Papers

Post-training is central to mathematical reasoning in modern large language models (LLMs), but endpoint pass@1 alone underidentifies what has changed. Gains may reflect newly reachable solutions, cheaper sampling of latent solutions, surface robustness, or memorisation. We compare three post-training paths under a common diagnostic readout: our sufficiently trained off-policy distillation trajectories, released Qwen3 off-policy-plus-on-policy distillation endpoints, and a released DeepSeek-Math endpoint trained with Group Relative Policy Optimisation (GRPO). Our probe uses cross-surface pass@K over verbatim prompts, paraphrases, numerical isomorphisms, and translations, plus consistency, distribution-shape, and verified supervised-fine-tuning (SFT) membership analyses. We find two regimes. On easier AMC problems, large-K ceilings are near saturation, so post-training mainly compresses sample cost. On harder AIME problems, post-training expands the large-K ceiling over the base model: sufficient off-policy distillation already raises this ceiling, Qwen3 released endpoints raise it further, and DeepSeek-Math GRPO does not dominate sufficient off-policy distillation at large K. English-dominant distillation improves non-English reasoning but preserves language-tier gaps. A controlled-overfit audit finds limited sensitivity in current SFT-membership probes. Compression is one regime of post-training, not a universal explanation.

Decision-making under uncertainty often relies on predicted parameters, yet accurate prediction does not necessarily lead to good operational decisions. Aligning prediction with downstream optimization requires learning from the consequences of the decisions those predictions induce. We introduce RL-PaO, a reinforcement learning framework that integrates system formulation, optimization, and decision execution into a single environment. This yields a Markov decision process in which prediction is regarded as action: it shifts the environment to produce subsequent context and reward that explicitly aligns prediction error with realized cost, and learning the optimal policy does not require differentiating through the black-box solver. We evaluate RL-PaO on day-ahead energy scheduling using real historical data. On the test year, RL-PaO achieves the lowest annual cost among the non-oracle baselines, achieving on average $10\%$ cost reduction. Moreover, RL-PaO is capable of further analyses to provide strong interpretability both from the policy evolution perspective and the cost-accuracy trade-off.

Dynamic layer skipping reduces LLM computation by allowing each token to execute only a subset of the model's layers. However, existing skippers rely on specialized generation loops and do not integrate with modern serving engines. As a result, fewer executed layers do not necessarily translate into lower serving latency: FlexiDepth skips 8 of Llama-3-8B's 32 layers on average, yet its standard generation loop decodes 14.6–21.0% more slowly than the base model. We present vSkipper, a virtualization layer that makes dynamic layer skippers pluggable in serving engines while preserving continuous batching, fixed-shape batches, paged KV caching, and captured decode graphs. At each routed layer, vSkipper groups tokens by the skipper's decision and uses routed execution only when predicted to be profitable. We implement vSkipper in SGLang and evaluate the released FlexiDepth checkpoint against upstream SGLang under identical prompts, arrivals, output lengths, and launch settings. At the knee of upstream's load curve, vSkipper reduces mean end-to-end latency by 36.8% on GSM8K and 13.6% on BBH. Under saturation, it increases request throughput by 11.3% and 7.4%. Serving adds no statistically resolved quality loss beyond the checkpoint's own. Across synthetic skip policies, two Qwen3 skippers, and three GPUs, we demonstrate reuse without workload-specific tuning. To our knowledge, vSkipper is the first system to realize serving-efficiency gains from per-token interior layer skipping within a modern LLM serving engine. The code is open-sourced as an SGLang fork at https://github.com/AKafakA/sglang-vskipper/tree/vskipper-ref

We view fairness as a property of distributional stability. Rather than assessing a predictor under a fixed data distribution, we study how its predictions change under perturbations that modify the composition of protected groups. A predictor is fair if it remains stable under such shifts. Under this perspective, several classical notions of fairness arise as stability with respect to specific perturbations, with the associated unfairness gap given by a Lipschitz constant of a prediction-rate functional. This formulation also yields guarantees that hold uniformly over a range of demographic compositions at test time, without requiring knowledge of the deployment distribution. It leads to a learning procedure based on convex combinations of reweighted predictors, formulated as a second-order cone program, for which we establish generalization bounds. Experiments on standard benchmarks illustrate the approach.

