Papers

Multiscale structure is central to time series forecasting: temporal signals contain slowly varying trends, intermediate seasonal patterns, and high-frequency residuals. Traditional forecasters model this multiscale structure in Euclidean space, without representing the ordering it induces among components. We identify that cascaded decomposition orders components by their characteristic frequencies, forming a natural frequency hierarchy. This hierarchy aligns with the exponential volume growth of hyperbolic space, which provides increasing representational capacity with radius and naturally accommodates nested hierarchies. We propose HyperForecast, the first long-term time series forecasting (LTSF) framework operating in hyperbolic space. HyperForecast embeds decomposed temporal segments on the Poincaré ball where radial distance captures this nested structure, from low-frequency components near the origin to high-frequency components near the boundary. We model geodesic velocity through two manifold-dynamics variants: (a) autoregressive forecasting via Poincaré residual dynamics, and (b) non-autoregressive forecasting that predicts all future segments in parallel. HyperForecast consistently outperforms existing and state-of-the-art baselines on 9 of 11 long-term forecasting benchmarks, achieving up to 58% lower mean squared error at long horizons. Further analysis reveals that the learned radial embeddings recover the frequency hierarchy and that hyperbolic geometry contributes substantially to forecasting performance.

Sentiment analysis is a key task in Natural Language Processing that determines the polarity of opinions in text. For low-resource languages like Marathi–where limited data prevents the direct use of standard statistical methods–models are often trained on single-domain datasets. While this yields strong in-domain performance, it leads to poor generalization to unseen domains. Recent studies highlight the need for domain-robust systems that can handle diverse real-world content through multi-domain modeling. This study investigates how multi-domain training improves sentiment classification for unseen Marathi domains. Models are trained using single-domain, two-domain, and three-domain dataset combinations. Results show that two-domain training improves accuracy on unseen domains by about 8% compared to single-domain training. Adding a third domain provides further improvement, though the gain is smaller, averaging around 2% for some domains. These results suggest that training with data from multiple domains helps build more robust sentiment analysis models for low-resource languages, though the benefits reduce as more domains are added.

Temporal graph neural networks (TGNNs) achieve superior performance in many dynamic graph learning tasks. These models use node state vectors (i.e., memories) to capture and record graph changes (i.e., events), and then exploit these memories to assist prediction. However, this memory-centric design makes multi-GPU training challenging because predictions for later events often depend on memory updates from earlier events. To maintain model quality, existing multi-GPU TGNN training schemes strictly preserve all event dependencies, which limits parallelism and causes expensive cross-GPU memory synchronization. In this work, we observe that many of these dependencies can be handled more flexibly without harming training quality. Specifically, (a) dependencies in TGNN training have high locality in both time and graph topology, (b) the short-range dependencies missed within a large batch can often be recovered cheaply, and (c) many memory updates are not immediately needed. Based on these observations, we propose DepBloom to accelerate multi-GPU TGNN training with three techniques: (1) temporally bounded spatial partitioning to reduce unnecessary cross-GPU synchronization and improve parallelism; (2) intra-batch memory refinement to recover missing short-range temporal dependencies inside enlarged batches; and (3) critical-path optimization to prioritize urgent memory updates while deferring non-critical work during multi-GPU pipeline execution. Experimental results across representative models and diverse datasets show that DepBloom achieves an average speedup of 2.84$\times$ and up to 5.16$\times$ over state-of-the-art methods, while maintaining comparable or better model accuracy.

