconvex optimization under unrestricted spatial queries and sample reuse. The core idea is to force any algorithm to advance through $T\asymp\min\{\Delta H,L_0^2\}/\epsilon^2$ hidden geometric stages and to prove that each fresh stage requires $\Omega(dL_0^2/\epsilon^2)$ adaptive scalar evaluations, yielding an overall $\Omega(dL_0^2\min\{\Delta H,L_0^2\}/\epsilon^4)$ bound. If correct, this would settle the open problem posed by Kornowski and Shamir (2024), though the manuscript is dated 14 October 2026, cites several future works, and explicitly states that its mathematics was primarily AI-generated.

In medical and crowdsourced annotation, the absence of clean ground truth biases standard expected calibration error (ECE) evaluation because annotator errors confound predictor miscalibration. This paper proposes Noise Corrected ECE (NC-ECE), which inverts annotator-specific class-conditional noise channels to recover clean-label ECE, and provides methods to estimate those channels from repeated annotations alone. It then derives post-hoc recalibration algorithms with either clean-risk or calibration guarantees. The work is directly motivated by settings such as medical imaging, where expert disagreement is common and reliable uncertainty assessment is essential.

Density functional theory (DFT) is accurate but expensive, while pretrained machine-learned interatomic potentials (MLIPs) are fast yet erratically wrong across configurations. This paper frames the decision of when to trust an MLIP and when to fall back to DFT as a risk-controlled selection problem solved with conformal risk control (CRC). A lightweight, chemistry-informed descriptor feeds a small neural network that estimates MLIP-DFT disagreement in energy and forces; CRC then calibrates a threshold so the expected retained error stays below a user-chosen fraction $\alpha$ of the fitting-set mean. The method cuts DFT costs—by 7–14% at $\alpha=0.3$ versus committee baselines—without requiring access to the target MLIP's internals, which matters for practitioners who want certified savings on a fixed, pretrained model.

Feel-Good Thompson Sampling (FGTS) addresses slow exploration in vanilla TS by adding an optimism term to the posterior. This paper proves the first high-probability regret bounds for both cumulative and current-step FGTS under general realizable function approximation, showing that in linear contextual bandits the regret scales as $O(d\sqrt{T}\log(2T)+\sqrt{T}\log(1/\delta))$ with probability at least $1-\delta$. The core technique is applying Markov's inequality to exponential quantities derived from the posterior normalizer, avoiding explicit confidence-set constructions.

This paper tackles measurement-constrained linear regression, where responses are expensive to collect and must be selected from a large candidate pool before being observed. The authors propose Expected Loss Optimal Selection (ELOS), which derives an A-optimality-type criterion that depends only on covariates and remains valid under potential model misspecification. The core insight is that averaging the expected prediction loss over uniformly random misspecification directions recovers the same trace-inverse criterion as under a correctly specified model, yielding a principled response-free selection rule.

Sequential conformal prediction struggles when the recent past is irrelevant and similar predictive states recur at nonadjacent times. This paper proposes State-Matched Sequence Conformal Prediction (SMSCP), which constructs an interpretable local-linear pre-target state and uses Mahalanobis similarity to select past calibration scores for ordinary conformal cutoff estimation. The work matters because it replaces fragile recency assumptions with an explicit state-matching mechanism, offering both modular implementation and a quantile-targeted theory that isolates when state matching helps and when it fails.

This paper addresses non-parametric estimation of the background intensity in Hawkes and ETAS models by treating the background as an unknown finite positive measure with a regular density. The core idea is to derive a distribution-valued Wasserstein-Fisher-Rao (WFR) gradient from the Hawkes likelihood and then project it onto finite-dimensional statistical manifolds, yielding an explicit finite-dimensional ODE system. This avoids spatial discretization and is motivated by seismic applications, though the practical algorithmic and statistical guarantees remain partially conditional.

Random reshuffling (RR) is the de facto standard for training machine learning models, yet theory has long lagged practice for last-iterate convergence. Existing guarantees required stepsizes as small as $1/(nL)$, while averaged-iterate analyses allowed $1/L$. Chen and Zhang close this gap for smooth convex objectives, proving that the last iterate of RR-SGD converges with stepsizes up to $1/(L(1+\log(nK)))$---removing the explicit $1/n$ barrier at the cost of only logarithmic factors. The result matters because practitioners return the final parameter, not an average, and large constant stepsizes are common in deep learning.

Bayesian posterior sampling offers a potentially 'free' source of differential privacy, but existing guarantees are fragmented and often require strong boundedness assumptions. This paper develops a unified Rényi-divergence framework that characterizes the inherent privacy loss of One-Posterior-Sampling (OPS) through exponential moments of the single-record log-likelihood ratio. The results yield exact, tighter bounds for a broader class of models and clarify how prior strength, sample size, and neighboring relations jointly shape privacy.

