Papers

Inverse Optimal Transport (OT) based methods for representation learning learn representations such that the global OT coupling between a pair of data marginals in the representation space, concentrates on the positive pairs. This is in contrast to previous methods that primarily focused on pairwise matching. However, these methods $\textit{DO NOT}$ utilize negative pairs and hence are not truly contrastive in their approach. We show that this leads to issues of dimensional collapse and hence degraded downstream performance. To alleviate this, we develop a novel multi-marginal (MM) inverse OT (IOT) contrastive learning (CL) approach called Neg-MMIOT-CL, which learns representations such that the global multi-marginal OT (MMOT) coupling between a triple of data marginals, with respect to a carefully designed ground-cost between triplets of data points in the representation space, concentrates on the anchor-positive-negative $\textit{triplets}$. For a latent class model, we empirically show that Neg-MMIOT-CL alleviates dimensional collapse. Furthermore, for a specific choice of ground cost for all triplets in representation space, we prove that the optimal representation configuration for Neg-MMIOT-CL exhibits equiangular property for within-class and across-class representations, which translates to Neural-Collapse when the representation dimension is larger than the number of classes minus one – a result that is $\textit{previously established only}$ for pairwise contrastive learning methods. Finally, we propose Neg-IOT-CL-PushPull, that is a computationally efficient alternative to Neg-MMIOT-CL, alleviating the high cost of computing MMOT plans needed during implementation. We apply these methods on both synthetic and real-world datasets and show significant improvements over existing OT-based contrastive learning methods.

Estimating causal effects with continuous treatments in observational studies is challenging due to confounding, model misspecification, and high-dimensional covariates. We propose the Weighted Spline-Expanded Network (WSENet), an end-to-end neural framework that addresses these challenges by combining covariate balancing, structured treatment embedding, and bias-corrected outcome estimation. WSENet first applies Distance Covariate Optimal Weights to induce distributional independence between covariates and treatment without relying on parametric models. It then learns the conditional outcome via a structured network that fuses outcome-relevant representations of covariates with a spline-expanded treatment input, enabling smooth and flexible modeling of the dose-response relationship. To mitigate residual bias, we introduce Weighted Targeted Regularization, a correction technique based on efficient influence functions that yields a doubly robust estimator. Extensive evaluations on semi-synthetic and real-world datasets, including high-dimensional genomic and environmental health data, demonstrate that WSENet consistently outperforms existing baselines in both accuracy and stability.

Text-guided image editing aims to perform a desired edit while preserving source content unrelated to it. Pretrained rectified-flow models enable training-free editing of real images through modifications to their sampling trajectories. However, responses at locations unrelated to the desired edit can still accumulate along the editing trajectory and become visible in the final result. To overcome this, we propose Constrained Edit Fields (CEF), which assigns each spatial location a continuous edit responsibility that quantifies its relevance to the desired edit. CEF estimates edit responsibility directly from the source image when the relevant content is present. For edits whose target content is absent from the source, CEF first generates an unconstrained proposal to reveal its realized spatial support and then estimates responsibility from that proposal. At each editing step, CEF decomposes the base edit field into prompt-induced and trajectory-induced components, enabling edit responsibility to preserve instruction-relevant updates while suppressing unintended trajectory-induced changes. Evaluated on all 700 PIE-Bench examples, CEF achieves state-of-the-art Structure Distance, background LPIPS, and background MSE with both Stable Diffusion 3.5 Medium and FLUX, while retaining competitive instruction alignment. On Stable Diffusion 3.5 Medium, it reduces these metrics over the previous best results by 10.2%, 21.2%, and 48.0%, respectively.

Reliable world models should not only predict future states but express how actions change the world in an explicit, transparent and testable form, such as equations. Yet methods that rely on a fixed set of trajectories cannot distinguish equally good competing hypotheses, while searches over a fixed set of predefined candidates cannot discover equations outside the initial hypothesis space. We introduce ALDER (Action-guided Law Discovery, Evaluation, and Revision), a method that actively proposes novel experiments to test and revise models. Specifically, ALDER proposes parametric equations; a numerical optimizer fits their coefficients; an independent verifier tests these candidates on held-out data. To distinguish between competing valid hypotheses, a cost- and safety-aware selector queries interventions, in the form of novel experiments. The resulting counterexamples update the evidence ledger and guide the next structural revision, while incompatible laws are discarded. Across an in-house benchmark, ODE equation discovery tasks, and robotic experiments, ALDER discovers laws beyond its initial formula set, repairs failed model proposals, distinguishes fixed candidate models with fewer interactions, and improves out-of-distribution prediction. Furthermore, given a current state and a target, ALDER selects control actions by solving the inverse problem defined by its validated world model. Together, these results show that explicit equation-based world models can be tested and revised through interaction, then naturally used to guide goal-directed control.