Denoising Diffusion Probabilistic Models have emerged as powerful generative priors across domains ranging from molecular design to high-resolution image synthesis. However, standard diffusion sampling is inherently biased toward high-likelihood regions, often limiting the diversity of outputs. In many domains, a single, high-likelihood sample is insufficient. Instead, diverse portfolios of high-performing solutions are required, motivating methods that uncover a model's full expressive range. Here we show that integrating Quality-Diversity (QD) optimisation with diffusion models enables the discovery of diverse, high-performing outputs. We first propose Quality-Diversity Diffusion, a framework that adapts QD to diffusion models by directly optimising the model's latent noise and conditioning embeddings and leveraging embedding models to quantify diversity. Second, we introduce a novel h-space Spectral Mutation operator, which guides search along directions of maximal semantic sensitivity by analysing principal singular vectors of the model's input-to-activation Jacobian. We evaluate our combined approach, Spectral-Guided Quality-Diversity Diffusion, on text-to-image generation. Against 12 baselines, our method consistently achieves the lowest FID score, demonstrating an excellent balance of image quality and diversity.

We study adaptive confidence sets for mean vectors of multivariate Gaussians with identity covariance under Huber contamination when the contamination proportion is unknown. We show that an information-theoretically optimal adaptive confidence set can be constructed by simultaneously quantifying uncertainty across all one-dimensional projections. The resulting confidence set achieves the optimal diameter and reveals a substantial adaptation cost compared with the minimax estimation error. Although statistically optimal, this construction is computationally infeasible. We establish a Statistical Query (SQ) lower bound showing that achieving diameter $O(m^{-1/2})$ requires either exponentially many queries or query tolerance $d^{-\Omega(m)}$. Thus, in contrast to robust mean estimation, adaptation to the unknown contamination proportion incurs both a statistical cost and a computational barrier within the SQ framework. Finally, we give a low-degree moment-matching algorithm that constructs an adaptive confidence set using $d^{O(m)}$ samples and time. Its diameter bound contains an additional $O(m^{-1/2})$ term beyond the information-theoretic rate, matching the dependence on $m$ in the SQ lower bound. Together, these results characterize the statistical limits of adaptive robust confidence sets under Huber contamination and quantify a computational barrier within the SQ framework.

Cross-model KV cache sharing reduces prefill computation by allowing a receiver model to reuse prefix KV states generated by a related sender model. Existing methods optimize such reuse for latency and generation quality, but its safety implications remain unclear. In this work, we systematically evaluate this issue across diverse sender-receiver pairs and reuse configurations. We refer to deviations from the receiver's native safety behavior as safety incompatibility. Our study shows that both the direction and magnitude of safety incompatibility depend on the model pair and reuse configuration, with value reuse causing substantially larger deviations than key reuse across all evaluated pairs. Furthermore, we propose VReparo, a technique that learns per-layer and per-KV-head affine maps offline to align reused sender value tensors with their receiver-native counterparts before decoding. Across two model pairs under full KV reuse and the state-of-the-art selective reuse setting, VReparo reduces the average HarmBench attack success rate (ASR) from 57.28% to 39.21% and the average StrongREJECT score from 0.4215 to 0.2163 upon our benchmarks, while retaining an average Time to First Token (TTFT) reduction of 85.62%.

Linear attention promises the efficiency needed for long-context language modelling, yet its fixed-size recurrent state must simultaneously support ongoing computation and preserve information from an ever-growing history. This coupling has reinforced a prevailing view that the state's memory capacity defines the model's long-context capability. We challenge this presumed ceiling: recurrent computation need not bear the full burden of long-term storage. We introduce NoteBank, a sparse episodic memory that archives selected text before future queries are known, uses the backbone's native features for writing and addressing, and reads retrieved evidence through its native forward computation via replay. This training-free, plug-and-play interface requires no external embedding model, separately trained retriever, or separate neural reader. At one million tokens, it raises Gated DeltaNet's mean accuracy across six RULER retrieval tasks from 1.7% to 70.3%, with no observed significant retrieval degradation from 4K to 1M tokens. This recovery adds $\leqslant$0.025% to analytical FLOPs, with persistent context storage approximately 1/2,600 that of a Transformer's full MHA KV cache at matched width, depth, and precision. Experiments extend from three 1.3B recurrent backbones to Mamba-2-8B and post-trained Qwen3.5-9B, demonstrating gains on LongBench v1/v2 and MemoryAgentBench. Together, these results show that sparse evidence storage and native replay can substantially expand the long-context capability of pretrained linear attention models while retaining the efficiency of recurrent computation.