Achieving strong performance with graph neural networks (GNNs) typically requires training and hyperparameter tuning for each dataset, incurring repeated costs and effort. Graph in-context learning (ICL) avoids this by using a single pretrained model to predict unknown node labels directly from labeled context nodes. Existing approaches, however, rely on dense attention across nodes, making inference increasingly expensive as graphs grow. In this work, we present Ephris, a new graph in-context learner built on sparse message passing, scaling linearly with the number of node-feature entries and graph edges. Ephris is pretrained entirely on synthetic graphs generated from structural causal models with diverse graph structures and relational dynamics, exposing the model to varied dependencies among topology, features, and labels. We evaluate Ephris on 51 node-classification datasets against 15 extensively tuned GNNs and existing graph ICL methods under both high- and low-label train/validation/test splits. Across both settings, Ephris ranks first on all four aggregate measures: Elo, improvability, average rank, and accuracy. Its inference cost remains comparable to training a single GNN once, while being over 10 times faster than previous graph ICL models. Together, these results advance the performance-runtime Pareto frontier, demonstrating that strong graph ICL does not require dense attention. Code and model weights are available at https://github.com/nums-ai/ephris.

We propose a new spiking neural network (SNN) design to process static images and event streams using time-to-first-spike (TTFS) latencies. Our key research question is which architectural choices best accommodate local and online learning in multi-layer convolutional SNNs. This question is addressed via an original framework combining residual-like connections with multi-depth feature aggregation and consensus. The full SNN pipeline features an early-vision front end, to convert raw visual data into sparse spike latencies, a four-layer convolutional backbone trained layerwise with unsupervised spike-timing-dependent plasticity (STDP), a deterministic Multi-Depth Temporal Fusion (MDTF) and a final classifier trained with reward-modulated spike-timing-dependent plasticity (R-STDP). Rather than replacing early features in deeper layers, the proposed MDTF preserves early temporal evidence, adding sparse residual events from intermediate layers, and incorporating deeper features only when they agree in time with earlier representations. The resulting architecture is experimentally validated across MNIST, Fashion-MNIST, CIFAR-10, and N-MNIST, delivering strong classification performance under a fully local learning regime. Selective multi-depth fusion significantly outperforms traditional STDP/R-STDP baselines on higher-variability visual tasks (achieving +18.2 pp on Fashion-MNIST and +29.2 pp on CIFAR-10). Furthermore, activity-budget analyses show that the network retains high accuracy even when removing a large fraction of late or weak spike events, confirming its high data efficiency and reduced event-processing requirements. The codebase is publicly available at github.com/aidinattar/multi-depth-temporal-fusion-snn.

Sampling from unnormalized distributions over large discrete state spaces becomes difficult when a multimodal target is far from a tractable reference. We introduce Iterative Exact Discrete Guidance (IEDG), a population-exact, trajectory-wise guidance framework for unnormalized discrete targets. Rather than learn the full reference-to-target correction in one step, IEDG introduces a global Boltzmann tilt along an annealing trajectory. Each stage learns a stage-local posterior correction for an incremental Boltzmann tilt of the current source, while the resulting corrections are accumulated relative to a fixed analytic posterior. At the population optimum, exact stage posteriors recover the correct reverse dynamics, whose exact simulation reproduces the target distribution. IEDG chooses stage increments by relative effective sample size (rESS), which controls Rényi-2 displacement and locally adapts the step size to the thermodynamic geometry of the annealing path. Our stagewise total-variation analysis shows that limited overlap amplifies Bregman fitting error by $1/\sqrt{\mathrm{rESS}}$, while posterior, simulation, and truncation errors enter additively. IEDG improves all distribution-level errors over the neural baselines on ordered, exactly enumerated Ising $4\times4$, while substantially reducing one-shot errors on Ising/Potts $16\times16$ across thermodynamic regimes and attaining the best neural-sampler result on several reported local-statistic and phase-coverage metrics. On Max-Cut, its best-of-512 and average-sample ratios exceed all the baselines. Code and artifacts are available at https://github.com/StillFantasy123/iterative-exact-discrete-guidance.