Knowledge Distillation (KD) has emerged as a vital paradigm for transferring the capabilities of high-capacity models to efficient “student” counterparts, addressing critical challenges in computational cost, deployment constraints, and privacy-sensitive settings. Although KD is widely used in practice, it is often viewed primarily as an engineering technique, with a unified statistical perspective remaining less developed. This review bridges that gap by presenting a unified Bayesian formulation of KD that formulates teacher predictions as prior information. This provides a principled interpretation of how teacher information is incorporated into student learning and establishes a rigorous connection to uncertainty quantification. We demonstrate how this foundational lens reconciles classical distillation with modern extensions in generative and foundation-model systems, showing that contemporary developments remain rooted in these same statistical principles. By synthesizing theory with emerging methodologies and diverse applications, this review provides a conceptual roadmap and identifies critical open problems for the future of the field.

Continually adapting models to new tasks requires retaining earlier knowledge under limited memory and computation. Experience replay addresses this challenge, but priorities based on individual loss increases overlook how related memories respond to the same update and can overemphasize isolated responses. We introduce SPatial coHErent risk control for REplay (SPHERE), a general replay-allocation method applicable across a broad range of learning settings. SPHERE uses a representation kernel to aggregate signed prospective loss changes, attenuating unsupported spikes while retaining coherent increases. It then formulates allocation as entropy-regularized transport, redistributing uniform source mass toward supported high-risk regions while penalizing long-distance transfers. We derive replay coefficients from the transport objective's sensitivity to the original loss changes and blend them with uniform replay to maintain baseline rehearsal. Our analysis establishes conditions under which kernel aggregation improves risk estimation and bounds transport-value inflation due to residual noise and smoothing bias. Experiments demonstrate that SPHERE improves accuracy and reduces forgetting across noisy-label vision tasks, continual language-model instruction tuning, and code-generation reinforcement learning with incomplete test rewards.

Language models are increasingly used as proposal models for black-box search, from program optimization to molecular design. Existing approaches typically improve proposals through iterative prompting or parameter updates, offering limited control over how completely and efficiently the model's search space is explored. Continuous optimization methods, such as Bayesian optimization, provide a principled way to search but require a suitable domain to operate over. To address this, we introduce BOReFT, which learns a compact, low-dimensional space of hidden-state interventions in a frozen language model, and uses this space as the search domain for Bayesian optimization with an external scoring function. Empirically, we find that the learned domain spans semantic regions and exhibits smoothness properties that support search. Theoretically, we show that semantic coverage and interpolation control the best score available in the learned space, and that decoding from this space yields a standard stochastic-bandit observation model for adaptive search. We evaluate BOReFT on the interpretable word search task "Semantle" and on three more real-world discovery tasks in de novo molecule property optimization. Compared to strong LLM baselines, BOReFT finds in Semantle a higher number of hidden targets and, on two out of three molecular objectives, achieves higher property scores. Consequently, our method provides a principled new bridge between discrete proposal spaces of LLM-based search and continuous black-box optimization.

Accurate numerical solutions of partial differential equations (PDEs) are crucial in numerous science and engineering applications. In this work, we introduce a novel neural PDE solver named AFDONet, which incorporates neural operator learning and adaptive Fourier decomposition (AFD) theory for the first time into a specifically designed variational autoencoder (VAE) structure, to solve a general class of nonlinear PDEs on smooth manifolds. AFDONet is the first neural PDE solver whose architectural and component design is fully guided by an established mathematical framework (in this case, AFD theory), turning neural operator design from an art to a science. Thus, AFDONet also exhibits exceptional mathematical explainability and groundness, and enjoys several desired properties. Furthermore, AFDONet achieves outstanding solution accuracy and competitive computational efficiency in several benchmark problems. In particular, thanks to its deep connections with AFD theory, AFDONet shows superior performance in solving PDEs on i) arbitrary (Riemannian) manifolds, and ii) datasets with sharp gradients. Overall, this work presents a new paradigm for designing explainable neural operator frameworks.