Do genomic foundation models (FMs) provide predictive information beyond simple sequence composition? We evaluate frozen representations from five DNA FMs against normalized k-mer frequencies across 57 genomic classification datasets and two exploratory gene-expression regression tasks. Simple k-mer features remain competitive with most models, whereas NTv3 shows a consistent advantage; the ranking is robust to globally fixed and multi-scale k-mer baselines and alternative downstream probes. To test incremental predictive utility directly, we compare global 6-mer features with their concatenation with each FM embedding under a matched Random Forest protocol. NTv3 improves 46 of 57 datasets (mean $\Delta$MCC = +0.072), while Caduceus provides smaller gains and the other models do not improve mean MCC. We separately decompose embeddings into a component linearly predictable from 6-mer frequencies and a ridge residual, finding that linear recoverability does not reliably indicate downstream utility. Exact 6-mer-preserving shuffles further reveal task-relevant sequence-order sensitivity, most pronounced for NTv3, although order sensitivity alone does not guarantee predictive improvements. Our results establish compositional features as essential controls and offer complementary diagnostics for evaluating the added value of frozen genomic representations, without making claims about fine-tuning capacity.

Linear attention and recurrent models compress past tokens into a fixed-size state that is updated at every step. However, storing these states in high precision incurs substantial memory and bandwidth costs at large batch sizes, motivating low-bit state quantization. Unlike weights and key–value caches, a recurrent state is requantized after every update, so its quantization errors accumulate across steps. Our analysis shows that these errors are highly coherent across steps, so reducing per-step errors alone is insufficient. This coherence arises mainly from small updates that are lost in rounding. To preserve these updates, we intervene both before and at rounding. Before rounding, we propose Low-Rank Bypass (LRB), which accumulates small updates in a compact low-rank buffer and periodically merges its sufficiently large elements into the state. At rounding, we observe that a state element can even move opposite to its update, and such reversals prove particularly harmful. Therefore, we propose Bounded Directional Rounding (BDR), which rounds reversed elements toward their updates without additional storage. Although BDR enlarges the rounding error, it improves the model, suggesting that the direction of an update matters more than its rounding error at a single step. Across Gated DeltaNet, GLA, Mamba2, and RetNet, our training-free method substantially outperforms INT4, while reducing state memory by up to 5.3$\times$ and speeding up decoding by up to 1.9$\times$ relative to FP32 states.

A central desideratum in model editing is generalization to complex tasks, which prior work formalizes under a direct generalization paradigm: treating and evaluating LLM behavior as an input-output mapping and expecting a factual update to alter outputs on reasoning tasks. Yet despite substantial empirical effort, the field consensus remains that such generalization is highly challenging and elusive. However, when we deploy the latest models in an in-the-wild chatbot-user setting, we surprisingly find that even classical editing methods exhibit remarkably fluent generalization behavior. This motivates us to revisit the obstacles to generalization and the limitations of the prevailing paradigm. We find that direct generalization is fundamentally constrained both theoretically and practically: theoretically, it suffers from an identifiability issue; and practically, existing approaches attempting to circumvent this are further hindered by the ambiguity of their constructed biases and by vulnerability to being overridden by other factors such as optimization dynamics. We instead identify compositional generalization, empowered by the increasingly strong reasoning and composition abilities of modern LLMs, as a theoretically grounded and empirically validated alternative. We validate this phenomenon across multiple models and editing methods, showing that such generalization behavior is widespread. Overall, we argue that generalizable model editing could be more than direct generalization, and call for a paradigm shift toward more generalizable and practically deployable knowledge update techniques.

