Papers

In the presence of feedback loops, algorithmic decisions at one time step can influence observed data in subsequent steps, potentially introducing selection bias or shifts in data distribution. Research has demonstrated that ignoring these effects can lead to unfairness, which may worsen over time as the model remains deployed within society. This raises important questions of how to measure and ensure fairness of algorithmic decision-making models over time. In this short paper, we present a taxonomy that distinguishes between different types of static and temporal fairness notions in recent advancements. We then suggest prospects for future research by identifying common implicit temporal assumptions, open questions to enhance our temporal understanding of fairness, and other open challenges.

Automated decision makers, such as AI agents that control robots or network devices, must often satisfy hard cost constraints while maintaining competitive performance. In such settings, a cost measure, such as a safety violation rate, energy consumption, or a distortion level, must stay within a given budget in every episode of operation. Furthermore, a cumulative reward metric, accounting for per-step performance, must stay close to the reward of a meaningful reference policy. We formulate this setup as an episodic sequential decision problem in which the state sequence is arbitrary, and the reward and cost may depend on past actions within the same episode. We propose the online conformal episodic agent (OCEA), a policy that selects one candidate action per episode using a regret-controlled algorithm, and switches to a zero-cost action when the remaining budget cannot absorb the maximum cost of one more round. We prove that OCEA satisfies per-episode cost constraints for every state sequence and for every realization of its internal randomness, while achieving a sublinear expected policy regret with respect to the best action sequence in hindsight from a comparator class satisfying the same per-episode cost constraints. We apply OCEA to risk-averse control and online compression with distortion guarantees.

We present DisCo algebra—a compositional framework for joint probability built from a symmetric cooperad (disintegration) and a symmetric operad (combination) on the bare family $\mathcal{P}_n=\mathrm{Prob}([0,1]^n)$. No probability integral transform, no external summary functions, no enrichment of objects with conditional kernels. The disintegration side uses block-wise joint CDFs as intrinsic, measure-determined 1D summaries, yielding a lossy compression. The combination side reads the same summaries and reconstructs via regular conditional measures, yielding a lossless embedding. We prove that combination followed by disintegration is the identity on admissible inputs, but disintegration followed by combination is not—the information loss is exactly the conditional KL divergence between the true conditional distribution and the conditionally independent product. This asymmetry reveals a hard limit on how much cross-block dependence can be captured by scalar block summaries.

Steering candidate generation toward user-defined objectives is central to inverse materials design, yet remains difficult when objectives are black-box, changing, or non-differentiable, as in many simulation- and experiment-derived properties. Generative models offer a solution but typically require retraining or fine-tuning for each new objective, demanding labeled data and substantial compute, or rely on differentiable guidance that is brittle to gradient noise and undefined for many practical targets. We present DiffGA, a retraining-free framework that injects evolutionary search into the sampling trajectory of a retrained diffusion model, evolving partially denoised states under an arbitrary black-box oracle. Because oracle evaluation often dominates campaign cost, we couple DiffGA with an on-the-fly Bayesian surrogate that reuses representations from state-of-the-art machine-learned force fields (MLFFs). A Gaussian process is fit during the campaign on the force fields's graph embeddings and, once it demonstrably ranks an unseen generation, replaces expensive property evaluations under an uncertainty-aware acquisition rule, reducing oracle cost with negligible loss of accuracy. Across three crystal-design tasks using a frozen MatterGen backbone, DiffGA outperforms diffusion-only, compute-matched, purely evolutionary, and fine-tuned baselines in oracle-assessed rates of stable, unique, and novel hits. Rather than proposing scientific compounds, we use density functional theory to quantify MLFF oracle fidelity, showing that it is a faithful proxy in key regimes but systematically biased in others, delineating when proxy-driven generative discovery can be trusted. On a representative sample, DiffGA's top hits survive first principles re-evaluation as physically realistic hits, while the surrogate-accelerated pipeline preserves this fidelity at a fraction of the cost.

