Papers

We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and consistent topological signature of grokking: a sharp increase in both the maximum and total persistence of first homology ($H_1$). Persistence diagrams reveal the emergence of a dominant long-lived topological feature together with increasingly structured secondary features, reflecting the underlying cyclic structure of the task. Compared to existing spectral and geometric diagnostics – specifically, Fourier analysis and local intrinsic dimension – persistent homology provides a unified geometric and topological characterization of representation learning, capturing both local and global multi-scale structure. Ablations across data regimes and control settings show that these topological transitions are tied to generalization rather than memorization. Our results suggest that persistent homology offers a principled and interpretable framework for analyzing how neural networks internalize latent structure during training.

LLM cascades, in which a cheap model defers to an expensive one on low-confidence queries, are widely used to reduce inference cost. Given a pool of models, a practitioner must decide how many models to include and where to set each deferral threshold. We derive first-order optimality conditions showing that, at an optimum, the ratio of expected accuracy gain to expected downstream cost is equal across deferral boundaries. A local search based on these conditions closely matches exhaustive search. We also derive an identity that decomposes the accuracy gain of score-based escalation over random escalation into two AUROC terms. Across five benchmarks and nine deferral scores, with model sequences and thresholds optimized from a pool of eight models, two-model cascades improve mean test-set accuracy over single-model selection by 2.1 to 8.2 percentage points. However, allowing more than two models does not improve mean test-set accuracy in 118 of 135 comparisons across scorers, datasets, and depth caps, and adds at most 0.43 percentage points. To understand the role of deferral scores in depth gains, we conduct counterfactual experiments with simulated confidence scores. When these scores have high AUROC and reflect only whether the current model answered correctly, allowing more than two models improves test-set accuracy on four of five benchmarks. However, these gains do not persist when the scores also reflect query difficulty shared across models, even at the same AUROC. These results suggest that gains from additional depth depend on how well the confidence score separates correct from incorrect answers for the current model compared with later models.

Continuous post-deployment compliance audits, mandated by emerging regulations such as the EU AI Act and Digital Services Act, create a class of strategic gaming distinct from the one-shot input/output gaming studied in prior work. Regulated systems can delay outcome reporting, drift their reports within plausible noise envelopes, exploit longitudinal sample attrition, and cherry-pick among ambiguous metric definitions. We formalize continuous auditing as a $T$-round Stackelberg game between an auditor that commits to a temporal policy and an adaptive auditee, and identify a structural feature of any noise-aware static-auditor design: a cover regime in which coverage gaps and granularity gaps cannot be closed simultaneously. We make this formal as Observation 1 and show that two minimal extension policies, each derived from the observation, close the regime along orthogonal axes: a sample-size-aware static rule (Periodic-with-floor) closes the granularity-failure case, while a history-conditioned suspicion-escalation policy closes the coverage-failure case for the naive Drift strategy – and neither closes both, exactly as the observation predicts; an audit-aware OffAuditDrift strategy that exploits Stackelberg commitment defeats both. To support empirical study we contribute a non-additive harm decomposition (welfare loss $W$, coverage loss $C$) that exposes how attrition shifts harm from the regulator-accountable surface to a regulator-invisible one; an initial library of five auditee strategies (Delay, Drift, Cherry-pick, Attrition, OffAuditDrift) and five auditor policies, calibrated to summary statistics from published audits of the DSA Transparency Database; and a reproducible simulator with a small, extensible Python interface.

The training data of large language models (LLMs) comprises a wide range of biomedical literature, reflecting data from many different patient populations. We investigate how it might be possible to recover information on correlation and causal links between patient characteristics, as a key building block for medical decision making. To avoid the pitfalls of direct elicitation, we propose an approach based on structured comparison questions, specifically patient comparison triplet questions. This is combined with a statistical model for the LLM representation that provides estimates of correlations without access to activations or model internals. Intuitively, we consider how similarity decisions of LLMs based on a first variable are affected by providing information on a second variable for one of the patients being assessed. We then induce prompt-level environment shifts to obtain correlation estimates for different subpopulations, which enables an invariant causal prediction (ICP) approach to obtain conservative candidate parent links. We demonstrate the method in two clinical domains, chronic obstructive pulmonary disease (COPD) and multiple sclerosis (MS). Across prompted environments, the elicited correlations are smooth, stable, and clinically interpretable, yet vary in a statistically significant way that supports downstream invariance testing, such that ICP provides a small set of candidate invariant parent links. These results show that indirect elicitation via triplet comparisons can recover meaningful association structure from LLMs and offer a cautious route from implicit correlations to causal statements that are congruent with LLM answering patterns.