Respiratory auscultation provides a low-cost means of assessing pulmonary function, yet transient crackles and sustained wheezes can be difficult to recognize in noisy clinical recordings. Conventional deep learning classifiers often operate as black boxes, offering limited insight into the temporal acoustic evidence supporting their predictions. We present RespFocus, a weakly supervised framework that uses multiple instance learning (MIL) to learn inspectable temporal evidence from cycle-level labels and integrate it into classification. We also introduce PedResp2026, a multicenter pediatric respiratory sound cohort collected in routine clinical environments with adjudicated cycle-level annotations. In classification experiments, RespFocus achieves four-class Scores of 69.55% on public ICBHI 2017 and 72.91% on PedResp2026. Evidence diagnostics and matched temporal interventions support the functional contribution of the learned evidence to model predictions. Together, these findings highlight RespFocus's potential as a tool for automated respiratory sound diagnosis.

Generative modeling for tabular data has advanced to the point where models can synthesize realistic records, recover missing values, and generate samples conditioned on class labels or observed attributes. Despite recent advances, existing approaches either require table-specific training or restrict in-context learning to single-cell prediction. In this work, we formulate these tabular generative tasks as a single problem: modeling the joint conditional distribution of an arbitrary set of target cells given the observed cells of an unseen table. To this end, we turn to diffusion, whose denoising objective is defined jointly over all target cells rather than one cell at a time. Under the pretraining distribution, this objective is minimized by the posterior predictive distribution over the target set. Building on this, we propose TabMosaic, a unified in-context diffusion model for generating mixed-type target cells in unseen, potentially incomplete tables without table-specific training. We further show that its pretraining objective bounds the conditional negative log-likelihood and the divergence from the posterior predictive for arbitrary target sets, extending the Bayesian account of in-context learning from a single-value prediction to joint multi-cell generation. Across 48 real-world tables, TabMosaic ranks first on all evaluated generative tasks against 20 baseline approaches

We present DRanker (Disney+ Ranker), a transformer-based multitask ranking model serving personalized recommendations on the Disney+ homepage. We describe the encoder-only architecture over enriched engagement-history sequences paired with a lightweight causal debiasing mechanism, and the inference stack that enables transformer-based ranking at scale. Through iterative development, we systematically evaluated more complex alternatives and found that simpler designs consistently outperformed them on offline metrics, qualitative behavioral evaluation, and in production. Deployed globally, DRanker drives over 1% lift in our key engagement metric and 0.5% lift in daily active users across all experiences powered by the ranker. We share practical lessons on data engineering, debiasing, and architectural choices that shaped our ranking system at scale.

We establish uniform score bounds and Lipschitz continuity for truncated Gaussian, Cauchy, Boltzmann, and softmax policies under explicitly stated parameterizations.

Flow matching can learn structure directly from data, raising the question of when additional constraints improve generation. We study penalties that encode such constraints, with physics-informed flow matching as a motivating example. Satisfying a constraint more closely need not make the generated distribution more accurate. We therefore compare penalised and unpenalised generative modelling through their expected squared $2$-Wasserstein error. Our analysis covers both vector-valued and functional data in a Hilbert-space setting. We first derive geometric criteria that account for constraint violations and the distribution of samples after projection onto the constraint set. We then solve the statistical comparison explicitly for specific velocity-field classes and constraints via flow matching. In this model, penalisation improves accuracy exactly when the reduction in estimation variance outweighs the increase in squared bias. The resulting formula shows how this trade-off depends on sample size, the model class, the noise schedule, and the penalty weight.