Tabular foundation models adapt to new datasets through in-context learning (ICL), and, like most transformers, they tie computational depth to the number of independently parameterized layers. We ask whether the ICL stage of such a model needs a distinct set of parameters for every layer, or only depth. We introduce Tab-Loop, which replaces the 12 untied ICL blocks of TabICLv2 with 4 tied blocks applied $k$ times and changes nothing else: the encoders, decoder, synthetic prior and training recipe are shared with an untied baseline trained for the same compute. At matched pretraining compute (18.2 EFLOP) and matched inference compute (12 block applications), Tab-Loop matches the baseline with 62% fewer parameters (10.4M vs.\ 27.6M): held-out log loss is 0.4583 vs.\ 0.4588, mean accuracy on 200 TALENT datasets is 84.10% vs.\ 83.92%, and Elo on 38 TabArena datasets is 1409 vs.\ 1396. A 4-block untied control with Tab-Loop's parameter count, which sees 32% more training tables for the same compute, trails both (83.46%; Elo 1343). Because weights are shared, depth becomes a choice made at inference. Accuracy rises with the number of loops through the trained range and holds beyond it, and continued training with deeper loops extends the useful range, reaching the baseline's stage-2 scores at 4–5$\times$ its inference compute. At this scale, the ICL stage of a tabular foundation model needs depth more than it needs distinct parameters.

Prior-data fitted networks (PFNs) are transformers pretrained on simulated datasets to approximate Bayesian posterior predictive distributions. Standard PFN theory assumes a separable task prior, under which the feature distribution and the mechanism generating labels from features are independent. We show that common PFN priors are non-separable, even in simple settings. Consequently, standard pretraining targets a predictive distribution based on a task posterior updated using both the labeled context and the query features. We characterize its difference from the predictive based on the context posterior alone and show that this difference vanishes under posterior concentration. Under misspecification (i.e., when the true joint distribution lies outside the prior's support), however, prior non-separability can favor better feature fit at the expense of conditional label fit. We illustrate the consequences for feature attribution, Bayesian optimization, and martingale checks of Bayesian behavior. The same dependence also enables PFNs to learn from additional unlabeled observations. We demonstrate this with SemiTabICL, a PFN explicitly pretrained to use these observations, which improves accuracy over a matched supervised baseline. Our findings highlight the need for explicit rules on unlabeled data use in PFN evaluation and establish the dependence between feature and label distributions as a consequential prior design choice.

The average-reward setting for reinforcement learning is challenging because its Bellman operator is known to contract in span only when the underlying Markov chain is mixing. Whereas existing work typically assumes a contraction property, e.g., through environment mixing, we consider the setting where we are given a reward-agnostic $m$-step mixing policy, and we control the contraction and exploration properties of the learned policy by regularizing toward the mixing policy. We provide finite-time analysis of $Q$-learning algorithms that can be instantiated with multiple choices of regularization, with guarantees measured with respect to the regularized fixed point. Our framework exposes novel regularizer-dependent objects that control contraction, exploration, and operator bias. In the one-step setting, our rates match the best known rates for $Q$-iteration and synchronous $Q$-learning, and for $m$-step mixing we derive new rates. We also study $Q$-planning variants, and show that planning acts as time-localized learning, where the planning horizon $H$ trades off the bias from the boundary value against the sample complexity. Finally, we present numerical studies validating the analysis: (i) knowledge of a strong mixing policy improves convergence and exploration, and its advantage increases with bottleneck severity and, (ii) our theory predicts the convergence and bias rankings of regularizers from the $\alpha$-divergence family.

Recurrent algorithmic reasoners are trained with per-step hints on small graphs and run for many more steps on large ones. On breadth-first search in SALSA-CLRS, we find that a reasoner can reproduce every training hint and still fail on deep graphs: after some exact steps, it declares nodes reached before the search gets there. We call this a premature flood and trace two routes to it. In our GRU processor with a degree input, the flood is carried in the hidden state and set off when that input is in the tail of the training distribution. Setting the input higher at inference brings the flood sooner, and none of the six flooding models counts steps. Without the input, summing the neighbors' states instead of averaging them also breaks the processor. In the benchmark's own GIN and PGN, trained with its code, some seeds instead flood from a fixed step, on sparse and dense graphs alike. Clamping the degree input or adding 200 dense training graphs removes every failure of the GRU processor. Detaching the state between steps avoids the flood in that processor (0 of 23 seeds, against 6 under full backpropagation) but not with sums or a residual update, and two published remedies leave floods. None of the benchmark's test sets is both deep and dense, but its deepest one shows the second route: on its Delaunay graphs at 1,600 nodes, one GIN seed floods from step 18. We therefore recommend auditing the range of every input and aggregate, which catches the first route, and testing on deep graphs, which catches both.