Video Large Language Models (VideoLLMs) have achieved strong video understanding capabilities but incur substantial inference overhead due to the large number of visual tokens. Existing VideoLLM token compression methods largely rely on selection-independent scoring, overlooking cross-frame complementarity and consequently retaining redundant evidence across frames. Instead, we view video token selection as a progressive evidence accumulation process. It aims to retain visual evidence that is individually informative and collectively complementary under a limited token budget. Building on this insight, we introduce GleanVID, a training-free inference acceleration framework for VideoLLMs. Specifically, GleanVID first allocates the global token budget across frames according to temporal novelty and then selects tokens by jointly considering local representativeness and subspace complementarity, thereby preserving richer and less redundant visual evidence. Extensive experiments across diverse VideoLLMs and benchmarks demonstrate that GleanVID consistently achieves state-of-the-art performance. Notably, with only 25% of visual tokens, GleanVID preserves 98.6% of Qwen3-VL's original performance while reducing its prefill latency by 44.7%. On LLaVA-OV-7B, GleanVID at a 25% retention ratio even slightly surpasses the original model.

Self-Distillation Fine-Tuning (SDFT) enables a language model to act as its own teacher: by conditioning on a demonstration, the model produces an implicit reward via pointwise mutual information, which guides on-policy learning without external supervision. However, SDFT operates at training time: it requires gradient updates and access to expert demonstrations, making it inapplicable at inference. We propose test-time self-distillation, a decoding-time method that extracts a steering signal from the self-distillation framework without any parameter updates, reward models, or training data. Our key insight is that counterfactual contexts, i.e. fixed textual templates that hypothetically prime the model for excellent versus poor reasoning, can substitute for the demonstration. The log-odds ratio of a candidate answer under these two counterfactual conditions defines a new reward signal. We derive the optimal KL-regularized policy under this reward, which takes the form of a Gibbs reweighting of the base distribution. Crucially, this reweighting is global: it cannot be decomposed into independent per-token operations without ignoring future trajectory quality. We therefore approximate the target distribution via beam search. Experiments on mathematical reasoning (MATH500), code generation (HumanEval), and graduate-level science QA (GPQA) across multiple model scales show that test-time self-distillation improves over standard sampling, low temperature, beam search and power sampling baselines on average, demonstrating that the self-distillation principle can be operationalized at inference time.

Precipitation nowcasting demands accurate short-term forecasts under strong spatiotemporal variability. Diffusion models are well suited to modeling complex precipitation distributions, yet existing approaches often introduce increasingly specialized designs, leaving the capability of a standard diffusion architecture underexplored. We show that a standard Diffusion Transformer already provides a simple and scalable foundation for precipitation nowcasting, with domain-specific requirements accommodated naturally within its design space. Based on this principle, we develop NowcastDiT and instantiate this flexibility through two complementary adaptations: a dynamics-aware noise prior for temporally coherent forecasts, and end-to-end reinforcement learning with timestep-aware rewards for meteorological skill. Experiments on SEVIR and MRMS benchmarks show that NowcastDiT achieves state-of-the-art performance in both perceptual quality and meteorological skill. These results suggest that standard DiT can serve as an effective foundation for precipitation nowcasting.

High-resolution dynamic functional connectivity (DFC) can reveal rapidly evolving brain-network interactions, but short temporal windows yield noisy, often low-rank covariance estimates. Graph-Variate Dynamic (GVD) connectivity addresses this by modulating fast instantaneous interactions with stable trial-level support. This suppresses spurious fluctuations and emphasizes persistent, informative connections. We show that the Hadamard construction lifts low-rank instantaneous connectivity from the positive-semidefinite to the positive-definite cone, keeping high-resolution trajectories on the SPD manifold without ridge regularisation or post-hoc projection. We introduce GVD-CFM, a class-conditional generative model for high-resolution dynamic connectivity. Each trial is represented as SPD GVD matrices on a product Riemannian manifold, then mapped through a global log-Euclidean diffeomorphism and an invertible temporal DCT basis. A Transformer-based conditional flow models all spectral modes jointly and generates the full trajectory non-autoregressively in Euclidean coordinates while preserving exact correspondence with valid SPD sequences. Retaining the full DCT basis also enables decoding on denser temporal grids without retraining. Across multiple EEG motor-imagery datasets, GVD-CFM delivers the strongest overall results for held-out distributional fidelity, temporal-dynamics preservation, and synthetic-to-real classification. It also remains computationally efficient relative to strong raw-signal and direct GVD-space generative baselines. GVD-CFM therefore provides a practical framework for realistic, temporally coherent, high-resolution brain-network generation with preserved manifold structure and resolution-flexible decoding from a single trained model.

