Agentic reinforcement learning (RL) enables LLM agents to improve continuously from environment rewards, yet the resulting policies do not systematically accumulate reusable strategies that generalize across tasks. Modular skills can provide such reusable strategies, yet existing skill-augmented RL methods decouple skill creation from policy optimization, risking adopting skills that conflict with the evolving policy. Inspired by Anthropic's Skill Creator, we introduce RESKILL, an RL-in-the-loop skill creation framework that reconciles skill evolution with policy learning. RESKILL exploits the group-wise structure of GRPO to naturally embed three mechanisms with only marginal additional overhead: (1) an assertion-driven skill creator that diagnoses failures from past experience and proposes conditional, trigger-based skill revisions; (2) within-group rollout sampling that enables controlled comparison of skill versions, capturing which version best supports the policy's ongoing learning; and (3) Thompson Sampling with adaptive discounting to balance exploration and exploitation in skill version selection as the policy evolves. Across several domains, RESKILL consistently outperforms existing memory and skill-based RL methods, with the largest gains on unseen tasks. Analysis of the skill lifecycle shows skills being automatically created, tested, refined, and pruned as the policy improves, demonstrating reconciled skill-policy co-evolution.

Reinforcement Learning from Human Feedback via Proximal Policy Optimization often suffers from policy mode collapse, brittle exploration loops, and distribution drift. This paper introduces Variational Proximal Policy Optimization (\(\textsc{VP}_2\textsc{O}\)), a particle-based variational inference framework that maps policy optimization to Stein Variational Gradient Descent within a Mixture-of-Experts architecture. By leveraging functional kernels over localized expert prototypes alongside an expert orthogonalization loss, \(\textsc{VP}_2\textsc{O}\) introduces a geometry-based proximal-control mechanism that can reduce reliance on fixed clipping or KL schedules. Our results on a 33B/4B sparse Mixture-of-Experts model show several improvements across complex reasoning benchmarks, establishing a \(+\mathbf{179}\) ELO gain on Codeforces and a \(\mathbf{32\%}\) reduction in token count on AIME mathematical reasoning tasks.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear. We study hidden-state stability through \emph{backward coherence}: the extent to which $h_t$ can be reconstructed from $h_{t+1}$ by a learned backward projector $g_ϕ$. Under contraction and summable backward drift, the hidden-state sequence forms a quasi-reverse-martingale. This yields almost-sure convergence, rates under mixing, an interpretable limiting representation, finite pathwise stopping times, and a theoretical framework for time-uniform confidence sequences. Simulations support the theory. Backward-coherence regularisation reduces the empirical quasi-martingale total $\hat Q$ by $43$--$58%$, reaches stability $28$--$44%$ earlier than an unregularised RNN, and gives tracking-error recovery consistent with geometric bounds. Additional tests confirm echo-state forgetting rates bounded by $ρ$ and verify the increment-sum tube $R_t$ with $100%$ simultaneous coverage, although $R_t$ is conservative; in practice, the defect-tail proxy $\hat Q_t$ is the more useful monitor. The backward-coherence loss is also equivalent to minimising a Kullback--Leibler divergence in a Gaussian backward model, linking the method to variational inference. Extensions cover $ϕ$-mixing inputs, change-point tracking, and finite-sample concentration. Three real-data studies further validate the approach. On PhysioNet 2012 ICU data, the Reverse Martingale RNN (RMRNN) matches RNN mortality-prediction AUC while reaching stable representations 13 hours earlier. On FRED-MD, it reduces one-month-ahead forecast error by about fourfold under concept drift. On UCI Human Activity Recognition, it maintains lower post-transition tracking error with geometric decay. The guarantees apply under the stated assumptions; universality is not claimed.

Undirected graphical models provide a fundamental framework for representing conditional independence structures among high-dimensional random variables. While undirected graphical model selection has become a central problem in high-dimensional statistics, most existing methods are restricted to parametric settings. In this paper, we develop a nonparametric approach to undirected graphical model selection based on diffusion models. Recent work has shown that diffusion models can adapt to the unknown graph structure of the underlying distribution, yet utilizing these models for explicit graph estimation remains unexplored. To bridge this gap, we introduce a novel diffusion-based method for nonparametric undirected graphical model selection. We establish the model selection consistency of the proposed method and demonstrate its empirical performance through extensive simulations and two real data analyses.