Large Vision-Language Models (LVLMs) have excelled in joint visual and language understanding, particularly in image captioning. However, LVLMs remain prone to object hallucination, describing non-existent entities in the given image. Previous remedies, including dataset-enhanced supervised training and reinforcement learning from human feedback, show promise but rely heavily on costly human involvement, limiting scalability. To address this, we propose a reinforcement learning framework to mitigate object hallucination in LVLM-based image captioning, driven entirely by natural language processing (NLP) metrics. While optimizing reinforcement learning solely on NLP metrics offers scalability, it also introduces pitfalls: reward hacking, sparse feedback, and costly training. Our framework sidesteps these by introducing an Object Consistency Score (OCS) capturing both correctness and coverage of objects, incorporating KL-regularization for denser token-level guidance, and designing a lightweight PPO variant that fine-tunes adapters atop a frozen LVLM backbone, achieving efficiency and stability. Extensive experiments on the InstructBLIP baseline demonstrate the effectiveness and generalizability of our framework, achieving a substantial hallucination reduction of up to 41% on the COCO dataset and 29% on the Visual Genome. Furthermore, the framework can enhance caption quality by incorporating complementary evaluation metrics such as BERTScore and METEOR. These results reveal a broader insight in multimodal learning: LVLMs can effectively self-correct hallucinations using metric feedback, motivating deeper exploration into scalable reinforcement frameworks that significantly reduce human effort.

WavePhaseNet introduced frequency-resolved semantic representations, QuantumPhaseNet introduced gauge-covariant phase connections, and ModularPhaseNet made a finite cyclic phase channel and its cycle holonomy computable in an ordinary Transformer. These constructions are complementary, yet they do not by themselves separate an observed collection of pairwise relations into a globally consistent direction, circulation around local compositions, and circulation that persists around a larger unfilled cycle. HodgePhaseNet addresses this separation by representing semantic transitions as an antisymmetric real-valued 1-cochain on a finite oriented simplicial complex. With vertex-edge incidence matrix $B_1$ and edge-face incidence matrix $B_2$, every such field has a unique orthogonal decomposition $\Omega = B_1^T\Phi + B_2\Psi + H$, where $B_1H=0$ and $B_2^TH=0$. The three component fields are unique even when their potentials are not. We give explicit projectors, a sparse implementation, integrability and gauge results, a verified numerical example, and a redesigned attention interface. The attention bias is defined on allowed ordered query-key pairs, remains consistent under arbitrary choices of edge orientation, and preserves a decoder's causal information boundary by constructing its complex from the visible prefix. Gauge invariance of the attention output is conditional on using invariant or appropriately compensated features. A simple difference of vertex embeddings has no coexact or harmonic component; a genuine relation encoder is therefore indispensable. Local circulation is not automatically contradiction, and harmonic flow is not automatically missing knowledge. These interpretations and any reduction in factual error require controlled empirical evaluation. This paper presents a mathematical and architectural proposal, not external natural-language performance results.

Large Language Models (LLMs) can generate functionally correct code while introducing exploitable security weaknesses, particularly when developers specify functionality without explicit security requirements. Recent state-of-the-art approaches mitigate this problem using external security knowledge, but largely rely on flat similarity-based retrieval over independent artifacts, making it difficult to infer the relevant vulnerability space and retrieve targeted knowledge when direct matches are unavailable. We propose SEEK, an agentic Graph RAG framework for secure code generation that constructs a security knowledge graph using the Common Weakness Enumeration (CWE) taxonomy as its structural backbone and injects it with curated real-world CVE vulnerability-fix instances. At inference time, a Planner Agent predicts potential CWE weaknesses associated with the developer query, which guide Graph Scoping to restrict retrieval to relevant regions of the CWE taxonomy before deterministic multi-faceted candidate ranking. A Selection Agent subsequently validates the predicted weaknesses and retrieved candidates prior to code generation. Across five open-source LLMs, we evaluate SEEK in an out-of-distribution setting on CodeGuard+ and CyberSecEval, spanning C, C++, and Python. SEEK achieves the highest SecurePass@1 of 77.45% on CodeGuard+ and the highest aggregate ICD pass rate of 79.45% on CyberSecEval, surpassing prior approaches. Moreover, SEEK achieves 85.2% SecurePass@1 across 13 unseen CWE types with no directly linked vulnerability-fix instances, demonstrating strong generalizability, while maintaining acceptable inference latency costs.