Speculative decoding accelerates autoregressive inference by verifying multiple draft tokens in a single target forward pass. However, as the context grows, existing state-of-the-art drafters become increasingly expensive, eroding the very efficiency advantage they are designed to provide. We argue that this scaling is unnecessary. A standalone language model must grow with its prefix because it is solely responsible for every token it produces. A drafter, by contrast, only proposes candidates; the target catches and corrects every error before any token is committed. The drafter's decoding cost can therefore be made entirely independent of the prefix length. We introduce LongSpark, a block-diffusion drafter that achieves this by extracting fixed-size, multiscale views from the target's verification pass, thereby eliminating the need for a growing persistent state. Extensive evaluations demonstrate that LongSpark achieves state-of-the-art end-to-end efficiency across multiple model scales and realistic serving conditions. Notably, it delivers the lowest time-per-output-token on long-context tasks while reducing the drafter's context state by several orders of magnitude.

Knowledge Graph Embedding models have been extensively used to learn representations of entities and relations in Knowledge Graphs for predicting missing links. However, the quality of the learned representations varies a lot across different areas of the graph. If previous research has loosely linked the problem to relation types or degree bias, we show that it is more widespread and it correlates with the degree imbalance of the entities in test triples. In particular, the prediction of a target entity that has a degree much smaller than the degree of the anchor entity is extremely problematic. This is critical in recommender systems and other use cases, where these triples represent important corner cases. To address this issue, we propose an inference-time latent search optimization method capable of significantly improving model predictions on the most imbalanced triples. Built on top of a pre-trained model, it explores the embedding space at evaluation time, blending known and out-of-band information to mitigate the degree imbalance bias. We show the value of our approach on imbalanced triples from common benchmark datasets, where we outperform conventional methods, opening the door to the successful adoption of Knowledge Graph Embedding models on these critical corner cases.

The central challenge of world modeling is to learn representations that capture how the world evolves. However, existing world models predominantly represent future states without explicitly capturing the latent causes underlying their evolution, limiting their ability to reason about why and how the world changes. To address this limitation, we propose Abductive World Modeling (AWM), a framework that learns structured causal representations by abductively inferring latent causes from predicted futures. Specifically, we realize AWM through the Hierarchical Abductive State Pyramid (HASP), which organizes the inferred world state into three complementary components - Entity, Dynamic, and Relation - capturing what exists, how it changes, and how entities interact, respectively. By jointly reasoning over the current observation and its predicted future, HASP abductively infers these latent factors and integrates them into a structured state representation for downstream reasoning. To the best of our knowledge, AWM is the first framework to introduce abductive state inference into latent-space world modeling for learning structured representations of world dynamics. Experiments across physical prediction, causal reasoning, and action understanding demonstrate the effectiveness of our approach. Compared with V-JEPA, a state-of-the-art latent-space world model, AWM improves physical prediction AUROC by 10.7%, causal reasoning accuracy by 16.8%, and action Top-1 accuracy by 68.0%.

The Rashomon effect describes the existence of multiple near-optimal models that achieve comparable performance while offering fundamentally different explanations. This creates a critical vulnerability in AutoML: x-hacking, the selective post-hoc choice of a model based on its explanation rather than predictive merit. No existing AutoML framework exposes this risk. We introduce ARSA ML, an open-source Python framework that quantifies Rashomon set structure and predictive multiplicity within AutoML pipelines. Using ARSA ML, we benchmark AutoGluon and H2O across 28 binary classification datasets, and conduct a post-hoc x-hacking analysis revealing a consistent structural asymmetry: AutoGluon produces larger, diverse sets with stable explanations, while H2O generates compact sets with markedly higher prediction divergence and explanation instability – making H2O users considerably more exposed to x-hacking. This gap persists across all evaluated metrics and epsilon thresholds, pointing to a fundamental difference in each framework's model-building strategy. ARSA ML is available at https://pypi.org/project/arsa-ml/ .

Unsupervised tabular anomaly detection (TAD) aims to identify anomalous rows in tabular data using normal training samples. While conventional methods rely on dataset-specific training and configuration search, recent tabular foundation models (TFMs) enable zero-shot anomaly detection on unseen datasets via in-context learning. Most TFM-based approaches, however, require anomaly-specific pretraining from scratch, making detection inherently dependent on synthetic TAD-specific priors and costly to update. Some approaches instead repurpose pretrained general-purpose TFMs for TAD to avoid this burden, but rely on computationally expensive formulations with restrictive anomaly inductive biases. In this work, we introduce TaskBridge, a new framework that efficiently repurposes pretrained general-purpose TFMs for unsupervised TAD by constructing virtual supervised tasks that directly recast anomaly detection as supervised in-context inference of TFMs. The resulting virtual tasks induce predictive structures under which normal queries and their target pairs receive high support, whereas anomalies tend to violate the induced structures and receive lower support, providing direct anomaly evidence. Across 790 real-world datasets, TaskBridge consistently outperforms 30 baselines, including state-of-the-art TFM-based approaches, without anomaly-specific TFM pretraining or dataset-specific model optimization.

