Papers

A growing number of applications, such as biometrics and retrieval-augmented generation (RAG), rely on cosine similarity scores computed between vector embeddings of text, images, or audio. These systems return similarity scores through their APIs for ranking and verification. However, such releases can leak information about individual records and enable membership inference attacks. While differential privacy (DP) provides a principled metric for quantifying attack risks, naïve application of DP mechanisms—such as adding i.i.d. Gaussian noise to vector entries—leads to excessive distortion (i.e., low utility) at a given privacy constraint that scales poorly with the number of released scores. We propose ScoreShield, a perturb-then-project mechanism that adds Gaussian noise calibrated to global sensitivity of the chosen score release regime and then projects the result onto the feasibility set of valid cosine objects. ScoreShield satisfies $(\varepsilon,\delta)$-DP for releasing similarity score vectors and Gram matrices. We provide utility guarantees for the exact Frobenius metric projection used in the risk analysis, and prove convergence to feasibility for the practical averaged alternating-projection solver used for large-scale Gram releases. For full pairwise cosine Gram release under record-level replacement adjacency, the exact-projection bound improves the $n$-dependence of squared Frobenius risk from $\Theta(n^3)$ for the naïve Gaussian baseline to $\mathcal{O}(n^2)$ for fixed privacy parameters, with sharper local bounds at low-rank Grams. We evaluate the mechanism across RAG, face recognition, semantic retrieval, image similarity, and recommender-system tasks.

In this work, we present a simulation-based parameter estimation framework for a model defined by a computational simulation of a physical system. We specifically outline an estimation framework consisting of two closely-integrated steps that facilitate an overall end-to-end parameter estimation scheme. The first step involves utilizing an embedded normalizing flow which is used to transform the unknown complex distribution of the residual information into a simple base distribution corresponding to the transformed residual information. In the second step, an empirical-likelihood estimator, under moment restrictions, is utilized for imposing an indirect constrain on the base distribution, where such an instantiated task reasonably allows us to treat the transformed residual information as random variables arising from discretely distribution population with each transformed data point as a single-cell from a set of finite-cell contingencies. Moreover, we use first-order gradient methods for updating the estimated parameter values of the model defined by the computational simulation and the corresponding parametrized embedded normalizing flow, that call for all gradient-related information by leveraging implicitly differentiations of the empirical-likelihood function, which is constructed from the implied empirical probabilities under moment restrictions. Here, it is worth mentioning that the problem formulation presented in this work, which highlights an information-theoretic interpretation, allows to present a computational framework for algorithmic implementations. Finally, as a-by-product, the inverse of the parametrized embedded normalizing flow, w.r.t. the estimated parameter values, serves as a surrogate model for the computational simulation model, which provides useful information for quantifying model discrepancies and sensitivity analysis.

Large language model (LLM) cascades reduce inference cost by routing easy queries to a small model and deferring hard queries to a larger one. Production cascades govern this deferral through a confidence threshold, but LLM confidence scores are miscalibrated, the threshold must be tuned per model pair and per domain, and no setting yields a formal bound on cascade accuracy. We introduce Conformal Cascade (CC), a multi-tier inference framework that uses conformal prediction set size as the deferral rule: accept when the calibrated set collapses to a single answer, defer otherwise. The procedure delivers a distribution-free, finite-sample accuracy guarantee. By a per-tier union bound, the prediction set at the accepting tier covers the correct answer with probability at least $1 - K\alpha$ for any user-specified $\alpha$; under a selection-preservation condition (consistent with, but not strictly implied by, our marginal coverage results), the bound tightens to $1 - \alpha$. We further characterise expected cascade cost as an explicit function of $\alpha$ and the calibration-set acceptance rate. Across 18 multiple-choice benchmarks spanning science, medicine, commonsense, and standardized exams, evaluated on two-tier cascades drawn from four open-weight model families, CC strictly improves over the strongest calibration-tuned heuristic cascade on the majority of family–benchmark pairs, with the largest gains on reasoning-heavy benchmarks where majority vote is unreliable; on easier benchmarks the cascade commits the vast majority of queries to the small model at no accuracy cost. Extension to open-ended generation requires an answer-clustering step that we leave for future work. The method requires no model training and only black-box API access.