Tool-using large language model (LLM) agents are increasingly deployed in settings where their reliable behavior is governed by strict procedural manuals. Ensuring that such agents comply with the rules from these manuals is challenging, as they are typically written for humans in natural language while agent behavior manifests as an execution trace of tool calls. Existing evaluations of LLM agents rely on manually constructed benchmarks or LLM-based judges, which either do not scale or lack reliability for complex, long-horizon manuals. To overcome these limitations, we present MANTRA, a framework for automatically synthesizing machine-checkable compliance benchmarks from natural-language manuals and tool schemas. MANTRA independently generates (i) a symbolic world model capturing procedural dependencies, and (ii) a set of trace-level compliance checks for a given task, and validates their consistency using SMT solving. A structured repair loop resolves inconsistencies, requiring human intervention only as a fallback. %This yields benchmarks that are formally validated. Importantly, MANTRA supports arbitrary domains and long procedural manuals, and provides a tunable notion of task complexity which is utilized to automatically derive challenging tasks accompanying compliance checks. Using MANTRA, we build a new benchmark suite with 285 tasks across 6 domains scaling to 50+ page manuals with minimal human effort. Empirically, we show that the compliance checks are richer with stronger constraint enforcement compared to existing benchmarks. Additionally, the granularity of the checks can be used for debugging the agents' failure modes. These results demonstrate that combining automated benchmark generation with formally grounded validation methods enables scalable and reliable benchmarking of tool-using agents.

Cocoa (Theobroma cacao) is a critical cash crop for millions of smallholder farmers in West Africa, where Cocoa Swollen Shoot Virus Disease (CSSVD) and anthracnose cause devastating yield losses. Automated disease detection from leaf images is essential for early intervention, yet deploying such systems in resource-constrained settings demands models that are small, fast, and require no internet connectivity. Existing edge-deployable plant disease systems rely on end-to-end deep learning without uncertainty quantification, while Bayesian methods for edge devices focus on hardware-level inference architectures rather than agricultural applications. We bridge this gap with TinyBayes, the first framework to combine a closed-form Bayesian classifier with a mobile-grade computer vision pipeline for crop disease detection. Our pipeline uses YOLOv8-Nano (5.9 MB) for lesion localisation, MobileNetV3-Small (3.5 MB) for feature extraction, and the Jacobi prior; a Bayesian method that provides a closed form non-iterative estimators via projection, for the classification. The Jacobi-DMR (Distributed Multinomial Regression) classifier adds only 13.5 KB to the pipeline, bringing the total model size within 9.5 MB, while achieving 78.7% accuracy on the Amini Cocoa Contamination Challenge dataset and enabling end-to-end CPU inference under 150 ms per image. We benchmark against seven classifiers including Random Forest, SVM, Ridge, Lasso, Elastic Net, XGBoost, and Jacobi-GP, and demonstrate that the Jacobi-DMR offers the best trade-off between accuracy, model size, and inference speed for edge deployment. We have proved the asymptotic equivalence and consistency, asymptotic normality and the bias correction of Jacobi-DMR. All data and codes are available here: https://github.com/shouvik-sardar/TinyBayes

Constructive neural routing solvers usually score the next action by matching a decoder context against candidate embeddings computed once per instance from static node features such as coordinates, demands, and time windows; deterministic one-step consequences such as travel, waiting, slack, and capacity changes are not provided as inputs and must be inferred implicitly by the model. We propose LINC, a decoder-side candidate decision architecture that decouples computing these consequences from learning how much they matter. The environment computes the consequences explicitly at each step; candidate-level consequences are scored by a state-conditioned shared linear comparator, while feasible-set summaries modulate the decoder context. This keeps the cached embeddings and standard global matching while giving the scoring function direct access to deterministic transition quantities. The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) serves as the main constrained-routing testbed, and the same interface extends to the Capacitated Vehicle Routing Problem (CVRP) and Traveling Salesman Problem (TSP). Across external benchmarks and no-retraining scale-transfer settings, LINC consistently improves strong neural baselines, with the advantage becoming more pronounced as test size moves further beyond the training scale, especially on constrained routing problems.