Cross-material magnetic core loss prediction requires adapting to new material responses with limited measurements. Global feature alignment overlooks differences in source and target excitation coverage. This motivates selecting comparable samples and controlling each source measurement's alignment contribution. This paper proposes T-PCOT, a Transformer transfer method based on condition-supported partial optimal transport. Frequency, flux excursion, temperature, and waveform descriptors define a sparse graph of comparable operating conditions. A capacity-constrained transport plan distributes alignment across source measurements and leaves costly target mass unmatched. The plan is constructed from measured inputs before training and guides local waveform-feature consistency. An importance-weighted sampling scheme preserves both uniform source regression and the transport objective during minibatch optimization. Experiments on three material pairs and three target label budgets show that T-PCOT reduces mean relative error (MRE) and 95th-percentile error (P95) relative to Transformer-based multiple-kernel maximum mean discrepancy (T-MKMMD) in all nine comparisons. Macro MRE decreases from 12.60% to 9.65%, and macro P95 from 30.94% to 25.06%, corresponding to relative reductions of 23.41% and 19.01%. Controlled comparisons and ablations examine the roles of input processing, condition correspondence, and source capacity. The results demonstrate the predictive advantage of organizing cross-material alignment through operating-condition support over the compared global alignment method. The proposed method achieves state-of-the-art predictive performance in magnetic core loss transfer learning.

We present HiPAD, a single fusion network submitted to all six sub-tracks of the MPDD-AVG 2026 depression-detection challenge, covering the Elder and Young cohorts and three modality sets (gait, audio-visual, and both), each combined with personality descriptions. The network encodes each available modality with a shared BiLSTM, zero-pads absent modalities, and applies cross-modal attention only when at least two of gait, audio and video are present. Personality, which dominates our results, is kept out of the attention and fused by concatenation. Because the architecture is identical in every sub-track, differences between them reflect the data rather than the model, and we use this to study three questions. Our main finding is that the personality description, roughly 150 tokens about who the subject is, carries more depression signal than audio, video, and gait combined: gait plus personality alone (TLS 0.647) beats every configuration that includes audio and video. First, a four-level ablation of the personality description (L0-L3) quantifies this: removing every personality-derived feature, including the Big Five scores that earlier MPDD ablations keep, lowers the Track-Level Score by 0.499 to 0.507 and leaves the model at chance. Second, domain-adapting the personality encoder with LoRA (7B) or QLoRA (72B) on PHQ-8/9 data raises binary Cohen's $\kappa$ by 0.13 but lowers the overall score by distorting the PHQ-9 regression; a frozen RoBERTa-large encoder does better at this sample size. Third, at fixed architecture, handcrafted clinical features (eGeMAPS, OpenFace action units) outperform generic deep features (wav2vec2, DenseNet) on the audio-visual tracks. The unified system reaches a cross-track G-Score of 0.482; with under 100 subjects per cohort, the limiting factors are the size of the representation and the calibration of the outputs, not the choice of architecture.

Formulaic alpha mining seeks to discover executable expressions that capture predictive market signals in a vast, noisy search space. Recent LLM-based approaches use prompting, iterative search, or seed-factor evolution, leaving direct factor construction through policy learning less explored. To address this, we introduce AlphaRLM, a reinforcement-learning framework that trains LLMs to construct executable symbolic factors from financial literature without input factor expressions. AlphaRLM incorporates Literature-Guided Operator Assembly (LEGO), which conditions factor construction on literature-derived ideas and executable operators, providing semantic priors for exploration. It further aligns the generation policy with market feedback through executable-validity and grouped-return-separation rewards that capture non-monotonic structures across factor quantiles. Extensive experiments on CSI 300, CSI 1000, and S&P 500 show that AlphaRLM outperforms strong factor-mining and LLM-based baselines in annualized excess return. Notably, the 8B model achieves strong cross-market performance, highlighting the promise of literature-conditioned, market-aligned factor generation.