Covariate effects vary across contexts and shift over time, requiring forecasters to assess how to use them for each forecasting context. As forecasting proceeds, observations for earlier forecasts become available, providing feedback on past covariate use for subsequent forecasts. However, when multiple covariates act together, the forecast error reveals the numerical discrepancy from the observation but not how the covariates should have been used. We introduce JudgeCast, an experience-based framework for time series forecasting with covariates. Following the judgmental adjustment practice, a frozen TSFM provides the base forecast, while a frozen LLM uses the current context and relevant experience to adjust it. Within the adjustment, assessing covariate effects and determining the numerical adjustment serve distinct roles, so JudgeCast first forms explicit covariate-wise judgments and then determines the adjustment. After observation, JudgeCast uses the observed residual of the base forecast to reconstruct alternative judgments and evaluates the original and alternatives through their resulting adjustments. The best-performing decision is selected and retained as validated experience for subsequent forecasts. Across diverse real-world datasets, JudgeCast outperforms strong baselines. Ablations show that explicit covariate-wise judgment can improve forecast-time adjustment, while residual-guided experience construction yields more reliable forecasting gains than retaining raw decisions as experience.

Repeated verifier calls are useful only when they contribute conditional information. We introduce VStress, an auditable replay contract, and VStress-CA, a correlation-aware allocation policy that estimates the conditional marginal information of an unqueried verifier on a sealed calibration split, discounts uncertainty, normalizes by call cost, and stops or abstains when the next call is not informative. The controller freezes its decision and cost ledger before joining the clean oracle; a dependence-shift alarm disables channel preference and falls back to exact-stop. The controlled audit gives the mechanism boundary: at 35% symmetric corruption, majority-5 improves balanced accuracy from 0.6578 to 0.7739, whereas at 65% it loses 0.1226 points. In the matched fixed-budget comparison, breadth, redundancy, and adaptive allocation obtain balanced accuracies 0.6048, 0.6375, and 0.6538, with 3.4216 calls per item and an RLVR score of 0.6417 for VStress-CA. Dependence diagnostics also increase from same-model repeats to cross-family channels, with conditional marginal gains of 0.0126, 0.0462, and 0.0913. These measurements turn correlation from a post-hoc warning into an auditable allocation decision.

Production RL for language models lets the sampler fall behind the learner and repairs the resulting mismatch with a truncated importance weight. We ask how long the sampler can go without a refresh under that correction, and find a cliff: on Qwen2.5-Math-1.5B and GSM8K, importance-corrected GRPO refreshed every 192 updates learns well for 180 steps and then degrades severely in all three data seeds before the refresh arrives. Published remedies for staleness act on the update; we act on the sampler instead. Decoupled cooling draws samples at temperature 0.8 while the learner, the reference model and the importance weights stay at temperature 1, with the behaviour probability recorded from the tempered distribution, so the learner's objective is unchanged. All corresponding cooled runs are stable, and the longer interval keeps what the short one delivered: at the same update budget, a cooled sampler refreshed every 192 steps matches an uncooled sampler refreshed every 96 at the end of training (0.857 for both) and averaged over it (0.79), whereas lowering the learning rate to a safe value ends 3-7 points lower. On Qwen2.5-Math-7B the degradation points at interval 192 predict that an interval of 144 is fatal without cooling and survivable with it; on two data seeds the uncooled runs degrade before their first refresh and the cooled runs pass it and end at 92-93% against 68-81%, with one cooled run degrading transiently late in the second cycle. The benefit has a window: at three times the safe interval and in a high-mismatch MATH setting cooling delays degradation without preventing it, stronger cooling is not better, and cooling without the correction collapses. Sampling temperature is a control on staleness tolerance, and temperature and refresh interval should be chosen together.