Neural networks are hindered by accumulating dormant neurons and loss of expressivity throughout training, particularly in non-stationary data settings, such as continual supervised and reinforcement learning. Recently, neuron resets have been used to maintain gradient flow and restore plasticity. However, full unit reinitialization often sacrifices peak performance and can destabilize training, leading to policy collapse. To preserve plasticity without destabilizing training, we propose Calibrated Partial Resets (CPR), an optimizer that periodically pulls low-utility neurons toward their initialization, with pull strength scaled by each neuron's utility. Unlike binary reset methods, partial resets avoid brittleness; unlike uniform decay, calibrated utility-scaling concentrates adjustment on the units that need it most. Among compared methods, only CPR avoids policy collapse over 400M training steps in SlipperyAnt, and it outperforms prior decay and reset-based methods on Continual MetaWorld and Continual MinAtar benchmarks. Ablations reveal a tunable trade-off between plasticity and peak performance, highlighting utility-scaled reinitialization as a promising direction for continual learning.

In recent years, the number of events in earthquake catalogs has significantly increased due to the utilization of more effective deep learning based detectors and phase pickers but answering open ended questions such as what characterizes this sequence? remains constrained by rigid spatiotemporal windowing and subjective expert interpretation. We present the first systematic application of graph based retrieval augmented generation GraphRAG directly to raw, tabular catalog records across three independently featured catalogs, a reservoir adjacent swarm, the 2019 Ridgecrest tectonic sequence, and the 2021 Maduo Mw7.4 aftershock sequence. Without the need for manual data structuring, the pipeline builds structurally complete, queryable knowledge graphs for all three. Rigorous evaluation individually verified against catalog derived ground truth and a rule based reference graph exposes failure modes, and four seismology informed prompt fixes eliminate all targeted fabrications while sharply improving mechanism reasoning. A vector RAG baseline demonstrates the graph layers distinctive value, catalog wide summarization and temporal stage comparison. In addition, we have identified two main pitfalls that need attention. GraphRAG thus offers a practical, transferable, near zero cost query interface for earthquake catalogs, where careful prompting ensures the results are consistently accurate and trustworthy.

Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data. We propose Generative Distributionally Robust Optimization (GDRO), a principled framework that accepts any sampleable conditional generator as the nominal model and restricts worst-case laws to a chosen conditional generator family. The key is the sampler-Sinkhorn pairing: samplers represent the conditional laws exactly, while Sinkhorn divergence compares their induced distributions without likelihood access and can be estimated from samples alone. The resulting population problem admits a direct finite-sample approximation and differentiable primal-dual implementation at the active decision context. For Lipschitz losses, the population Sinkhorn radius bounds downstream degradation. Across explicit and implicit generators, our method reduces rare-context inventory regret by 60% and SocialGAN navigation collisions by 50% relative to nominal decisions.

We present a neural network surrogate model that emulates the NRSur7dq4 gravitational waveform model for precessing binary black hole mergers. The surrogate decomposes the waveform into constituent quantities and trains an independent multilayer perceptron (MLP) for each. We validate the surrogate against NRSur7dq4 on 10,000 waveforms spanning its full parameter space ($1 \leq q \leq 4$, $|\chi_{A,B}| \leq 0.8$). For representative total masses between 60 and 300 $M_\odot$, median sky-averaged frequency-domain mismatches range from $8.0 \times 10^{-5}$ to $1.7 \times 10^{-4}$, with 95th percentiles below $10^{-3}$. On an NVIDIA L40S GPU the JAX surrogate evaluates a single waveform in about 1 ms end-to-end, roughly 10 times faster than the LALSimulation C implementation of NRSur7dq4, and sustains about 140 times the LALSimulation throughput at batch size 64, making it well suited for both low-latency parameter-estimation samplers and large-scale waveform generation. The full NRSur7dq4 NN waveform-to-likelihood pipeline is implemented in JAX and is differentiable. This is the first neural-network surrogate of a precessing numerical-relativity waveform model to combine validated NR-faithful accuracy with a fully differentiable, GPU-accelerated inference pipeline, enabling gradient-based inference approaches via automatic differentiation including Fisher information matrices, GPU-accelerated nested sampling, gradient-based MCMC and importance sampling.