We study component recovery and mixing-matrix estimation from unlabeled finite mixtures whose observable distributions share the same latent components but have unknown mixing weights. The main identifying signal is marginal independence: each component is assumed to be independent on at least one coordinate pair, but no labels, clean component samples, or mixing weights are observed. We first prove a structural result for product components: under linear independence of the univariate marginals, any independent affine combination of the components must coincide with a single component. We then extend this principle to observable mixtures and show that, under full-rank and no-cancellation conditions, marginally independent affine combinations recover the corresponding latent components. When every component is independent on some coordinate pair, all components are identifiable, and the mixing matrix is recoverable under the stated completion conditions. Finally, we propose a Product-Marginal Maximum Mean Discrepancy (PM-MMD) estimator over affine combinations of the observable mixtures and prove uniform convergence and stability under approximate marginal independence. This framework also separates the empirical roles of the assumptions: irreducibility is, in general, not directly testable from the unlabeled mixtures alone, whereas marginal independence yields a candidate-level diagnostic through held-out PM-MMD. Controlled and flow-cytometry experiments show when marginal independence provides a useful recovery signal. In the reported multi-component comparisons, condition-aware representative selection stabilizes PM-MMD and improves recovery relative to clustering, factorization, and pairwise mixture-proportion baselines using the same unlabeled mixtures.

Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

Scientific machine learning is limited less by model size than by the data it is trained on. Observational data records what happened but not why; template synthetic data has a known generating process but only for the simulator's template, not the case a user faces. We argue a third option is now operationally feasible: instrumented data, in which every datum carries the mechanistic model that produced it, an explicit uncertainty over that model, and an executable family of counterfactuals. Verification-and-validation (V&V) instrumented image-to-simulation pipelines are one realisation: a sensor observation becomes a fully specified, solver-backed simulation with explicit, editable parameters and a propagated aleatoric/epistemic uncertainty. The substrate is case-specific, mechanistically supervised, and supports causal interventions through Pearl's do-operator.

In regression modelling, the primary objective is to approximate the true conditional mean of a response given a set of features. To this end, various statistical models are used to fit a regression function that provides a mean estimate for each single set of features. This function is said to be calibrated if the resulting mean estimates match the true conditional means for almost all features. Aiming for calibration seems not achievable in practice as models are fitted on finite samples of noisy observations. A weaker notion of calibration is auto-calibration (sometimes also called mean-calibration or well-calibration); see, for example, Kr uger-Ziegel [22] and Denuit et al. [7]. This notion goes back to earlier works on the reliability of probabilistic forecasts in meteorology; we refer to Bross [2], Sanders [26] and Murphy-Winkler [23]. It means that when responses are grouped according to their mean estimates, the average of the responses within each group matches this estimate. This property is important in various applications where sums of mean estimates have to match sums of responses at a global and local level. This is, for example, the case in insurance pricing as an auto-calibrated pricing system avoids systematic cross-subsidy between different price cohorts; we refer the reader to Pohle [24], Denuit et al. [6], Fissler et al. [9] and W uthrich-Merz [30].

Pretrained models are often evaluated on multi-task leaderboards to measure their applicability in diverse contexts. However, current methods for aggregating performance across tasks into leaderboard-level rankings do not address the uncertainty and variability at the task level. While recent works have proposed interval-based model rankings, the principled aggregation of uncertainty from individual tasks to leaderboard-level rankings remains unaddressed, and variation in models' performance across tasks is frequently obscured. In this work, we introduce a hierarchical framework that constructs model rank intervals with statistical guarantees at both levels: task-level rank confidence intervals from pairwise comparisons, and leaderboard-level rank prediction intervals using a conformal approach. This enables reliable quantification of model rank for each observed task and for new potential tasks. Experiments on simulated data and the TabArena and PromptEval (MMLU) benchmarks show that our method yields statistically valid and informative intervals, enabling reliable, uncertainty-aware model ranking on leaderboards.