Simulation-based inference is challenging when many heterogeneous observations must be composed, hierarchical latent structure must be preserved, and the simulator is misspecified relative to observed data. We develop sampling and fine-tuning methods for diffusion-based inference in design-conditional settings, where the same simulator is queried across different experimental conditions $\xi$. We extend compositional score-based inference with a continuous-time diffusion coefficient that accounts for the number of observations, avoiding Jacobian and auxiliary-covariance corrections. We introduce Hierarchical Blockwise Diffusion Sampling (HBDS), which infers shared parameters and group-specific latent states using a single pretrained model, with the hierarchy specified only at sampling time. Together, these methods support variable observation sets and groupings without retraining. To address misspecification, we introduce path-regularized fine-tuning that adapts the learned likelihood to observations and transfers corrections to posterior inference. Using Girsanov's theorem, we quantify path divergence between pretrained and fine-tuned models across experimental designs and interpret it alongside predictive errors to distinguish candidate misspecification correction from unnecessary adaptation. We evaluate compositional sampling on exact-score Gaussian and Simple Likelihood, Complex Posterior benchmarks, HBDS with analytic and learned scores on a controlled hierarchical model, and fine-tuning and localization on a separate analytic model with known design-dependent discrepancy. Finally, we apply the framework to 940 measurements across four cell lines in a mechanistic Bone Morphogenetic Protein signaling model, where fine-tuning improves posterior-predictive accuracy relative to the pretrained model and shifts posterior marginals toward the least-squares reference while retaining spread.

We study the learning dynamics of fine-tuning a policy model on self-generated and reward-weighted data, with particular focus on a generalized version of REINFORCE – referred to as RE(S) – that updates the rollout distribution once every $S \ge 1$ gradient steps. Prior work in bandits and reinforcement learning has developed rich theory for policy gradient methods, and on-policy sampling (i.e., a small $S$, ideally $1$) is often viewed as crucial to their success; yet in prominent application like post-training large language models, reward-guided self-training has proved to be effective even when the rollout distribution is updated infrequently, but theoretical understanding remains limited for the convergence properties of these off-policy methods. To bridge these gaps, we develop a unified theory for RE(S) that covers the full spectrum of $S \ge 1$: it can be interpreted as a stage-wise optimization process, where each stage takes $S$ gradient steps for minimizing the Kullback-Leibler distance to a fixed reward-weighted rollout distribution. For multi-arm bandits with softmax policies, our in-depth analysis and numerical experiments reveal three key findings: (1) for any fixed $S$, RE(S) enjoys global convergence to the optimal policy as the number of rollout distribution updates $B = \lfloor T / S \rfloor \rightarrow \infty$, where $T$ denotes the number of gradient steps; (2) we prove tight two-sided bounds showing that the suboptimality gap of RE(S) achieves an asymptotic $\Theta(1 / T)$ convergence rate, while $S$ only affects the length of a burn-in phase; (3) when initialized at a weak policy with a small optimal-action probability, RE(1) gets trapped around suboptimal policies for a long period, whereas RE(S) with a suitable $S$ avoids the detour and achieves significantly faster convergence to the global optimum, highlighting the benefits of off-policyness in this case.

Learning neural-network models of dynamical systems with safety guarantees is a fundamental requirement for their deployment in safety-critical settings. Safety is commonly established by proving the invariance of a desired subset in state-space, ensuring that every trajectory initialized in this subset remains confined to it for all time under admissible inputs. Existing frameworks, however, either rely on computationally expensive post-hoc verification or employ safety-enforcing mechanisms without formal correctness guarantees. In this paper, we introduce a novel neural architecture grounded in energy-based modern Hopfield networks to guarantee safety-by-design while retaining sufficient expressiveness to model complex nonlinear dynamics. Specifically, we integrate modern Hopfield networks with a port-Hamiltonian neural ODE, enabling by design the construction of barrier functions yielding explicit admissible-input sets and quantitative robustness radii. Across several benchmarks, including an 12-dimensional nanodrone model, our framework achieves state-of-the-art performance while producing certified invariant sets that are more robust to external solicitations than comparable existing approaches.