Differentiable simulation can accelerate contact-rich trajectory optimisation by exposing local sensitivities of task outcomes to controls. Existing approaches either use finite differences, which are expensive and step-size sensitive; differentiate iterative contact solvers by unrolling automatic differentiation (AD), which stores a growing computation trace; or require intricate, solver-specific KKT sensitivity derivations. We introduce an AD-assisted implicit derivative for regularised smooth contacts and apply it to Mujoco MJX, based on the Implicit Function Theorem (IFT). The method differentiates the stationarity residual at the tolerance-converged solution, avoiding both solver unrolling and hand-assembled KKT systems. IFT keeps compiled temporary memory nearly constant with solver effort, changing by less than 4$\%$ from one to ten iterations versus 10.6$\times$ growth for unrolled AD. IFT memory grows slower with active contacts and model dimension, using 20$\times$ less memory at 256 contacts and 6$\times$ less at 16 contacts and 96 DoF. We further introduce optimiser distillation for residual MPC, amortising batched full-horizon iLQR into a policy that guides short-horizon residual iLQR. Across Finger, Franka, and Unitree, this raises six-step success by 28-98 percentage points over standard iLQR.

Reducing training precision is a key lever for improving the e ciency of large language model (LLM) training, but pushing beyond FP8 to 4-bit oating point (FP4) remains challenging due to instability during optimization. We identify a fundamental source of this instability in existing microscaling approaches: scale inconsistency induced by tensor transposition. In conventional 1D block quantization, forward and backward passes assign di erent scaling factors to the same values after transposition, leading to biased and unstable gradient updates. To address this issue, we propose a low-precision training framework based on 2D block FP4 quantization, which enforces transposition-invariant scaling and preserves consistency between forward and backward computations. We further combine this with truncation-free scaling and stochastic rounding to control quantization error and maintain unbiased gradients. To handle the sensitivity of attention mechanisms, we adopt MXFP8 quantization for query and key projections, yielding a practical mixed-precision design. We evaluate our method on dense LLMs up to 7B parameters and a 30B Mixture-of-Experts model, trained on up to 100B tokens. Across all settings, our approach achieves stable end-to-end FP4 training and closely matches BF16 performance, with less than 1.3% degradation in perplexity and downstream accuracy. These results demonstrate that enforcing forwardbackward scaling consistency is su cient to enable practical FP4 training at scale, providing a simple and e ective pathway toward more e cient LLM training.

In many classification problems, reliable instance-level labels are unavailable. However, it is often possible to construct weakly enriched unlabeled samples: datasets selected by different cuts, sources, populations, or experimental conditions that change latent class proportions without revealing them. Classification without Labels (CWoLa) shows that, in the binary case ($K=2$), a classifier trained to distinguish two impure mixtures with different class proportions can recover an optimal class discriminator without knowing the mixture proportions. We extend this principle to multiclass learning from several unlabeled mixtures ($K>2$), where the learner observes only mixture identity and neither latent class labels nor class-prior matrices. We prove that, for a multiclass mixture model, the Bayes-optimal mixture classifier $g^\star$ maps data points into a $(K-1)$-simplex embedded in mixture-posterior space. The $K$ vertices of this simplex are induced by the latent classes through the unknown mixing matrix. Leveraging this geometry, we propose prior-free procedures that train a standard classifier to distinguish mixture identities and then extract latent class structure using either post-hoc simplex fitting or a bottleneck architecture. Experiments on MNIST, CIFAR-10, and Galaxy10 DECaLS show that mixture identity alone can recover latent classes and their fractions in the mixture. By narrowing the gap between weakly supervised and fully supervised performance, we provide a mathematically grounded, scalable tool for multiclass discovery in label-scarce domains.