Safety benchmarks are routinely treated as evidence about how a language model will behave once deployed, but this inference is fragile if behavior depends on whether a prompt looks like an evaluation. We define evaluation-context divergence as an observable within-item change in behavior induced by framing a fixed task as an evaluation, a live deployment interaction, or a neutral request, and present a paired-prompt protocol that measures it in open-weight LLMs while controlling for paraphrase variation, benchmark familiarity, and judge framing-sensitivity. Across five instruction-tuned checkpoints from four open-weight families plus a matched OLMo-3 base/instruct ablation ($20$ paired items, $840$ generations per checkpoint), we find striking heterogeneity. OLMo-3-Instruct alone is eval-cautious – evaluation framing raises refusal vs. neutral by $11.8$pp ($p=0.007$) and reduces harmful compliance vs. deployment by $3.6$pp ($p=0.024$, $0/20$ items inverted) – while Mistral-Small-3.2, Phi-3.5-mini, and Llama-3.1-8B are deployment-cautious}, with marginal eval-vs-deployment refusal effects of $-9$ to $-20$pp. The matched OLMo-3 base also exhibits the deployment-cautious pattern, identifying alignment as the inversion stage; within Llama-3.1, the $70$B model preserves direction with attenuated magnitude, ruling out a simple “small-model effect that reverses at scale.” One caveat: the cross-family heterogeneity is judge-dependent. Re-judging with a different-family safety classifier (Llama-Guard-3-8B) preserves the within-OLMo eval-cautious direction but flattens the cross-family contrast, indicating that the two judges operationalize distinct constructs.

Online-safety regulation under the UK Online Safety Act and the EU Digital Services Act increasingly treats scalar metrics as compliance evidence. Once announced, such a metric also becomes an optimization target: a strategic platform can improve its score by routing recommendations through semantically equivalent content variants, without reducing true harm. We ask when such an audit metric can still certify a genuine reduction in harm. The protocol is modeled as a published transformation graph whose connected components form semantic classes, and the metric itself is treated as a security object. Three results follow. First, any metric that scores variants directly is manipulable as soon as two equivalent variants in a harmful class disagree in score. Second, the semantic-envelope lift, which assigns each variant the maximum score in its class, is the unique pointwise minimum among conservative classwise-constant repairs. Third, a class-stratified certificate, $H^\star(x) \le (1/\hat\alpha) M_{\mathrm{Env}(m)}(x) + \bar\eta$, holds for every platform strategy, with $\bar\eta$ absorbing annotation and protocol error. We check the claims at three levels: exhaustive enumeration on a finite-state grid of mixed strategies, an SMT encoding in Z3 cross-replayed in cvc5, and a bounded single-player MDP encoded in PRISM-games. The fragile metric fails manipulation invariance and cannot support the same useful predeclared class-coverage certificate; under the envelope-level certificate, it produces large violations at every tested instance, with a large mean gaming gap across random catalogs at a fixed audit budget. The semantic-envelope metric exhibits no such violation in the tested instances.

Language models for molecular design have scaled to hundreds of millions of parameters, yet how they learn chemical grammar is poorly understood. We train SMolLM, a 53K-parameter weight-shared transformer, to generate novel SMILES with 95% validity on the ZINC-250K drug-like-molecule benchmark, outperforming a standard GPT with 10 times more parameters. Mechanistically, the same block resolves SMILES constraints across passes in a fixed hierarchy: brackets first, rings second, and valence last, as shown by error classification and linear probing, with ablation isolating the bracket-matching head. Together, these results yield a compact, mechanistically interpretable molecular generator and a testbed for studying iterative computation in formal-language domains.

Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning – most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization – and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a spike-and-flat shape – a few dominant eigenvalues followed by an approximately uniform tail – across layers and training stages, holding exactly under a rank-$\rho$ signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked $r$-dimensional subspace, single shared eigenvalue across the remaining $n-r$ directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

Learning identifiable representations in deep generative models remains a fundamental challenge, particularly for sequential data with regime-switching dynamics. Existing approaches establish identifiability under restrictive assumptions, such as stationarity or limited emission models, and typically rely on variational autoencoder (VAE) estimators, which introduce approximation gaps that limit the recovery of the latent structure. In this work, we address both the theoretical and practical limitations of this setting. First, we establish identifiability of a broad class of recurrent nonlinear switching dynamical systems under flexible assumptions, significantly extending prior results. Second, we introduce $\Omega$SDS, a flow-based estimator that enables exact likelihood optimization using expectation-maximisation. Through empirical validation on both synthetic and real-world data, our results demonstrate that $\Omega$SDS achieves improved disentanglement compared to VAE-based estimators and more accurate forecasting of underlying dynamics.

Benign overfitting is well-characterized in $\ell_2$ geometries, but its behavior under the $\ell_1$ implicit bias of greedy ensembles remains challenging. The analytical barrier stems from the non-linear coupling of coordinate selection thresholds, which invalidates standard spectral resolvent tools. To isolate this algorithmic bias, we characterize the high-dimensional risk of continuous-time $\ell_2$-Boosting over $p$ features and $n$ samples. By coupling the Convex Gaussian Minimax Theorem with delicate asymptotic expansions of double-sided truncated Gaussian moments, we analytically resolve the non-smooth $\ell_1$ interpolant. Under an isotropic pure-noise model, we prove that benign overfitting fails at the linear rate: greedy selection localizes noise into sparse active sets, and the excess variance decays at a logarithmic rate $\Theta(\sigma^2/\log(p/n))$ for noise variance $\sigma^2$. We remark that while this localization mechanism should persist in the presence of signals, the exact signal-noise decomposition remains an open problem. For spiked-isotropic designs with $k^*$ head eigenvalues and $r_2 = p - k^*$ tail dimensions, the risk converges to zero when $r_{2} \gg n$, but only at a logarithmic rate $\Theta(\sigma^2/\log(r_2/n))$, which is slower than the linear decay observed in $\ell_2$ geometries. To avoid this slow convergence, we analyze the non-smooth subdifferential dynamics of the boosting flow. This yields a tuning-free early stopping rule that, under a bounded $\ell_1$-path condition, recovers the Lasso basic inequality and attains the minimax-optimal empirical prediction rate for $\ell_1$-bounded signals.

Local temporal patterns in real-world time series continuously shift, rendering globally shared transformations suboptimal. Current deep forecasting models, despite their scale and complexity, rely on fixed weight matrices applied uniformly to all temporal tokens. This creates a static pattern response: models settle into a compromised average, unable to adapt to changing local dynamics. We introduce Dynamic Pattern Recalibration (DPR), a backbone-agnostic mechanism that resolves this via token-level recalibration. Through a lightweight "Perceive-Route-Modulate" pipeline, DPR computes a soft-routing distribution over a learned basis of adaptive response patterns, generating a time-aware modulation vector that recalibrates hidden states via a residual Hadamard product. As a backbone-agnostic adapter, DPR enhances forecasting across diverse architectures with minimal overhead, confirming it addresses a general bottleneck. As a minimalist standalone model, DPRNet achieves competitive performance across 12 benchmarks, validating dynamic recalibration against macroscopic parameter scaling.