Activation steering has recently been used as a memory for skills: past experiences of an agent are stored as steering vectors and retrieved later. Facts and preferences about the user are assumed to need text instead. We test that assumption with a training-free activation memory beside a frozen LLM. The change an experience causes in late-layer states is stored as a shift, filed under a whitened key for the conversation's gist, and added back in a later session only when the gist matches. We argue that such a shift is a fixed average of an effect that attention, in context, recomputes for every question, so only question-independent content can survive. In a pre-registered study on Qwen3.5-2B and 9B, with judges from four model families, the memory is selective (about 98% of unrelated replies are unchanged), but facts are stored as the word to say, in the last layers only, and are almost never used (at most 15% clean use, against 96-98% in context). Leanings transfer only in a narrow strength window. Most strikingly, the reference subtracted when writing a preference decides whether its concept or its direction survives: unless the opposite is subtracted, a stored dislike is recalled as a like.

Contrastive reinforcement learning (CRL) learns goal-conditioned values by associating state–action pairs with the states subsequently reached, assuming that no unobserved variable jointly affects the recorded action and its outcome. When offline demonstrations come from a demonstrator with information hidden from the learner, this assumption fails and the critic absorbs spurious action–outcome associations. We formalize this setting with confounded Markov decision processes and introduce counterfactual transitions that separate what the data identify from what they do not; minimizing over all compatible transitions yields a worst-case occupancy that lower-bounds the true one. Causal Contrastive Reinforcement Learning (CauCRL) learns a pessimistic counterfactual transition from positive and negative offline demonstrations and trains the critic on counterfactual rollouts, substantially improving success rates over standard CRL on confounded goal-reaching tasks.

Temporal point processes are used both to measure market mechanisms, for example how fast prices absorb news and how much of the reaction is the market responding to itself, and to predict the next event. We show that one algebraic object, the phase-type (Erlang-chain) state space, serves both purposes with exact likelihoods. For measurement, we build a multiscale phase-type Hawkes process whose parameters all enter linearly. Its log-likelihood is concave, and we compute the global maximum together with a Fenchel duality-gap certificate. A Markov embedding gives the response to an exogenous shock, echoes included, in closed form, and this response is stable if and only if the spectral radius of the branching matrix is below one. Applied to six markets around 670 scheduled macroeconomic releases (2022-2026) with a built-in placebo test, the model shows that the direct reaction to CPI, payrolls, PPI and the FOMC statement is absorbed in about a second, while the market's own echoes stretch half of the response to 16-137 s. For prediction, we introduce EPT-X, a neural point process that adds a history-dependent mixture-of-Erlang renewal channel to a linear Hawkes backbone. Its intensity and compensator remain in closed form, its states follow an affine recursion that trains with a parallel scan, and it can start from the certified fit of the measurement model. EPT-X has the best test likelihood on all five LOBSTER order-book streams and on Retweet and Taobao, and is level with the best published model on StackOverflow. We also find that the EasyTPP implementation of IntensityFree clamps short inter-event times before scoring, and that the gaps of the EasyTPP Amazon data are uniform on two fixed intervals.

Bilevel data selection is a fundamental task with numerous applications in machine learning and statistics. A common strategy for tackling this problem is to relax the original bilevel combinatorial optimization into a continuous one. However, existing methods, including 0-1 relaxation and probabilistic relaxation, still suffer from several limitations, such as unstable gradient estimation and infeasible rounding. To address these issues, this paper proposes a new probabilistic relaxation for the multi-source bilevel data selection problem. Our key idea is to introduce multiple learnable categorical priors to parameterize a probability distribution supported only on feasible data subsets, thus naturally yielding a lossless rounding scheme. We further show that our proposed relaxation admits an effective two-point gradient estimator, which can simultaneously avoid the inverse-Hessian computation required by existing 0-1 relaxation and the unbounded score term appearing in prior probabilistic relaxation. Furthermore, we develop a reducible representation of this estimator, which substantially reduces the number of lower-level retrainings required for gradient computation. Built upon this reducible two-point estimator, we then design a novel stochastic gradient algorithm, termed ReSGD, for multi-source bilevel data selection problem, and establish a rigorous approximation guarantee for the subset returned by ReSGD under weak submodularity. Finally, extensive experiments are conducted to validate the effectiveness of our proposed ReSGD.