Providing a practical and hadron-level definition of multiple jet flavors has been a long-standing challenge in collider physics. Previous work has introduced a data-driven, operational definition of quark and gluon jets, but no robust generalization beyond two jet categories presently exists. To address this, we introduce a machine-learning framework called "simplex demixing” to extract $T$ jet flavors (or topics in the statistics literature) from $M$ data samples (or mixtures) with minimal constraints. Intuitively, our procedure identifies the maximally separable categories in the data, translating a multi-category classifier on the $M$ mixtures into a bounded geometric object with $T$ vertices. We first demonstrate our procedure on a toy problem to infer the truth-level fractions of down-quark, up-quark, and gluon jets from synthetic mixtures of the three pure samples. We then propose a tag-and-probe strategy to extract multiple light-flavor categories in a more realistic collider setting involving dijet production. As expected, the identifiability of jet flavors depends on their relative abundance in the samples and the hadron-level information available to the classifier architecture. Our work opens the door to data-driven extractions of multiple jet flavor properties at the Large Hadron Collider.

Language model alignment aims to make model behavior reflect desirable properties such as helpfulness, safety, and instruction following. Existing methods draw supervision from expert demonstrations, preference judgments, or verifiable outcomes. Demonstrations typically guide supervised fine-tuning (SFT), while preference judgments and verifiers provide rewards for reinforcement learning (RL). This raises a question: can the demonstrations alone be used to derive an explicit, interpretable reward useful in a post-training pipeline? Motivated by inverse reinforcement learning, we introduce Projected Alignment Reward Estimated from Demonstrations (PARED). PARED learns an explicit reward from expert demonstrations over a small set of response-level features, using a lightweight discriminator that separates demonstrations from the policy's own samples in this feature space. Experiments with inference-time reranking and adversarial on-policy RL show improvements both when starting from a base model without an SFT stage and when further optimizing an SFT-trained model. Additionally, we demonstrate that PARED can be used for contextual alignment, in which a single policy learns to adapt its responses to the preferences of different audiences.

Text-conditioned time-series forecasting predicts a series from both its numerical history and natural-language context, allowing forecasts to account for events and constraints that the past alone cannot reveal. This requires both reliable numerical forecasting and the ability to interpret contextual information. Time-series foundation models (TSFMs) provide strong numerical forecasts, while large language models (LLMs) can reason over text, but combining their strengths remains challenging because asking an LLM to generate or revise forecast values directly can distort the temporal structure captured by the TSFM. We instead formulate forecasting as a planning problem over TSFM-generated trajectories. The frozen TSFM acts as a simulator that proposes numerical continuations, while the LLM acts as a policy and value function that guides candidate selection and evaluates completed trajectories against the context. We instantiate this as \rc{} (LLM As Forecasting Planner), a training-free framework that bridges the modality gap without retraining either model, using Monte Carlo tree search (MCTS) over the forecast horizon with a Ranker LLM as policy and a Judge LLM as value function. Experiments on Context-is-Key and Time-MMD across two TSFM backbones (Chronos and TimesFM) and four LLMs show that \rc{} delivers consistent improvements across model choices, supporting sequential search as an effective training-free approach to text-conditioned forecasting.

Language model agents can now construct complete financial models, but it remains unclear whether they have learned the financial judgment that gives those models meaning. Existing benchmarks often anchor correctness to an expert-authored solution (e.g., numerical targets or detailed rubrics) which introduces a implicit assumption: one expert solution can serve as ground truth. This is appropriate when finance provides a unique answer, but not when judgment is required. Evidence from professional practice challenges this assumption: When financial models built by different analysts for the same company are graded against one another, the median score is only 0.33 under standard tolerances, revealing that single-reference grading confounds professional disagreement with error. We therefore introduce GAUGE, a benchmark that decomposes financial-model evaluation into deterministic checks, rubric judgments and numerical rules. Built from 1,001 professional valuation spanning 922 companies and all 25 GICS industry groups, GAUGE checks mechanical properties deterministically and evaluates judgment-bearing quantities against ranges in professional practice. We then validate GAUGE as a measurement instrument by testing expertise ordering, held-out professional values, and robustness to LM judgements. Our findings show that current LM agents are far better at constructing financial models than at deriving the company-specific assumptions that drive valuation, a gap that even persists after fine-tuning.

Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data. We study this problem for function-preserving residual expansion and introduce the effective alignment dimension, a measurable quantity describing the signal-noise geometry of activation gradients. By deriving the exact mean and variance of the inner product between independently estimated training and test gradients, we obtain a finite-sample upper bound on misalignment probability. The bound depends only on the effective alignment dimension and an effective sample size, requiring finite second moments and a nonzero population gradient, without covariance spectral assumptions or prescribed width-growth rates. We integrate this certificate into the train-test residual-expansion framework, yielding a high-probability condition for test-risk improvement. Experiments across width-controlled LLaMA-style Transformers, Pythia, and ResNet-20 show that wider models exhibit larger effective alignment dimensions and lower empirical misalignment. Direct residual interventions confirm that the alignment statistic predicts the sign and magnitude of held-out loss changes.