Molecular generative models often assume meaningful latent geometry, but apparent property predictability can reflect sequence-level shortcuts rather than chemical organization. We study this issue in an unsupervised autoregressive Transformer-VAE trained on SELFIES. After training, we freeze the model, fit linear probes to RDKit descriptors, and use the probe weights as candidate global steering directions. To separate chemical signal from SELFIES artifacts, we introduce a confound-aware evaluation based on residualization, confound-direction alignment analysis, and decoded-molecule traversal. This is necessary because SELFIES length, branch tokens, ring tokens, and token entropy are strongly encoded in the latent space. Under this confound-aware evaluation, we find robust monotonic steering for cLogP, FractionCSP3, HeavyAtomCount, TPSA, BertzCT, and HBA. Nonlinear probes further show that some properties admit stable global directions, while others are better described by local latent gradients. Overall, our results show that chemically meaningful steering can emerge in entangled molecular latent spaces, but only when validated through decoded molecules and controlled for representation-level confounds.

Deep networks with continuous piecewise affine activations induce polyhedral partitions of the input space, making the number of realized affine regions a natural measure of expressive capacity and a key determinant of how well the model can approximate nonlinear target functions. In practice, standard training realizes far fewer region refinements in data-visited neighborhoods than the architecture could in principle support, while existing region-count theory is primarily architectural and offers little guidance on how optimization shapes the realized partition near the data. Our theory provides a sufficient condition under which bringing neuron switching surfaces sufficiently close to data points ensures their intersection with local neighborhoods, which in turn implies a strict increase in the local affine-region count, yielding a principled training-time handle for seeding data-relevant partitions early in optimization. Guided by these results, we propose a plug-and-play region-seeding regularizer that encourages early partitioning while allowing task-driven refinement to dominate later in training. Experiments show that the regularizer increases the number of realized affine regions via exact enumeration and improves overall performance on toy datasets, while also improving early-stage accuracy and achieving comparable (or slightly improved) final accuracy on ImageNet-1k for classical models.

How can an arbitrary attribution method be generalized from first principles to capture interactions? We answer this with the metagame, a conceptual framework for quantifying second-order interaction effects of model explanations. We cast the attribution value $\phi_i$ of feature $i$ as a cooperative game among the other features and compute its Shapley value, which measures how much feature $j$ influences the attribution of $i$, yielding the directional meta-attribution $\varphi_{j \to i}$. By decomposing attribution itself rather than the model directly, meta-attributions extend any gradient- or attention-based method to interactions, uniting removal-based perturbations with model internals. Theoretically, we prove that meta-attributions sum to the first-order attribution they explain, a hierarchical decomposition that Shapley interactions and integrated Hessians turn out to perform implicitly. Empirically, we demonstrate that meta-attributions deliver insights across diverse interpretability applications: (i) quantifying token interactions in instruction-tuned language models, (ii) explaining cross-modal similarity in vision-language encoders, and (iii) interpreting text-to-image concepts in multimodal diffusion transformers.

The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploits the likelihood hypothesis: that machine-generated text should appear more probable to a detector language model than human-written text. However, we demonstrate that the token-level signal distinguishing human and machine text is non-uniform across the hidden space of the detector model, and naively averaging likelihood-based token scores across regions with fundamentally different statistical structure, as most detectors do, causes a form of Simpson's paradox: a strong local signal is destroyed by inappropriate aggregation. To correct for this, we introduce a learned local calibration step grounded in Bayesian decision theory. Rather than aggregating raw token scores, we first learn lightweight predictors of the score distributions conditioned on position in hidden space, and aggregate calibrated log-likelihood ratios instead. This single intervention dramatically and consistently improves detection performance across all baseline detectors and all datasets we consider. For example, our calibrated variant of Fast-DetectGPT improves AUROC from $0.63$ to $0.85$ on GPT-5.4 text, and a locally-calibrated DMAP detector we introduce achieves state-of-the-art performance across the board. That said, our central contribution is not a new detector, but a precise diagnosis of a significant cause of under-performance of existing detectors and a principled, modular remedy compatible with any token-averaging pipeline. This will serve as a foundation for the community to build upon, with natural avenues including richer distributional models, improved calibration strategies, and principled ensembling with hidden-space geometry signals via the full Bayes-optimal decision rule.