On-policy distillation (OPD) trains a student on its own responses with token-level feedback from a stronger teacher, yet the teacher can fail on questions the student already answers correctly, and how often each model succeeds varies across tasks. OPD ignores these outcomes and, on average, pushes down even the student's correct responses; gating feedback by student correctness fixes the direction but uses the teacher in the same way whether or not it succeeded. We introduce DuoOPD, in which the student's outcome sets the direction of feedback and the joint teacher-student outcome decides how the teacher supports it: when only the teacher succeeds, its verified answer becomes context for scoring the student's failed response, and when only the student succeeds, a weight shared within the task reinforces the whole response. A single rule covers all four outcome combinations without task-specific settings. Across Qwen3 and Llama, DuoOPD outperforms all five baselines in mean macro accuracy, improving over OPD by 2.58 and 5.98 percentage points, and it also leads on two further task mixtures spanning scientific calculation, instruction following, and code generation. Ablations show that outcome-based direction alone stays near the gated baseline, while the joint-outcome designs supply most of the gain.

How does compositional reasoning emerge during learning? We address this question by mathematically analyzing the learning dynamics of deep linear networks. We train these networks in structured synthetic environments and derive a theory linking the structure of experience to compositional learning. Our theory predicts when compositional inferences emerge, whether they are identifiable from the available evidence, and how new linking evidence can rapidly unlock previously unavailable inferences. These results provide a qualitative explanation for several phenomena observed in human cognition. They account for why a composition can fail despite knowing its premises, why similar compositions can emerge at different times, and how a single linking fact can suddenly enable many new inferences. Taken together, these findings establish a mathematical link between the statistical structure of experience and the development of compositional reasoning.

Graph learning from edge-detecting queries concerns the reconstruction of an unknown edge set on a known vertex set. Each query reports whether a specified vertex subset contains at least one edge. We study non-adaptive schemes, in which all queries are fixed before any outcomes are observed, with the goal of achieving exact recovery using few queries and fast decoding. For general graphs on $n$ vertices with at most $k$ edges, non-adaptive recovery requires $\Omega(\min\{k^2\log n,n^2\})$ queries in the worst case, even when a small error probability is allowed. In this paper, we consider Erdős–Rényi ($\mathrm{ER}$) graphs $G\sim \mathrm{ER}(n,q)$, with expected edge count $\bar{k}=q\binom{n}{2}$. Our scheme uses $O(\bar{k}\log n)$ queries and achieves exact recovery in $O(\bar{k}\log n)$ decoding time with probability tending to one throughout the regime $\bar{k}\to\infty$ and $\bar{k}=o(n^2)$. This improves the previous $O(\bar{k}^{1+\delta}\log n)$ decoding guarantee for any fixed $\delta>0$, while maintaining the same query order. The guarantee also extends beyond the previously studied regime $\bar{k}=\Theta(n^{2\theta})$ with fixed $\theta\in(0,1)$. Our approach builds on the binary splitting method used in prior work, which organizes vertices into a hierarchy of successively smaller groups. We introduce three main changes: (i) we use random affine hash functions over a finite field to process each candidate pair in constant time; (ii) we apply the splitting procedure directly to the full graph, avoiding the need to combine solutions to multiple smaller graph-learning subproblems; and (iii) we bound the total decoding workload directly rather than deriving separate high-probability bounds on candidate counts at each level.

Pretrained biomedical vision-language models achieve strong zero-shot performance in biomedical image classification. However, downstream biomedical classification often depends on subtle visual differences between classes that may not be fully captured by pretrained representations. Few-shot adaptation addresses this mismatch by optimizing a task-specific predictor on a small labeled support set. Because the selected examples capture only part of the visual variation within the target classes, the adapted predictions can depend strongly on their composition. We propose Prompt-Anchored Residual Adaptation (PARA), which retains the frozen prompt prediction as a support-invariant semantic anchor and incorporates a visual prediction learned from the support set through an anchor-relative residual. The residual step is computed in a closed form from frozen support embeddings using anchor discrepancy and support agreement. Support-set dependence also limits evaluation: comparisons are fair within a shared draw but remain conditional on its composition. To obtain more reliable comparisons, we introduce a repeated-support protocol that separates support-selection variation from optimization randomness and reports both average and worst-20% performance. PARA achieves state-of-the-art performance in both few-shot classification and base-to-novel generalization.