Diffusion-based policies have recently emerged as a powerful paradigm for offline reinforcement learning, but their reliance on multi-step denoising introduces substantial computational overhead and requires backpropagation through time during training, limiting scalability and practical deployment. In this work, we propose Instant Flow Q-Learning (InsQL), a single-step generative policy learning framework that retains the expressive capacity of diffusion models while eliminating iterative sampling and BPTT. InsQL builds on the flow-matching perspective of diffusion policies, but replaces marginal velocity parameterization with average-velocity modeling and introduces a principled compositional mechanism, yielding a theoretically grounded objective that learns average velocity consistently across scales. This formulation provides a direct noise-to-action mapping and enables single-step action generation. InsQL further unifies compositional average-velocity modeling with behavior-regularized actor–critic optimization in a single framework, requiring only a single policy network and avoiding distillation, multi-stage procedures, and Jacobian computations during training. At inference time, actions are generated in a single forward pass and can be refined via value-guided candidate selection to improve performance. Extensive experiments on standard offline RL benchmarks and real-world robotic manipulation tasks show that InsQL matches or surpasses state-of-the-art diffusion-based methods while substantially reducing both training and inference time. Overall, these results establish compositional average-velocity modeling as an efficient and scalable alternative to multi-step generative policies for offline RL.

Diffusion policies are increasingly used in robotic control and manipulation, vision-language-action models, and world-model-based agents. Their ability to represent multimodal action distributions offers rich opportunities for exploration in reinforcement learning (RL). However, optimizing diffusion policies with RL can reduce the behavioral diversity and further limit their exploration capability. In RL post-training, directly fine-tuning a pretrained policy may also disrupt its acquired capabilities, while action-space residuals may lack the expressive power for multimodal exploration. Together, these issues reveal a common challenge across online and offline-to-online diffusion RL: improving task performance while retaining the behavioral diversity and capabilities needed for continued adaptation. We introduce CFG-Policy, a unified, plug-and-play framework that separates exploration and exploitation into two generative policies and combines their score or velocity fields during sampling through classifier-free guidance. For online RL, a frozen exploration branch sustains behavioral diversity while an exploitation branch learns from task rewards; for offline-to-online RL, a pretrained exploitation branch remains frozen while a trainable branch steers the composed behavior. CFG-Policy preserves the underlying RL objectives and improves performance with QSM and QVPO on 5 MuJoCo tasks and with Flow-SDE+PPO on 4 RoboTwin manipulation tasks. Project page is at https://zhy-liu.github.io/cfg-policy-page.

Pipeline parallelism has become a critical technique for training large language models. To address the throughput limitation of existing sequence-level methods that schedule subsequences unidirectionally, we propose bidirectional sequence-level interleaved pipeline parallelism (BSIPipe), which co-schedules two opposing V-shaped interleaved pipelines at the subsequence level. To bound the activation accumulation from subsequence scaling, BSIPipe introduces a basic-unit concatenation mechanism that keeps activation memory invariant to the subsequence count. To eliminate communication deadlock risk from bidirectional scheduling, BSIPipe employs a communication optimization strategy that combines topology-aware device mapping with communication-computation overlap. In addition, BSIPipe composes with tensor parallelism to overcome the memory limitation of single-dimensional parallelism, neutralizing its bidirectional memory overhead while maintaining throughput. Experiments on GPT and LLaMA3 demonstrate that BSIPipe achieves average speedups of 1.11$\times$ to 1.13$\times$ in long-sequence training over SOTA sequence-level baselines.

Clustering is typically performed using only object features, although additional information about relationships between objects may be available and can be incorporated through constraints. Among these, pairwise constraints require two objects to belong to the same cluster or to different clusters. Several extensions of the k-means algorithm accommodate such constraints, but they sometimes fail to find a feasible assignment or incur high computational cost. Motivated by these limitations, we propose an algebraic approach to k-means clustering with pairwise constraints. The algorithm simplifies the constraints using Gröbner bases before optimization, improving the efficiency of cluster assignment. It can also detect whether the constraint set has a feasible assignment before optimization. Comparative experiments with existing algorithms showed that the proposed algorithm achieved comparable or better clustering quality at a lower computational cost, particularly when the numbers of constraints and clusters were small.

The TLA+ (temporal logic of actions) formal specification toolkit has seen widespread adoption in modeling modern distributed software systems including databases, storage systems, ledgers and coordination protocols. This popularity is despite its two significant limitations for software verification: Firstly, TLA+ offers no way to detect drift between software implementation and mathematical specification; secondly, TLC and TLAPS cannot provide satisfactory proofs of arbitrary temporal logic properties. We address the second limitation and take a first step towards the first by translating TLA+ specifications into Verus, an auto-active verifier built for Rust, via both a deterministic transpiler and an agentic translator. We demonstrate that our LLM-based pipeline is able to generate proof obligations from TLA+ specifications at scale, and to produce fully machine checkable proofs of both safety and liveness properties. Since temporal logic reasoning in Verus is a largely new task for LLMs, our work yields a valuable evaluation dataset, which we use to map out current generation model capabilities in Verus theorem proving.