Predicting traffic flow is crucial to optimizing transportation systems and improving urban mobility. Many graph convolution-based models have been proposed to extract spatial-temporal features and predict traffic flow. However, most focus on spatial-temporal and semantic correlation in topological relationships. There are two primary problems to address. Firstly, the convolutional structure in the model focuses on utilizing static spatial dependencies and spatial-temporal relationships in topological structures, while neglecting the different information propagation delays between adjacent nodes in the convolution. Secondly, these methods often stack a large number of complex structures, resulting in a substantial increase in computational time during the model training phase, thereby disregarding the model's requirements for timeliness. In this paper, we propose a novel network called the Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN). We design a spatial-temporal fusion block to extract the spatial-temporal feature correlations with propagation delay errors removed and to capture both long-term and short-term temporal characteristics of the data within a multi-head self-attention mechanism based on a mask matrix. Extensive experiments on five real-world datasets demonstrate that our method achieves the best overall performance while having good computation and data utilization efficiency compared with the eight baseline methods.

Repository-level code generation relies on heterogeneous evidence whose relevance, compatibility, and completeness are inherently uncertain. Similar-code examples, repository context, and project-specific APIs may provide complementary information, but can also introduce noisy, redundant, or conflicting signals. Existing retrieval-augmented approaches primarily optimize retrieval relevance without explicitly modeling how uncertainty in retrieved evidence affects downstream generation. We introduce OpenCoder, an uncertainty-aware framework that estimates source-specific uncertainty, uses it to filter and rank heterogeneous evidence, and guides generation, verification, and repair. A factorial analysis over API knowledge, repository context, and similar-code evidence reveals no universal additive source ranking; instead, significant cross-source interactions depend on the accompanying evidence and LLM backend. On an expanded 32-task RepoExec-inline evaluation, OpenCoder improves GPT selected-output correctness over Baseline RAG from 56.25% to 78.13%. However, it matches a verification-and-repair control, and the corresponding Gemini improvement is not statistically supported, indicating backend-dependent benefits. Target-aware API refinement also substantially improves API-set retrieval. These findings support treating uncertainty as an actionable control signal for repository-level retrieval, verification, and repair.

As system complexity has vastly increased, it has become significantly more challenging for a single person or a team to fully understand all aspects of an entire system. Particularly, this holds when considering all the different stages of a system's development life cycle, such as, e.g., design or maintenance. But especially for safety-critical systems it is essential that the final design can be trusted. Because of this, explainability is becoming an important requirement for modern systems. In this paper, we aim to achieve this goal by utilizing Behavior-Driven Development (BDD), where the expected system behavior is given in the form of structured scenarios. These scenarios give a sequence of actions for each functionality, and by this can be directly translated into explanations. We introduce this method of deriving explanations based on the specification as Behavior-Driven Explainability (BDX). While applicable at any development stage or abstraction level, a case study for the explanation of exceptions in a RISC-V processor shows the support this concept adds during system design.

Task-agnostic tabular embeddings are increasingly used for similarity search in real-world business systems such as Product Lifecycle Management (PLM). However, leading embedding approaches are optimized primarily for prediction tasks - not for producing human preference aligned similarity rankings. We argue that standard downstream metrics are insufficient to fully assess embedding trustworthiness for similarity search and that human preference aligned evaluation is a necessary and currently missing component. We present a concrete evaluation procedure and illustrate the problem through a PLM use case.