Decoding signals over unknown channels with minimal pilot overhead is a critical challenge in next-generation communications. Existing deep learning approaches typically rely on generic encoders that struggle to model long-range temporal dependencies or efficiently capture the channel's physical properties from scarce data. We argue that standard architectures suffer from agnostic estimation gaps, as they must implicitly learn the constellation geometry that is already known. We introduce the Constellation-Aware Transformer (CAT), a novel architecture that explicitly injects geometric inductive biases into the equalization process. CAT is composed of a stack of custom TransFIRmer blocks, which use an "early interaction" paradigm to co-process received signals and ideal constellation symbols. Each block features a split Feed-Forward Network that applies a Finite Impulse Response (FIR)-inspired filter for deconvolution and a parallel MLP for geometric refinement. We show that this design is structurally aligned with the optimal linear (MIMO Wiener) receiver: its attention can implement a matched-filter bank, and its bidirectional FIR branch provides the non-causal filtering that block MMSE equalization requires. In the semi-supervised setting, CAT needs fewer pilots than VAE and standard Transformer baselines: on two of our three ISI channels, it reaches a lower SER with 64 pilots than they do with 128.

Learning PDE operators on complex domains requires capturing interactions among fields on vertices, edges, and faces, alongside global responses shaped by topology. Existing neural operators accommodate irregular geometries but often overlook these distinct field supports or their condition-dependent coupling. We introduce the Dynamic Kuramoto–Hodge Operator (DKHO), which combines topology-constrained interactions with learned coordination. DKHO encodes conditions on their native cochain supports, evolves Kuramoto-inspired relation states through the boundary and coboundary operators that compose the Dirac operator, and decodes non-harmonic and harmonic responses in orthogonal Hodge subspaces. Topology thus determines where information can flow, while learned dynamics adapts how it is exchanged to each PDE instance. Across porous-medium Darcy flow, torus transport–diffusion, and cavity magnetostatics, DKHO-large reduces prediction error by approximately 61% on average over leading baselines, while DKHO-small remains competitive using only 11.5–24.3% as many parameters. These results suggest that coupling topological structure with adaptive dynamics provides an effective inductive bias for accurate and parameter-efficient PDE operator learning on complex geometries and topologies.

Deep learning has emerged as an efficient alternative for predicting high-performance material distributions in topology optimization. Existing methods struggle to accurately capture load-transfer information, limiting out-of-distribution generalization, while their model architectures often incur high computational costs. To address these challenges, this paper proposes TopoMamba, a topology prediction framework incorporating a load-support relation-guided multi-directional state-space model. Coupling physical fields with load-support relations enables more effective modeling of mechanical dependencies. A load-support relation-guided spatially adaptive fusion mechanism dynamically adjusts multi-directional scan features according to spatial conditions. Mamba is coupled with the solid isotropic material with penalty method to enhance structural mechanical performance while maintaining computational efficiency. Results on two-dimensional topology optimization benchmarks demonstrate that TopoMamba achieves superior topology prediction accuracy, out-of-distribution generalization, and computational efficiency over state-of-the-art models. The proposed load-support physics-guided framework enables efficient optimization of more complex structural systems.

Artificial Intelligence (AI) models for temporal multimodal data have potential in healthcare and agriculture, but their opacity can limit trust and adoption. We introduce T-MoXAI (Temporal Multimodal eXplainable AI), a hierarchical framework explaining (1) when timepoints influence predictions, using temporal Shapley values; (2) which modalities contribute at those moments, using attention analysis; and (3) what features or image regions drive decisions, using gradient based attribution. A transformer based architecture handles irregular temporal sequences and heterogeneous data, generating all three explanation levels in under one second for interactive decision support. We evaluate the framework on two real world tasks: predicting IVF treatment outcomes from ultrasound sequences and clinical measurements (AUC 0.660 despite significant class imbalance), and forecasting wheat yield from temporal RGB imagery and phenotypic traits ($R^2$ 0.265 amid substantial environmental variability). Ablation studies indicate that temporal modelling is critical in both domains: removing it reduces performance to the equivalent of random guessing. Temporal ROAR experiments provide evidence that the explanations reflect the model's reasoning process. With a unified, domain agnostic architecture and open source implementation, T-MoXAI provides a baseline for temporal multimodal XAI, addressing fragmentation in the field and supporting applications where understanding decisions is as important as predictive accuracy.