When modeling class-imbalanced data, it is crucial to address the imbalance, as models trained on such data tend to be biased towards the majority classes. This problem is amplified under partial supervision, where pseudo-labels for unlabeled data are predicted based on imbalanced labeled data, propagating the bias. While recent semi-supervised models address class imbalance, they typically assume single-modal input data. However, with the growing availability of multimodal data, it is essential to leverage complementary modalities. In this article, we propose a multimodal deep generative model for semi-supervised learning under class imbalance. Our approach uses separate encoders for each modality, sharing latent variables across modalities, and simplifies joint posterior computation with a product-of-experts method. To further address class imbalance, we replace typical Gaussian distributions with Student's t-distributions for the prior, encoder, and decoder, better capturing the heavy-tailed latent distributions in imbalanced data. We derive a new objective function for training the proposed model on both labeled and unlabeled data using $\gamma$-power divergence. Empirical results on benchmark and real-world datasets demonstrate that our model outperforms baseline methods in generalization, achieving superior classification performance for partially labeled multimodal data with imbalanced class distributions.

Single-step retrieval-augmented generation (RAG) provides an efficient way to incorporate external information for simple question answering tasks but struggles with complex questions. Agentic RAG extends this paradigm by replacing single-step retrieval with a multi-step process, in which the large language model (LLM) acts as a search agent that generates intermediate thoughts and subqueries to iteratively interact with the retrieval system. This iterative process incurs substantial latency due to the autoregressive generation of lengthy thoughts and subqueries. To address this limitation, we propose LatentRAG, a novel framework that shifts both reasoning and retrieval from discrete language space to continuous latent space. Unlike existing explicit methods that generate natural language thoughts or subqueries token-by-token, LatentRAG produces latent tokens for thoughts and subqueries directly from the hidden states in a single forward pass. We align LLMs with dense retrieval models in the latent space, enabling retrieval over latent subquery tokens and supporting end-to-end joint optimization. To improve transparency and encourage semantically meaningful latent representations, we incorporate a parallel latent decoding mechanism that translates latent tokens back into natural language. Extensive experiments on seven benchmark datasets show that LatentRAG achieves performance comparable to explicit agentic RAG methods while reducing inference latency by approximately 90%, substantially narrowing the latency gap with traditional single-step RAG.

In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling and reformulates PIDE solving as a sequence of recursive regression problems. Like Physics-Informed Neural Networks (PINNs), INEUS learns global solutions over the entire space-time domain, yet it offers a more efficient treatment of nonlocal terms and avoids the computationally expensive differentiation of full PIDE residuals. These features make INEUS particularly well suited for high-dimensional PDEs and PIDEs. Supported by a contraction-based convergence proof for linear PIDEs, our numerical experiments show that INEUS delivers accurate and scalable solutions for various high-dimensional linear and nonlinear examples.

Ensemble models achieve state-of-the-art performance on prediction tasks, but usually require aggregating a large number of weak learners. This can hinder deployment, interpretability, and downstream tasks such as robustness verification. Remedies to this issue fall into two main camps: pruning, which discards redundant learners, and compression, which generates new ones from scratch. We introduce PACE, a framework that interleaves these paradigms in a two-phase strategy. First, new learners are actively generated via a theoretically grounded procedure to enhance the diversity of the initial ensemble. When no more relevant learners can be found, a second phase of pruning is performed on this enriched ensemble. During both operations, PACE allows fine control on the faithfulness to the original ensemble. Experiments show that our method outperforms prior pruning and compression methods while offering principled control of faithfulness guarantees.

Standard cross-entropy is the default classification loss across virtually all of machine learning, yet it treats all misclassifications equally, ignoring the semantic distances that a class hierarchy encodes. We propose Hierarchy-Aware Cross-Entropy (HACE), a drop-in replacement for standard cross-entropy that incorporates a known class hierarchy directly into the loss. HACE combines two components: prediction aggregation, which propagates the model's probability mass upward through the class hierarchy to ensure that parent nodes accumulate the confidence of their children; and ancestral label smoothing, which distributes the ground-truth signal along the path from the true class to the root. We evaluate HACE on CIFAR-100, FGVC Aircraft, and NABirds in two regimes: end-to-end training across six architectures spanning convolutional and attention-based designs, and linear probing on frozen DINOv2-Large features. In end-to-end training, HACE improves accuracy over standard cross-entropy in 15 out of 18 architecture–dataset pairs, with a mean gain of 4.66%. In linear probing on frozen DINOv2-Large features, HACE outperforms all competing methods on all three datasets, with a mean improvement of 2.18% over the next best baseline.