The paper tackles sampling from Gibbs distributions on matrix spaces with potentials that are neither convex nor globally gradient-Lipschitz. Its core idea is to replace the quadratic kinetic energy of underdamped Langevin dynamics with a non-quadratic, relativistic-like energy $K_\delta(p)=\delta^{-1}\operatorname{Tr}[(I_n+\delta pp^\top)^{1/2}-I_n]$, whose gradient tames momentum singular values smoothly. By carefully coupling a momentum-dependent diffusion matrix $M_\delta(p)$ and its divergence correction $\Gamma_\delta(p)$, the authors preserve the exact target Gibbs measure, recover regularised Muon in the zero-temperature limit, and prove exponential convergence of the diffusion plus uniform-in-time moment bounds for an explicit Euler-Maruyama scheme.

Contextual linear optimization faces a discontinuity: small prediction errors can flip the LP solution to a different vertex, making regret non-differentiable pointwise. This paper proves that, after averaging over the data distribution, the population regret is locally quadratic with curvature concentrated on the walls of the normal fan. The authors derive the exact curvature measure $K_0$, provide a tractable single-projection approximation $\mathsf{K}_{\lambda,s}$, and apply it to scenario generation, showing a $30.8\%$ regret reduction on a battery arbitrage task.

Comparing high-dimensional discrete distributions is notoriously difficult because the state space grows exponentially and differences can hide in complex joint dependencies. This paper introduces Zero Flux, a flow-based discrepancy that extends the continuous Zero Flow criterion to discrete state spaces. The core idea is to construct a discrete bridge between two distributions via coordinate-wise independent coupling, measure local probability fluxes at the midpoint, and show that all fluxes vanish if and only if the distributions are identical. This yields a decomposable, sample-based discrepancy with finite-sample guarantees, offering both a global comparison score and interpretable coordinate-wise contributions.

IQS-BO tackles the per-iteration cost of Bayesian optimisation by replacing surrogate fitting and acquisition-function maximisation with a single transformer forward pass. The core idea is to cast query selection as supervised classification: given a finite candidate set, the model predicts which candidate maximises the objective, trained with cross-entropy on synthetic priors where the true best candidate is known for free. The method can run fully in-context or on top of a fixed surrogate, and it introduces a mixture prior of GP and non-stationary functions to improve optimisation performance.

Policy-gradient methods suffer from high variance, while pathwise actor updates require accurate action derivatives that standard value-function training does not guarantee. FERPO addresses this by deriving an entropy- and KL-regularized target action distribution from critic values alone, then fitting the policy with forward KL via self-normalized importance sampling---never differentiating the critic with respect to actions. The method targets massively parallel on-policy robot learning, where reliable policy improvement is critical for both sample and wall-clock efficiency.

This paper studies gradient descent with a large constant stepsize on linearly separable logistic regression, a canonical model for the Edge of Stability phenomenon. It proves that the worst-case exact transition time from oscillatory loss to monotone decrease scales as $\Theta((\log \eta)^{\min\{n-2,d-2\}})$ uniformly over dimension $d \ge 2$, disproving a conjecture that stepsize independence holds beyond $d=2$. The result translates into substantially stronger finite-horizon optimization guarantees by permitting exponentially larger constant stepsizes than prior $O(\eta)$ transient bounds.

Many recent sampling algorithms built on Wasserstein gradient flows (WGF) and forward-only diffusion processes (FODP) come with exponential-convergence guarantees that are often read as proof of fast practical mixing. This paper argues that guarantee is misleading: the canonical KL-induced WGF and overdamped forward diffusion produce the same marginal Fokker--Planck evolution, so they inherit the same metastability and exponentially slow inter-mode transport known in statistical physics. Using spectral-gap and mean-first-passage-time analysis on multimodal targets, the authors show that well-separated modes induce mixing times that scale exponentially with barrier height, and that standard log-linear annealing does not remove this scaling. The conclusion is that purely local, gradient-driven sampling is structurally limited for multimodal distributions, motivating nonlocal transport mechanisms.

Many applications require sampling from high-dimensional categorical distributions with local dependence, but discrete diffusion models lack end-to-end statistical guarantees. This paper introduces a pinning decomposition of the discrete score under uniform noising, showing that time dependence separates multiplicatively from target dependence for Markov random fields of order $d$. Building on this, the authors design a weight-sharing neural score learner and prove a sample-complexity rate of $\widetilde O_{\mathbb P}(S^d/n)$, replacing the ambient dimension $D$ with the interaction order $d$.

This paper studies fixed-confidence best-arm identification for Bernoulli bandits using the top-two $\beta$-EB-TCI rule, where the challenger is selected by a penalized Bernoulli GLR index. Its core contribution is a sharp non-asymptotic analysis: once the true best arm becomes the permanent leader and its sampling fraction stays near $\beta$, the stopping time is $T_\beta^\star(\mu)\log(1/\delta)$ up to lower-order terms. The paper also identifies exactly where the analysis stalls for the unguarded rule when suboptimal means are tied, and closes the gap with a mild $O(\sqrt{Kt})$ exploration guard.