A language model that keeps learning online must not slowly erode its own base capabilities. We ask which part of a modern LLM should absorb continual updates, by measuring how each choice changes the model's internal representations. On a 48-layer mixture-of-experts model with a native pretrained N-gram memory, we train a seven-task chain under three update mechanisms with identical data and budgets: updating only the N-gram memory table, continually training one shared LoRA adapter, and training a fresh LoRA per task that is merged into the backbone. We capture fixed-context representations at every layer and task boundary. Updating only the N-gram memory changes the base model's representations of general math and code inputs by 26%/15% (relative RMS), against 64%/35% for merged and 97%/39% for shared LoRA. This drift does not grow with the number of tasks: it reaches 25% after the first task and stays there for all seven, while both LoRA variants keep accumulating. Its generic behaviour is essentially unchanged (no code problem lost, math NLL -0.01), and every change is confined to inspectable, reversible table rows. The cost appears elsewhere: N-gram memory acquires new tasks more weakly and its stored tasks interfere with one another, losing as much old-task NLL as shared LoRA. We show that this forgetting is governed by drift on the learned tasks' own inputs, measured from the checkpoint at which each was learned, not by generic drift (Spearman rho=0.85; rho=0.71 on Llama-3-8B), and we derive the exact relations behind it: with a frozen head, every pairwise logit margin changes by the projection of drift onto a head-difference direction. These results support a design principle for long-running online learning: write new knowledge only into the memory table and keep the backbone fixed; the remaining problem, interference between stored tasks, then lies inside the memory.

Reinforcement learning (RL) is essential for adaptive decision-making, e.g., robust Meta-RL and domain randomization (DR), and efficient post-training of large language models (LLMs), where tasks are commonly structured as Markov decision processes or prompts. A central bottleneck in all these settings is the cost of agent-environment interactions required for task selection and policy optimization. Model predictive task sampling (MPTS) has emerged as a promising approach to improve sample efficiency by querying informative tasks via a risk predictive model (RPM) trained on optimization history. However, existing RPMs suffer from two failure modes: (i) sparse optimization histories, which limit RPMs' generalization across the task space, and (ii) a one-step lag in risk approximation, which causes biased difficulty estimation as the policy evolves. This work formalizes these failure modes, derives lagged-risk decompositions that expose the resulting temporal bias, and recasts risk prediction as an in-context sequence modeling problem. The developed RPM integrates a one-step look-ahead mechanism with a temporal-weighted sliding window to mitigate data non-stationarity and scarcity, without requiring additional rollouts. Empirically, our approach yields more reliable difficulty estimates and consistent performance gains across robust Meta-RL, DR, and prompt curriculum RL post-training of LLMs.

Optimal transport (OT) enables multivariate conformal prediction (CP) to construct flexible prediction sets that reflect the underlying complex distributional geometry while retaining distribution-free coverage guarantees. Existing OT-based methods typically rely on a fixed Euclidean transport cost, which can be suboptimal in terms of the volume of prediction sets. We propose Minimum-Volume OTCP, a framework that learns a Mahalanobis ground cost to directly minimize prediction-region volume over a class of positive-definite metrics. Using a metric Brenier representation, we derive a volume-based objective that depends explicitly on the Mahalanobis cost matrix and optimize it jointly with the transport map. We establish finite-sample marginal coverage of the output prediction sets and optimality of volume metrics. We further develop an individualized extension that learns covariate-dependent transport metrics, adapting the shape and orientation of prediction sets to heterogeneous conditional distributions. For this extension, we also show the asymptotic conditional coverage of our method. Simulations and real-data experiments demonstrate substantial reductions in prediction-set volume.