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this end, we propose Function Projection for Flow Matching (FP-FM), an algorithm that directly conditions generation on samples from the target distribution. FP-FM learns basis functions to span the velocity fields corresponding to a set of training distributions, and adapts to new distributions by computing a simple least-squares projection onto this basis. This enables efficient generation of samples from diverse target distributions without additional training at inference time. We further introduce multiple variants of FP-FM that provide a trade-off in expressivity and compute by enriching the coefficient calculation, e.g., by making the coefficients dependent on time. FP-FM achieves greatly improved precision and recall relative to baselines across synthetic and image-based datasets, with especially strong gains on unseen distributions.

Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of convolution-smoothed quantile ReLU neural networks, which yield smooth objectives while preserving the underlying quantile structure. We establish general nonasymptotic risk bounds for ConquerNet under mild conditions, providing minimax guarantees over Besov function classes. In numerical studies, we demonstrate that the proposed approach outperforms standard quantile neural networks at multiple quantile levels, showing improved estimation accuracy and training efficiency across the board, with particularly pronounced advantages at high and low quantiles.

End-to-end autonomous driving models generate future trajectories from multi-view inputs, improving system integration but introducing opaque decisions and hard-to-localize risks. Existing methods either rely on auxiliary monitoring models or generate textual explanations, but are decoupled from the planning process and fail to reveal the visual evidence underlying trajectory generation. While attribution offers a direct alternative, planning differs from image classification by taking six-view camera images as input and predicting continuous multi-step trajectories, requiring attribution to capture both critical views and regions and their influence on outputs. Moreover, whether attribution maps can support risk identification remains underexplored. To address this, we propose a hierarchical attribution framework for end-to-end planning. Specifically, using L2 consistency with the original trajectory as the objective, we design a coarse-to-fine region attribution strategy that searches candidate regions across the full six-view input and refines attribution within them. We further extract three attribution statistics as predictive signals for planning risk, including attribution entropy to measure how concentrated the planner's reliance is over the joint visual space, within-camera spatial variance to characterize how spread out the attribution is within each view, and cross-camera Gini coefficient to quantify how unevenly attribution is distributed across the six cameras. Experiments on BridgeAD, UniAD, and GenAD show that these statistics correlate with planning risk, achieving Spearman correlations of $0.30 \pm 0.07$ with trajectory error and AUROC of $0.77 \pm 0.04$ for collision detection. The signal generalizes to held-out scenes with negligible degradation and remains stable under an alternative attribution baseline.

Diffusion-based generators set the current state of the art for synthetic tabular data. These methods approach but rarely exceed real-data utility, and closing this synthetic-real gap has so far been pursued exclusively at training time, via architectural advances, scaling, and retraining of monolithic generators. The inference-time alternative, i.e., refining the outputs of a pre-trained backbone with parameters left untouched, has remained largely unexplored for tabular synthesis. We introduce TARDIS (Tabular generation through Refinement, Distillation, and Inference-time Sampling), an inference-time refinement framework that operates on a frozen pre-trained backbone, configured per dataset by a Tree-structured Parzen Estimator search over score-level guidance during reverse diffusion, with each trial's objective set by an inner grid search over post-hoc sample selectors and an optional soft-label distillation step. The search space encodes a single mathematical pattern we name Bidirectional Chamfer Refinement (BCR): the symmetric Chamfer functional between synthetic and real samples is minimized both continuously, via a score-level gradient, and discretely, via batch-ranking post-generation. The per-dataset search recovers BCR-aligned configurations on most datasets, evidence for BCR as the dominant refinement pattern. Across 15 binary, multiclass, and regression benchmarks TARDIS achieves a median +8.6% downstream-task improvement over models trained on real data (95% CI [+3.3, +16.4], Wilcoxon p=0.016, 11/15 strict wins) and improves over the TabDiff backbone on all 15 datasets (mean +12.9%, p<10^-4), matching the backbone on manifold fidelity, diversity, and sample-level privacy. Inference-time refinement of a pre-trained tabular diffusion backbone reaches and exceeds real-data utility in 1 to 80 minutes on a single consumer-grade GPU.