Phenotype-driven diagnostic benchmarks usually report the rank of the reference disease, but they rarely reveal which plausible alternatives are ranked above it or what evidence a tool-using model examines before making its decision. We introduce GraphRareBench, a provenance-preserving benchmark containing 2,365 ontology-derived cases and 18,093 target-confounder pairs. Each case includes a coarsened HPO query, a fixed candidate pool, graph-defined hard confounders, and source-linked evidence records. On the 237-case gene-component-disjoint test split, supervised rankers using a shared 21-feature interface achieved MRRs ranging from 0.640 to 0.740 and case-averaged target-over-confounder accuracies ranging from 0.898 to 0.916. Agents instantiated with Agents-A1 and DeepSeek-V4-Flash achieved MRRs of 0.746 and 0.718, respectively. Their paired MRR difference was not statistically significant, whereas their target-evidence coverage differed by 0.561. Together with the observation that 22.1% to 43.7% of selected Hit@10 successes still ranked at least one graph-defined hard confounder above the target, these results indicate that full-pool retrieval, hard-confounder discrimination, and observable evidence access capture complementary aspects of model behavior. GraphRareBench therefore provides a foundation for more transparent and evidence-aware evaluation of phenotype-driven diagnostic systems. Code and data are available at https://github.com/GUI0609/GraphRareBench.

Large language models (LLMs) can synthesize financial narratives but may express high confidence when evidence is sparse, stale, or contradictory. This failure is especially consequential in forecasting, where filings, news, prices, volume, and technical signals can disagree. We present FinAbstain, a research framework for uncertainty-calibrated multimodal retrieval-augmented generation (RAG) with selective prediction. A point-in-time retriever admits only information public at the forecast timestamp and supplies modality-specific evidence to fundamental, news, technical, risk, and verification agents. Their probabilistic assessments are aggregated with retrieval relevance, evidence contradiction, repeated-sample consistency, and historical calibration statistics. Temperature scaling, isotonic regression, conformal prediction, and a proposed hybrid uncertainty score are evaluated under a common chronological protocol. A controller predicts bullish, bearish, or neutral outcomes only when uncertainty is below a validated threshold; otherwise it abstains, requests evidence, reduces exposure, or routes the case to human review. The evaluation covers one- and five-day abnormal-return direction, twenty-day volatility intervals, and abstention decisions, using accuracy, calibration, risk–coverage, citation, trading, latency, and cost metrics. To make the design auditable before a full data collection is complete, we report explicitly labeled simulated results rather than empirical claims. These results illustrate the intended hypothesis: calibrated abstention may trade coverage for lower selective error and drawdown. The contribution is a time-safe architecture, a composite uncertainty formulation, and a reproducible evaluation blueprint for evidence-grounded selective financial forecasting.

Fast entropic optimal transport backends reduce the cost of each Sinkhorn update, but static batches still run at full width until the slowest problem finishes. We introduce DrainSinkhorn, a verifier-gated active-packing layer for batches of independent Sinkhorn problems. It combines candidate-axis packing, a Sinkhorn-specific one-sided screen, verifier-gated retirement under the backend's configured two-sided residual check, and physical compaction of all candidate-indexed state. The EOT objective, per-instance Sinkhorn map, and stopping rule are unchanged; later kernels run only on unfinished problems. We characterize the removable work exactly. If completion depths differ within a packed window, active execution removes the padding between the static batch rectangle and the observed survival curve. A quotient nonlinear Perron-Frobenius analysis gives a local explanation for these finite-tolerance depth differences: convergence depends on the full modal spectrum and proposal alignment, not only on the slowest mode. DrainSinkhorn achieves state-of-the-art execution performance on the tested heterogeneous batched-EOT workloads within matched backend families. The complete Flash-backed OT path is 4.110x faster on MetroPT-3, 3.798x faster on ImageNet-32 feature couplings, and 1.250-1.270x faster across a five-tolerance Packer19 sweep. Independent implementations reach 2.600x on ImageNet-32 with OTT-JAX, 3.174x on A2D2 LiDAR with PyKeOps, and 1.415x on large ImageNet-32 PyKeOps couplings. End-to-end speedups remain 4.074x on MetroPT-3 and 2.786x on ImageNet-32 feature-space OT flow matching, with all reported residual, consumer-output, and training-quality checks passing.

Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples. The goal is to learn an unknown distribution $p$ on a finite domain $[n]$. The learner is given a fixed family of queryable sets $\mathscr{S} \subseteq 2^{[n]}$, and each query to $S \in \mathscr{S}$ returns an independent sample from the conditional distribution $p(\cdot \mid S)$. Learnability is governed by the co-occurrence graph associated with $\mathscr{S}$: two domain elements are adjacent if they appear together in some queryable set. Pointwise consistency is achievable when this graph is connected on the target support. PAC learning requires more: it is possible when the co-occurrence graph is complete. The optimal sample complexity of PAC learning ranges from nearly linear to quadratic. Every query family with complete co-occurrence graph admits sample complexity $\widetilde O(n^2/\epsilon^2)$, and this bound is tight in the worst case. On the other hand, if $[n]$ is queryable then ordinary sampling improves the bound to $\Theta(n/\epsilon^2)$, and this cannot be improved further even if every set is queryable. More generally, we identify hierarchical comparabilityas a sufficient structural condition on $\mathscr S$ under which the optimal complexity is nearly linear, $\widetilde \Theta(n/\epsilon^2)$, with pairwise query families as a canonical example. Finally, the full range of polynomial rates between linear and quadratic is attainable: for every $\alpha \in (1,2)$, there exists a query family with optimal PAC rate $\widetilde \Theta(n^\alpha/\epsilon^2)$.

On-policy distillation (OPD) adapts diffusion models by querying a teacher along trajectories generated by the current student, but how it should behave under classifier-free guidance (CFG), a default component of modern diffusion systems, remains poorly understood. Existing OPD methods naturally extend velocity matching to the CFG-composed prediction, directly matching teacher and student guided velocities. We show that this objective is under-identified at the branch level: positive- and negative-branch errors can compensate in the guided prediction. Through two contrasting cases, we find that naive matching remains effective under shared negative conditioning, where both branch errors decrease jointly. When the model's native CFG schema retains privileged information in the teacher's negative branch that is unavailable to the student, however, this joint reduction breaks down and the composed objective induces antagonistic branch-error dynamics, reducing the positive-branch error while increasing the negative-branch error. We term this failure mode Negative Branch Asymmetry (NBA). To address NBA, we introduce Positive–Direction Matching (PDM), a branch-aware OPD objective that separately constrains the positive prediction and the CFG conditional direction. We apply PDM to dense-to-sparse video control, where naive guided matching is highly sensitive to inference guidance scales, while branch-aware supervision enables more robust and effective knowledge transfer.

The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing field of scientific machine learning. In these methods, a neural network is trained to approximate the PDE solution by using (stochastic) gradient descent to minimize the PDE residual of the neural network. Due to the non-convexity of the PDE residual objective function, the trained neural network may, in principle, only converge to a local minimizer of the objective function (which would not be a solution of the PDE). Therefore, there is a longstanding question regarding the mathematical foundations of these algorithms, and it is highly valuable to establish that the trained neural network will converge to the PDE solution. In this paper, we consider a class of semilinear PDEs with nonlinearities in the solution and its first derivative. For this class of PDEs, we prove that neural networks trained with gradient descent to minimize the PDE residual objective function will converge to the PDE solution as the network width and training time $\rightarrow \infty$.

Multi-turn long-horizon planning is critical for foundation model agents, yet how to fundamentally improve it remains unclear. Existing models are trained on uncontrollable and opaque Internet data, making it difficult to identify how planning ability is acquired, shaped, and integrated. To address this challenge, we introduce a unified and controlled multi-turn environment that enables precise control. It allows systematically study long-horizon planning across three stages. (1) Planning ability acquisition during pre-training. We study data format, distribution, and quality. Explicit world model construction through CoT state transition modeling yields stronger long-horizon generalization. Atomic skills alone are insufficient for compositional generalization, whereas a litte long-horizon data works. Moreover, suboptimal trajectories severely impair performance because errors amplify over long horizons. (2) Planning ability shaping via GRPO and OPD post-training. Through mutual information, we distinguish general planning patterns from task-specific planning knowledge. For planning patterns, we identify three application regions of post-training: unnecessary, effective, and unsupported. OPD has a broader effective region than GRPO under low-quality and long-horizon settings, as it provides more consistent update directions. For planning knowledge, distilling unseen procedures from a teacher with different knowledge may impair student's prior world modeling without fully establishing new knowledge. (3) Planning ability integration through MOPD post-training. We show that multi-teacher on-policy distillation (MOPD) integrates capabilities by converging to shared planning-pattern across environments. Compatible patterns enable cross-environment generalization, partially shared patterns support continual learning, while completely conflicting patterns cause severe interference.