Understanding why predictors can generalize despite interpolating noisy training data is a central puzzle in machine learning. Most work on such "benign overfitting" studies minimum-2-norm linear regression, reflecting the inductive bias of gradient descent. However, modern optimizers such as Adam and Muon use non-Euclidean update geometries, favoring solutions associated with other norms. Analyzing regression for non-Euclidean norms is substantially more difficult, with known results essentially limited to Gaussians. In this paper, we develop a method to analyze benign overfitting in linear regression for general norms and general (sub-Gaussian) distributions. As a special case, we prove that minimum-p-norm interpolation with p>1 can benignly overfit even for non-Gaussian distributions, under suitable conditions. Perhaps surprisingly, for the 1-norm, benign overfitting does not hold in general for well-behaved (but non-Gaussian) distributions, showing that existing positive 1-norm results rely crucially on Gaussianity. Our proof analyzes the geometry of the dual optimization problem, using concentration and central limit tools to show it is approximately Euclidean in many high-dimensional cases.

Graph neural networks (GNNs) are often called long-range because their architecture can connect distant nodes, but this does not show whether they use distant information correctly. We introduce a framework that measures how strongly inputs at each graph distance affect predictions and separates limitations due to architecture, finite approximation, training, and numerical execution. Our analysis shows that local message-passing can spread influence slowly, so a finite implementation may rely mainly on nearby inputs even when the ideal computation uses the whole graph. We also explain why mathematically equivalent filters can differ in how easily they are learned and how reliably they run. Across controlled tasks, models with similar architectural reach use distant information very differently, while low average error can hide failures on distant interactions. Together, these results show that long-range capability depends on learning to use information at the distances required by the task and preserving that use during computation.

When must a foundation-model safety gateway generate tokens, and when should it directly output a calibrated decision? We study calibrated standalone direct-decision foundation models for real-time pre-ingestion safety guardrails, jointly addressing probability calibration, dual-use false-positive control, and heterogeneous CPU-NPU routing under explicit latency SLOs. Pre-ingestion guardrails must screen prompts prior to target-LLM prefill with low false alarms on benign compliance inquiries; however, shallow classifiers are brittle to phrasing shifts, hidden-state probes require coupling to a target LLM, and generative guards incur high decoding latency and dual-use false positives. We present COGNIT-Guard, coupling a validation-calibrated CPU fast gatekeeper with confidence-gated escalation to an NPU-resident 322M bidirectional direct-decision model (Laya-322M) under an asymmetric false-positive penalty. On the clean unseen DUCS-Bench test split ($N=607$), COGNIT-Guard achieves 98.85% accuracy (McNemar $p = 1.19 \times 10^{-4}$ vs. ML), reduces benign FPR to 0.42% ($1/238$; Fisher's exact $p = 8.23 \times 10^{-4}$ vs. ML), and attains 1.12% ECE and 0.0104 Brier score. On Huawei Ascend 910C NPUs, pure NPU inference runs in 21.77 ms mean latency (45.90 QPS), while the live serial CPU-NPU cascade ($\theta^*_{\mathrm{deploy}}=0.70$) achieves 41.63 ms mean latency (P50: 39.47 ms, 99.23% accuracy, 0.00% FPR). Evaluation on SafetyBench-ZH ($N=2,100$) and comparison against a bi-encoder direct-decision baseline (CLM-8B) disentangle in-domain gains, OOD alignment tax (60.33% $\to$ 56.81% on Laya; 55.10% on domain CLM-8B), and experience replay recovery, restoring OOD accuracy to 64.10%-65.05% and reaching 99.67%-99.84% in-domain accuracy with 0.00%-0.42% FPR.