Graph Federated Learning (GFL) enables collaborative representation learning across distributed subgraphs while preserving privacy. However, heterogeneity remains a critical challenge, as subgraphs across clients typically differ significantly in both semantics and structures. Existing methods address heterogeneity by enforcing the rigid alignment of model parameters or prototypes between clients and the server. However, these alignments implicitly rely on a restrictive global linearity assumption that summarizes local data distributions using a single and globally consistent representation space. This severely compresses the personalized representation space of clients and fails to preserve diverse local graph distributions. To overcome these limitations, we propose Federated Graph Manifold Calibration (FedGMC), a novel paradigm that tackles semantic heterogeneity and structural heterogeneity from a unified manifold perspective. Instead of enforcing rigid alignment, FedGMC introduces a dual manifold calibration mechanism that preserves global commonalities while maximizing the personalized representation space of local clients. Specifically, for semantic heterogeneity, the server constructs a geometrically optimal semantic manifold via equidistant semantic anchors, so as to guide the calibration of local semantic manifolds. For structural heterogeneity, the server constructs a global structural manifold by building global structural templates, so as to guide the calibration of local structural manifolds. Finally, the server dynamically refines both global semantic manifolds and structural manifolds by aggregating local manifolds. Extensive experiments on eleven homophilic and heterophilic graphs demonstrate that FedGMC effectively balances global commonality and local personalization, thereby significantly outperforming state-of-the-art baseline methods.

Within the $f$-DP framework, we derive a tight analysis of the trade-off function for Differentially Private Stochastic Gradient Descent (DP-SGD) with subsampling based on random allocation in which each sample is independently assigned to exactly one of $M$ minibatches per epoch, each minibatch corresponding to one of the $M$ SGD rounds within a single epoch. Our analysis holds under an explicit validity condition, whose hypotheses together force $\sigma \geq \sqrt{3/\ln M}$, where $\sigma$ is the DP noise multiplier. Unlike $f$-DP analyses for Poisson subsampling, which yield non-closed implicit formulas that can be machine computed but are non-transparent, random allocation admits a tight analysis yielding transparent and interpretable closed-form bounds. For a single epoch, our concrete bounds, derived via the Berry-Esseen theorem, are tight up to constant factors. We demonstrate worked parameter settings for a single epoch ($E=1$) with a corresponding trade-off function $\geq 1-a-\delta$, that is, only $\delta$ below the ideal random guessing diagonal $1-a$. For $\delta = 1/100$ and $\sigma = 1$, roughly $M \approx 1.14\times 10^6$ rounds and $N \approx 1.14\times 10^7$ training samples suffice to achieve meaningful differential privacy. This is in contrast to recent negative results for the regime $\sigma \leq 1/\sqrt{2 \ln M}$ for which no significant DP guarantee can exist.

Understanding how deep neural networks learn representations remains a central challenge in machine learning theory. In this work, we propose a feature-centric framework for analyzing neural network training by relating weight updates to feature evolution. We introduce a simple identity, the Feature Learning Equation, which identifies the weight Gram matrix as the key object capturing feature dynamics. This enables us to interpret gradient descent as implicitly inducing a hypothetical evolution of features, whose covariance structure, termed the Virtual Covariance, characterizes how representations evolve during training. Building on this perspective, we introduce Target Linearity, a measure quantifying the linear alignment between features and targets. By analyzing the training and layer-wise dynamics, we show that deep networks learn to sequentially transform representations toward target-linear structure. This linearization perspective provides a unified interpretation of several empirical phenomena, including Neural Collapse and linear interpolation in generative models.