Recent power measurements provide valuable information for photovoltaic(PV) power forecasting, but directly extrapolating short-term trends can introduce substantial errors over longer forecast horizons. To address this challenge, we propose state transport routing (STR), a lightweight adapter that refines the predictions of a frozen forecasting model. STR combines the original forecast with two complementary trajectories derived from the latest measured power level and its recent trend. A horizon-conditioned router adjusts their contributions over the first 120 min, while leaving subsequent predictions unchanged. Experiments on four public PV datasets show that STR consistently outperforms a parameter-matched residual adapter. On PVDAQ, the same approach improves five neural forecasting backbones, reducing all-horizon normalized mean absolute error by 0.0201-0.2364 percentage points, with paired 95% confidence intervals excluding zero. No reliable improvement is observed for LightGBM. These findings demonstrate the potential of structured state adaptation to improve short-term forecasting across different neural architectures without retraining the underlying models or altering their longer-horizon predictions.

In this thesis I develop methods for statistical inference when the distributions arising from complex biological systems are multi-modal, geometrically structured, and sometimes only defined up to a normalizing constant. I start from variational inference and, when analytic update equations are unavailable, move to black-box variational inference. To build intuition regarding inference challenges and the proposed methodologies, I introduce a novel unnormalized target density (the CoLN distribution) and reuse it as a controlled test case in the kappa. I then trace a trajectory of increasingly expressive approximations: ensembles evaluated with the multiple importance sampling ELBO (Paper A) and variational mixtures that automate component cooperation and exploration (Paper B). Because expressivity comes at a cost, I develop efficient mixture learning ideas, including Monte Carlo objective estimators to scale mixture learning more efficiently (Paper C). As a new result in the kappa, I overturn a three decades long misconception regarding the potential performance benefits of using mixtures in variational inference. Finally, I move from variational inference to flow matching, where I address the need for specialized treatment of interpolant learning in multi-marginal settings (Paper D). By combining insights from Papers A-D, I derive in Section 5.5 a new method: multi-marginal flow matching with mixtures of variational interpolants. I connect these methodological developments to biological applications, with special emphasis on three-dimensional spatial transcriptomics, where stacked tissue slices induce multi-modal dynamics across space.

In scientific machine learning, physical fields governed by partial differential equations exhibit low-rank structure and scale invariance. When solving equations on coarse grids, missing information leads to the closure problem: modeling unresolved physics to recover lost dynamics. Although closure terms depend on grid resolution, they represent scale-invariant physical laws. A model truly learning physics should capture these mechanisms with low-rank parameterization rather than memorizing grid-specific patterns. Inspired by this, we propose the Scale-Invariant Neural Operator (SINO), which learns on normalized physical scales via a dual-branch architecture operating in spectral and spatial domains. SINO uses bottleneck MLPs to generate continuous convolution kernels, embedding an explicit low-rank inductive bias that concentrates more than 95 percent of variance in 2-3 modes, as validated by PCA across benchmarks, while drastically reducing parameters. This principled design yields 38 times steeper scaling law exponents than FNO, demonstrating superior parameter efficiency. We compare SINO with traditional models (U-Net, DeepONet), Transformer models (Transolver, Oformer, GK-Transformer), and frequency-domain models (FNO, AMFNO, UFNO) on closure problems spanning externally forced Burgers turbulence, decaying Burgers turbulence, KS turbulence, Kolmogorov-forced NS turbulence, and decaying NS turbulence. Experiments show SINO achieves 1.5-38 times error reduction and 2-23 times parameter efficiency over baselines, with superior scaling laws reflecting exceptional data efficiency from principled low-rank design. Code is available at https://github.com/AI4Science-WestlakeU/SINO.

RNA design aims to identify sequences that fold into specified secondary structures. Existing methods formulate the task as target-specific search or conditional generation. However, natural RNA evolution proceeds through sequence variation and selection, with compensatory substitutions, whereas these methods do not explicitly model this process. To address this limitation, we propose a two-stage framework comprising RNA Inverse-Folding Flow (RNA-IFlow) and RNA-IFlow-RL. RNA-IFlow uses structure-conditioned Dirichlet Flow Matching to model coordinated variation across the sequence, while RNA-IFlow-RL maps the learned flow to a pairing-preserving finite policy and refines it with thermodynamic feedback. Our framework achieves leading performance on multiple benchmarks, reaching 85.19% Pass@1 on Rfam-27. Further analyses reveal thermodynamic gains, policy dynamics, and robustness across settings. Our work couples coordinated variation with thermodynamic selection, offering a novel paradigm for RNA design.