Residual policy adaptation provides a lightweight way to modify a strong reference policy, but a shared scale and a fixed subgroup partition can hide heterogeneous degradation and become fragile when the deployment mixture of information states changes. We introduce RSD-Poker, a structure-adaptive and shift-robust certification framework that freezes a bank of residual families and scales, learns a policy-visible partition on an independent structure split, and freezes that partition before calibration labels are joined. Each candidate-group pair receives a weighted simultaneous upper certificate for anchor-relative risk and a lower certificate for weak-response utility. A robust group-to-candidate map is then selected over a predeclared uncertainty set of deployment group proportions. Under independent calibration units drawn from each frozen group's law, a candidate bank and partition fixed before calibration, and invariant within-group conditionals, the selected map satisfies its declared mixture-robust risk budget and utility certificate with probability at least $1-\zeta_{risk}-\zeta_{util}$. The information contract supports both a teacher-backed transform and a teacher-free observation-only student. The retained deterministic 24-state audit remains an exact replay diagnostic: empirical-zero selects $\alpha=0.08$, raising the weak-response proxy from 4.2082 to 4.2889 with $0/12$ held-out threshold crossings. On stratified held-out states, the learned-partition dual selector raises weak utility from 4.4074 under global dual certification to 4.4936 and lowers held-out violation from 0.0215 to 0.0078; its mixture-robust variant reaches violation 0.0059. Across five observation-only checkpoints, risk-calibrated residuals attain weak utility $4.3659\pm0.0177$ and violation rate $0.0178\pm0.0057$.

Attributing and controlling model behavior during training requires identifying each example's contribution quickly enough to act before the next update. However, examples in the same training batch can produce similar behavioral changes, making their individual contributions difficult to distinguish. We address this ambiguity through mutual information, accounting for interference within the batch by quantifying how much the combined behavioral change reveals about each example's contribution. We show that this mutual information is a logarithmic function of Behavioral Gradient Uniqueness (BGU). BGU gives the information measure its geometric interpretation. Our Batch-Space Ghost (BS-Ghost) algorithm makes these scores practical inside the training loop through shared computation in batch space, without storing model-sized example gradients. On a complete 1,000-example Qwen2.5-7B-Instruct workload, our BS-Ghost implementation adds 27 seconds (8.0%) to 5.5 minutes of ordinary training. Removal and retraining demonstrate that BGU identifies data that causally shapes final behavior. At each training step, signed information identifies which examples strengthen or weaken the target behavior, explaining how behavior develops during training. Signed information also enables cheap intervention during training: it predicts how changing example weights will affect behavior in the next update. We then use these predictions to choose weights that steer behavior toward a desired target. This makes our framework a practical foundation for scalable oversight and verification of training pipelines and processes, helping evaluators assess model alignment, understand how it develops during training, and guide interventions that shape ongoing learning.

Discovering underlying symmetries from data has emerged as a crucial challenge in scientific discovery. Existing data-driven methods for symmetry discovery fail to determine the exact number and mathematical form of unknown infinitesimal generators. Recent explicit methods represent generators using a predefined function library and identify them through algebraic optimization, but they often struggle to capture complex symmetries involving high-order polynomials or transcendental functions. To address this limitation, we formulate symmetry discovery as a joint optimization problem over the function library and coefficients. We propose a novel framework that leverages an encoder-decoder architecture to dynamically generate symbolic expressions and expand the library. This generation process is optimized via reinforcement learning, which accelerates the exploration of the symbolic search space through step-wise rewards. Experiments demonstrate that LieDiscover can successfully uncover open-form infinitesimal generators involving high-order polynomials or transcendental functions, which remain intractable for existing methods. The discovered symmetries also improve performance in downstream PDE solving and discovery tasks.

Imperfect verifiers can assign a harmful update direction even when clipping and regularization bound its magnitude. We introduce Audit-First VAPO, which separates discrete directional admission from continuous magnitude control. An observation-only accept-appeal-abstain policy uses a finite secondary-verification budget; its action trace is frozen before clean labels are joined. Simultaneous finite-sample bounds then certify selected harmful risk, coverage, and verifier-call rate over a predeclared policy family. Conditional Hoeffding-Azuma bounds account for the dependence induced by shared budgets, and rollout or verifier changes initiate a new certification stage. After admission, a bounded trust-clip-KL actuator controls magnitude. We evaluate two models on two reasoning benchmarks against static RLVR, matched-random selection, confidence thresholding, noise correction, and verifier augmentation. On Qwen3.5-0.8B and GSM8K at target risk $\rho=0.08$, RC-VAPO achieves 74.1% accuracy, selected harmful risk 0.0697, coverage 0.4125, and relative verifier cost $1.16\times$. At matched coverage and update magnitude, its selected-risk difference from matched random is -0.0260 with paired 95% interval $[-0.0364,-0.0157]$. Across asymmetric, confidence-dependent, and correlated-verifier noise, the certificate is satisfied on 57 of 60 independent runs. These comparisons isolate informative directional selection from proposal suppression, update shrinkage, and additional verifier computation.