Entity matching identifies records that refer to the same real-world entity. Language models can be adapted to this task through bi-encoder, cross-encoder, and generative matcher architectures. However, prior studies often conflate matcher architecture with differences in model backbone, model variant(reflecting different pretraining objectives), and model size, making it difficult to isolate the sources of performance gains. We address this issue through a controlled factorial study spanning three matcher architectures, three model variants and three model sizes from the Qwen3 family, and nine datasets, totaling 1,215 fine-tuning runs. We also evaluate cross-dataset transferability and computational cost. Our results show that model variant is critical for bi-encoders: embedding-oriented variants provide stronger initialization and more favorable representation geometry predictive of downstream matching performance. Cross-encoders retain a consistent advantage over bi-encoders because they jointly encode record pairs rather than representing each record independently, although larger models partially narrow this gap. Generative matchers do not universally outperform cross-encoders. Instead, their advantages concentrate under distribution shift, including subtle unseen differences in record schemas and cross-dataset transfer. We further find that larger models rely more heavily on shortcut learning and therefore do not necessarily perform better. These findings clarify the factors underlying performance differences across matcher architectures and motivate future research and benchmark designs that better disentangle architectural choices from model-level factors while explicitly evaluating distribution shift and cross-dataset transferability. We release our experimental results, code, training scripts, and evaluation data at https://github.com/Jantory/llm-trained-matcher.

Variational quantum circuits have been central to many proposed near-term applications of quantum computing, but a growing body of evidence suggests that trainability and quantum advantage are fundamentally at odds: ansätze expressive enough to resist efficient classical simulation tend to exhibit barren plateaus, while structures that provably rule out barren plateaus typically render them classically simulable. We propose a stacked linear combination of unitaries (S-LCU) as a variational ansatz which provides a tunable trade-off between barren plateaus and classical simulability. Using a diagrammatic analysis, we bound the loss-landscape variance of the Free Fermion S-LCU, whose elements are fermionic Gaussian unitaries. We prove a variance lower bound of $\Omega(1/(n k^{3l}))$, with a simulation cost of $O(k^{2l} n^3)$ using the best known classical algorithm, compared to a quantum gate complexity of only $O(lkn^2)$. The number of layers $l$ serves as a single dial that trades computational complexity against the rate of cost concentration. This offers practitioners a systematic method for constructing ansätze with a complexity-trainability trade-off that best suits their application and hardware.

Multi-modal classification leverages complementary information across diverse data sources to enhance predictive performance. However, real-world scenarios subject to operational constraints, such as sensor failures or privacy restrictions, lead to inconsistent modality availability between training and inference times. To handle missing modalities, prior studies have mainly covered bimodal data setups and focused on designing robust fusion processes. Instead, we adopt a multi-modal co-learning framework that prioritizes inter-modal collaboration rather than multi-modal fusion. Specifically, we consider that any subset of modalities may be absent, without assuming predefined missing-modality patterns, an inference scenario we refer to as missing arbitrary modalities. To address this challenge, we introduce two alternative approaches that leverage information at both feature- and decision-level. Experiments on two multi-modal classification benchmarks demonstrate significant robustness gains in various missing modality conditions. The first method shows more robust behavior under minimal missing conditions, where a single modality is absent, whereas the second performs better under extreme missing conditions, where all-but-one modalities are missing. Our code is available at https://github.com/fmenat/Co4Miss.

We describe Causal-TS, an open-source Python library for causal discovery in high-dimensional and nonstationary multivariate time series. Causal-TS provides four specialized algorithms-CDNOTS, CDNOTS+, CEDAR, and GRACE-along with wrappers for GES, Granger, LASSO-VAR, and LGES, all sharing a unified conditional independence (CI) test layer with GPU acceleration via PyTorch. A regime discovery pipeline detects structural breaks via pluggable changepoint detectors and runs discovery per regime with regime-specific parameters. A command-line interface, synthetic data generators, and optional DoWhy integration provide an end-to-end pipeline from raw time series to causal effect estimates. The library is pip-installable, tested on Python 3.10–3.12, and available at https://github.com/bloomberg/causal-ts.