We study prediction with expert advice over $T$ rounds with $K$ experts under heavy-tailed losses whose $(1+\epsilon)$-moment is bounded by $\theta>0$ for some $\epsilon\in(0,1]$. In this setting, existing algorithms designed for the case $\epsilon=1$ can be suboptimal when $\epsilon<1$, suffering an additional polynomial dependence on $K$. We characterize the minimax pseudo-regret rate as $\Theta((\theta T)^{\frac{1}{1+\epsilon}}(\log K)^{\frac{\epsilon}{1+\epsilon}})$ and establish gap-dependent lower bounds in a self-bounded environment. To attain this minimax rate without prior knowledge of either $\epsilon$ or $\theta$, we propose Adaptive Heavy-Tailed FTRL, which uses robust data-dependent scale adaptation together with truncation. We further develop Adaptive Heavy-Tailed OMD, which likewise requires neither $\epsilon$ nor $\theta$ and achieves near-optimal regret guarantees in both adversarial and self-bounded environments. Finally, when $\epsilon$ and $\theta$ are known, an FTRL algorithm with Shannon-entropy regularization achieves optimal regret guarantees in both environments.

The sudden growth in AI data centers is raising numerous environmental concerns. Low-frequency noise pollution is a concern for local residents, that may not just be an annoyance but also carry significant health impacts. An FDTD model of sound propagation over the topography near an AI data center is presented. The topography plays a large role in the level of noise pollution, with areas of sudden elevation on either side of the river near the AI data center more susceptible to high noise levels, while areas further afield largely protected from noise pollution by the topography. Understanding the role that topography plays in noise pollution, and capturing the noise pollution in specific topographies, can help identify areas where noise mitigation strategies might be best employed.

We present a robust deep generative framework for unsupervised image prototype discovery, built on a heavy-tailed Student's t mixture prior, that bridges statistical robustness and mathematical tractability. Existing generative approaches typically rely on noise-prone Gaussian priors or computationally intensive diffusion models; neither simultaneously provides explicit latent structure nor exact analytic optimization. While diffusion models can yield strong priors, iterative sampling and intractable likelihoods limit scalability and interpretability for prototype discovery. We address these issues by constructing a Student's t latent space via a Bayesian scale-mixture formulation. This yields a fully closed-form augmented ELBO for unsupervised Student's t mixture variational autoencoders, which, to our knowledge, is the first such objective applied to robust image prototype discovery, avoiding biased variational approximations and high computational costs in prior heavy-tailed or diffusion-based frameworks. Treating precision as a latent variable automatically modulates each data point's influence, downweighting outliers to learn a data-dependent measure of trust. The result is improved robustness, accuracy, and efficiency, with well-separated latent representations and more stable manifold learning than state-of-the-art methods. We validate our model on standard vision benchmarks and challenging neuroimaging tasks. In brain MRI-driven neurodegenerative disease analysis, our model recovers clean, anatomically coherent prototypes where clinical noise often collapses rare subtypes. These results highlight the ability of our framework to preserve anatomy-associated patterns for precise discovery in clinical settings. Our code is available at: https://github.com/xuzhikangnba/torch-tvae.

We present MARL-BattleGrounds (MARL-BGs), an easy-to-use JAX-native benchmark for heterogeneous and competitive multi-agent reinforcement learning (MARL), designed to be sample-efficient, computationally efficient, and researcher-centric. MARL benchmarks are typically simple and efficient, like SMAX, where winning reduces to unit micromanagement, or rich and costly, like Dota 2. MARL-BGs fills this missing middle. Its first mode, Team Deathmatch, is a simultaneous turn-based game between two teams of five heterogeneous agents. The five classes have distinct basic, passive, and ultimate abilities designed to synergize with allies and counter enemies. Our 52 hand-designed maps with diverse obstacles include a 12-map curriculum and ten held-out validation and test maps. MARL-BGs provides two canonical evaluation modes. First, eight endgame scenarios form a hard generalization challenge: each asks a team to win an unseen, nearly lost position against a strong reactive controller within 5-10 ticks. Second, a monthly round-robin tournament retrains each submission on equal compute, plays it against every member of the current "Big Nine" field, and publishes the Elo results on the official leaderboard. All entrants are publicly released as downloadable opponents. MARL-BGs records 11,192 metrics per game in 28 topics. We also include three strong scripted opponents, an analytical replay viewer, and off-the-shelf tools for self-play, cross-play, curriculum learning, and zero-shot coordination evaluation. We even provide an API for LLM-based agents and use it to evaluate Qwen3.5-9B against our strongest policy. In our BattleClient, humans can play alongside or against any mix of policies, enabling human-AI evaluation. We benchmark MARL-BGs with six additional deep MARL baselines, which we release. On one RTX 5090 with 1,024 parallel games, the simulator runs 50,000 5v5 game steps per second.