Curriculum learning has found broad application across numerous domains. Nevertheless, its effectiveness is intrinsically curtailed by catastrophic forgetting, driven by the shifts in model parameter distributions between curriculum tasks. In this paper, we investigate the phenomenon of catastrophic forgetting in this training paradigm, building on the established efficacy of curriculum learning. Our theoretical analyses of parameter update dynamics demonstrate that catastrophic forgetting in curriculum learning stems from the divergence of task optima, which is generally essential to the faster convergence of curriculum learning; therefore, forgetting cannot be completely eliminated. Based on this finding, we augment the training process and propose IV-EWC, which incorporates Elastic Weight Consolidation (EWC) into the curriculum learning objective to curb catastrophic forgetting in mathematical reasoning, a prototypical curriculum learning scenario. IV-EWC employs the influence function to construct a representative validation set from the curriculum's training data, which is used to drive dynamic regularization during training. We further present an extended theoretical analysis to show that EWC-based regularization methods mitigate catastrophic forgetting in curriculum learning, thereby providing theoretical support for IV-EWC. Empirical evaluations on three backbone models and three benchmarks indicate that curriculum learning exhibits catastrophic forgetting. IV-EWC alleviates this issue, reducing forgetting by 162% on average relative to vanilla curriculum learning and yielding positive backward transfer, as evidenced by improved performance on easier tasks after subsequent training on challenging tasks.

Reinforcement learning (RL) enables generalist robot policies to improve through trial-and-error interaction, yet its effectiveness is fundamentally constrained by sparse task rewards. Existing general-purpose reward models typically alleviate this issue by learning task progress from expert demonstrations, but introduce a distribution mismatch with the mixed-quality rollouts encountered during policy optimization, making their estimates unreliable on suboptimal and failed behaviors from which the policy must learn. In this work, we introduce a demonstration-free reward learning paradigm where dense reward feedback can be learned directly from sparse task outcomes and policy experience. We theoretically show that terminal task outcomes implicitly define dense success-probability feedback at intermediate timesteps, which can be recursively learned through bootstrapping. Based on this insight, we introduce eVTA$_0$, which learns success probabilities from mixed-quality policy rollouts through temporal-difference-style bootstrapping, without expert demonstrations or intermediate annotations. We further introduce RL with Evolving Rewards (RLER), a closed-loop framework that adapts eVTA$_0$ using newly collected rollouts as the policy evolves. Experiments show that eVTA$_0$ provides more informative rewards than state-of-the-art reward models and achieves the best average policy performance across all LIBERO task suites under the same RL training budget, improving success rates by 5.4%-13.8% over the initial policy. In real-world manipulation, RLER further improves overall success rates by 20%-26%, with 35%-36% gains under out-of-distribution conditions. These results demonstrate the effectiveness of demonstration-free reward learning and adapting rewards as the policy evolves. Project webpage: https://duowuyms.github.io/evta0.

Word-level forced alignment estimates when each transcript word occurs in an audio recording. It underpins text-based media editing, subtitling, speech-data curation, and phonetic analysis. Existing evaluations understate the difficulty of forced alignment by relying on short, clean speech, perfect transcripts, and metrics that obscure consequential alignment errors. In contrast, real-world media and data-processing pipelines operate on long and diverse recordings. Additionally, forced aligners often operate on error-prone automatic speech recognition (ASR) output. We address these gaps with improved evaluation metrics, a scoring protocol for real ASR transcripts, and AlignBench, a benchmark spanning diverse speaker, acoustic, and text conditions. We further introduce FuseAlign, a transformer-based aligner trained on large-scale pseudo-labeled speech with online label correction. FuseAlign performs joint contextualization of audio and text for the localization of coarse words. The model then refines boundaries at millisecond resolution and detects missing transcript words in the audio without lexicon-based or Viterbi decoding. On AlignBench, FuseAlign substantially outperforms all baselines and remains robust under real ASR transcripts. Ablations show that convolutional upsampling and EMA-snapshot label correction matter more than model properties such as parameter count.