Tabular foundation models (TFMs) are increasingly popular because they deliver strong predictions on new datasets through in-context learning, without task-specific training or extensive tuning. Yet released TFMs differ simultaneously in their pretraining priors, architectures, and objectives, obscuring their respective inductive biases. We therefore examine one concrete capability: irrelevant-feature suppression. Across synthetic tasks and real-world datasets, adding null features causes substantially greater predictive degradation in the row-token model TabDPT, whereas the cell-token alternating-axis model TabPFN v2 and other TFMs remain comparatively stable. This gap motivates us to ask whether architecture contributes to irrelevant-feature suppression. Because released TFMs remain confounded by other design choices, we train streamlined row-token and alternating-axis transformers under identical sparse-to-dense linear priors. Exact Bayes analysis shows that sparse prediction requires context-dependent feature gating, whereas the dense endpoint requires only uniform feature weighting. Consistent with this distinction, the alternating-axis model is substantially closer to the Bayesian optimal predictor on sparse tasks, while the architecture gap becomes negligible on dense tasks; almost all of the sparse gap arises from linear coefficient-estimation error. Finally, in both the controlled model and frozen TabPFN v2, we examine the effect of interventions on the feature-attention outputs on the linear coefficients, finding evidence of task-dependent selective routing of computation through feature-indexed pathways. Together, these results support architecture-prior alignment: preserving an addressable feature axis provides an inductive bias for task-adaptive relevance inference. Code is available at https://github.com/Tianqi-Zhao/ArchitecturePriorTFMs.

Causal foundation models (CFMs) pre-trained on data generated from various structural causal models (SCMs) have been proposed for estimating causal effects from observational data. However, differences in pre-training environments and evaluation protocols make it difficult to assess how their performance depends on the information available for causal identification. To enable controlled comparisons, we introduce CausalIDView, a multi-view benchmark that holds fixed SCM realization and target estimand while varying only the observational view available to the estimator. Each observational view corresponds to a distinct identification regime under the benchmark's maintained causal assumptions. Across these matched views, no CFM consistently performs best and model rankings vary substantially. Under controlled structural changes, CFMs exhibit model-specific failures to maintain stable estimates when true effects are unchanged and to track genuine effect changes. We also examine whether combining explicit identification with strong predictive estimation is effective. A modular approach that pairs a predictive tabular foundation model with regime-specific identification procedures is competitive with CFMs and outperforms several of them. These findings motivate cross-regime comparisons to assess the empirical value of CFMs.

Multivariate Time Series (MTS) clustering is an important tool in temporal data mining, aiming to discover latent group structures from complex observations without supervision. Although existing deep clustering methods can learn discriminative temporal representations, the resulting latent clusters are often difficult to relate back to waveform characteristics that practitioners can directly inspect and compare, limiting their ability to assess whether the discovered patterns reflect meaningful temporal behaviors. This paper, therefore, proposes WAVE (Waveform Aligned Visual-temporal Embedding), which treats time series and their deterministically rendered waveform plots as complementary views of the same observations. To produce discriminative representations whose cluster structures can be traced to observable waveform characteristics, WAVE aligns and integrates fine-grained temporal variations with holistic visual patterns, while associating each discovered cluster with its centroid-nearest authentic sample. Accordingly, interpretability in this work specifically refers to waveform-level traceability rather than a general explanation of model decisions. Extensive evaluations across 10 real-world public datasets show that WAVE achieves the highest macro-averaged clustering performance and the best average rank among the compared methods, while qualitative case studies illustrate how the discovered clusters can be inspected through authentic waveform records. The source code is available at https://github.com/Zheng-Zhu1/WAVE.

Group-relative methods for reinforcement learning with verifiable rewards (RLVR) learn from differences in rollout outcomes. Independently sampling complete trajectories is costly and does not explicitly explore the decision space at critical positions. Feedback on a completed trajectory can reveal which earlier choices the policy reconsiders, suggesting where to sample alternative continuations. We introduce Hindsight-Divergence Localization (HDL), which uses hindsight-induced changes in token log-likelihoods to select branch points. HDL generates a small number of complete root trajectories and fills each training group with continuations from the selected positions under the original task context. Each continuation reuses its root prefix and contributes policy updates only through its newly generated suffix, reducing generation cost while focusing additional exploration and learning on decisions after branching. Experiments with three models across math, code, and agent tasks show gains in both rollout efficiency and task performance. Compared with GRPO at matched group sizes and training steps, HDL yields up to a 2.5$\times$ reduction in generated tokens and a 1.8$\times$ speedup in rollout wall-clock time. Despite this reduced generation budget, HDL improves performance across all three domains, with gains of up to 12.5 points on agent tasks.