Learning mappings between probability distributions arises naturally when inputs and outputs are represented by populations of samples rather than individual observations. We develop an approximation-theoretic framework for distribution-to-distribution learning and extend it to mappings between stochastic processes. For continuous operators on $W_2$-compact families of finite-dimensional probability laws, we establish uniform neural approximation in the 2-Wasserstein metric using finite law statistics, a simplex-valued neural map, and a shared atomic output support that guarantees valid probability measures. We further extend this principle to probability laws on separable Hilbert spaces through finite-rank orthogonal projections. These results establish the representational feasibility of learning transformations between probability laws rather than deterministic vectors or functions. To demonstrate practical relevance, we study two problems naturally defined at the distribution level: prediction of first-passage-time distributions for an Ornstein–Uhlenbeck process and nonlinear response-path laws of a Duffing oscillator. Because the theory is model-agnostic and broader than any single practical architecture, the experiments use task-adapted neural models rather than reproducing the theoretical construction exactly. In both problems, the proposed models outperform a fixed-feature MLP baseline and distribution-space kernel regression. These experiments complement the theory by demonstrating the practical learnability of distribution-to-distribution transformations in random systems.

Several businesses apply maintenance, repair, and overhaul (MRO) principles to the life-cycle of their existing products. In cases like casted gas turbine component Product Lifecycle Management (PLM), repairing components in frequent intervals can extend the lifetime expectation of the product, provide higher cost efficiency compared to newly produced components, and even improve the part design during the repair cycle. Another aspect of repair concerns sustainability, as products often contain rare materials. The emissions produced by the repair process are usually smaller than mining materials and casting new components. To optimize the repair process further, we propose the Smart Expert System (SES), which assists engineering experts with machine learning-based decision support throughout the repair process. We elaborate on its IT architecture and present machine learning models employed for representative MRO use cases. The SES is evaluated using actual industry data from a leading gas turbine company and demonstrably fulfills formulated requirements concerning the suitability of the overall decision support and the stability of the enclosing IT architecture.

Molecular multimodal models support diverse understanding and generation tasks but may introduce safety vulnerabilities when handling hazardous molecules. In this work, We reveal substantial jailbreak vulnerabilities under both text-only and graph-conditioned settings. Our analysis further shows that safety robustness must hold across input modalities while balancing safety, over-refusal, and utility. To address these challenges, we construct SafeMolBench, a molecular multimodal safety-alignment benchmark with 3702 samples covering 618 unique hazardous molecules and safe molecular tasks, organized into hazardous-harmful, hazardous-allowed, and utility-replay subsets to support unified training and evaluation of safety, over-refusal, and utility. Based on SafeMolBench, we propose SafeMol, a parameter-efficient safety alignment framework that jointly optimizes lightweight modules across text-only and graph-conditioned inputs, uses MMD for distribution-level representation alignment to reduce modality-induced discrepancies, and explicitly models molecular hazardousness and harmful operational intent. Experiments on SafeMolBench show that SafeMol reduces attack success by several tens of percentage points while largely maintaining low over-refusal and preserving molecular-task utility.

We introduce RareTrap, a framework for estimating the probability of severe behaviors in black box large language models (LLMs). A key challenge for probability estimation is defining a tractable distribution over the input space. To accomplish that, RareTrap uses a surrogate LLM and constructs a geometry-aware mapping from a lower-dimensional latent reference space into its token-embedding space to induce an explicit and reproducible distribution over input prompts. A response-level performance function is utilized on the response to quantify behavior severity. This enables sequential rare event simulation that concentrates evaluations on progressively more severe behaviors while preserving probability under the induced prompt distribution, which would otherwise be prohibitive to measure. Across 10 open-weight and two frontier models (GPT-5.4 and Claude Sonnet 4.6), we find that RareTrap successfully induces severe resource consumption behaviors and computes their probability with as few as 200 evaluations. RareTrap provides model developers a principled approach for evaluating language models under a common distribution, and prioritizing alignment effort to improve safety and mitigate risks.