Weak bag-level labels are widely available in computational pathology, whereas reliable instance-level annotations for whole-slide images remain expensive and ambiguous. Weakly supervised multiple instance learning (MIL) achieves strong bag-level classification, but instance-level supervision from attention scores, model predictions, negative bags, or spatial refinement may fail to identify class-specific local evidence. We propose ProtoPur, a prototype-purity pseudo-labeling method for weakly supervised instance-level learning in pathology whole-slide images. ProtoPur estimates class-balanced local purity over prototype regions constructed from frozen foundation-model features, and assigns pseudo-labels to high-purity regions strongly associated with a target class. This purity-first design separates class-specific evidence from negative or shared morphology, with coverage used only to ensure sufficient pseudo-label assignment. We provide a PAC-style analysis showing that the risk of an instance classifier trained with ProtoPur pseudo-labels can be decomposed into a standard uniform-convergence term and a ProtoPur-specific pseudo-label noise term, comprising selected-region mismatch and a coverage residual. Experiments on three public whole-slide image datasets with two pathology foundation encoders show that ProtoPur consistently improves instance-level performance across multiple MIL backbones while maintaining competitive bag-level performance. Pseudo-label quality comparisons on two public datasets further demonstrate that prototype-purity selection provides stronger instance supervision. These results suggest that the foundation-model features contain exploitable instance-level supervision signals, and ProtoPur is a way to reveal and use these signals from weak bag labels without requiring dense instance annotations.

Generative policies offer expressive action distributions for online reinforcement learning (RL), but many diffusion- and flow-based policies require costly iterative sampling. We propose DriftSpread, a one-step generative policy based on Drifting for online maximum-entropy (MaxEnt) RL. To incorporate entropy without a tractable policy density, we build on an energy-based view of Drifting and derive critic-guided Drift and entropy-induced Spread from the negative MaxEnt objective. Our method learns these updates sequentially in the same actor, using action regression for value improvement and distribution matching to capture the effect of entropy. The actor updates require neither direct samples from the critic-defined Boltzmann target nor policy-density or score estimation. Under exact fitting with a fixed critic, we prove convergence to the Boltzmann target in the small-step limit followed by the long-time limit. On MuJoCo, DriftSpread achieves the highest aggregate normalized return among all evaluated methods, while outperforming the diffusion- and flow-based baselines in both training and inference efficiency.

Centrality measures rank nodes even when the observed differences can be explained by ordinary structural variation. We therefore study a preceding question: whether a network contains a statistically identifiable central structure at all. We formulate this question as a network-level hypothesis testing issue using the adjacency spectral radius as the test statistic and estimate an empirical p-value from randomized networks generated under a specified null model. The framework is evaluated using G(N,M), Chung-Lu, and two implementations of the configuration model on simulated benchmarks and 55 real networks. Controlled experiments further vary the number and connection weights of designated central nodes while holding network size and density fixed. The results show a clear negative association between central-structure strength and the empirical p-value. They also demonstrate that rejection decisions depend substantially on the structural properties preserved by the null model: the detected network sets are not simply nested across models.

Small language models (SLMs) used as on-device agents must balance accuracy and latency as their context grows. Mixed precision helps manage this tradeoff by assigning different precisions to weight tensors according to their size and sensitivity. However, these choices depend on the operating conditions, so a configuration selected for a short context may no longer provide the best tradeoff at a longer one. We calibrate a timing model from measurements at different precisions and context lengths, and combine it with tensor sensitivities to choose configurations under a latency or accuracy budget. We argue that fewer bits do not always mean faster execution, so our predictor estimates latency from calibrated execution costs rather than weight bytes alone. Under a latency budget, reading the larger key-value (KV) cache leaves less time for weight operations, leading the allocator to select lower precisions. This gives a schedule of tensor changes that can be prepared before execution. Our runtime follows the schedule while retaining the session's KV cache. We evaluate executed schedules on a laptop GPU, including a longer-context schedule with three weight formats and a tool-use benchmark measuring full response time and correctness. Under an accuracy budget, measured error from a quantized KV cache determines the budget left for weights. The allocator can raise or lower weight precision as this estimate changes. These experiments show where context-aware precision helps and where accuracy recovery remains limited.

Knowledge graph (KG) foundation models (KGFMs) predict links on unseen graphs zero-shot. KGFMs have been pioneered by ULTRA which builds a relation graph from co-occurrences that match motif templates, and passes messages over it to obtain relation representations. More recent KGFMs such as MOTIF and TRIX increase the size of this relation graph, and FLOCK replaces message-passing with probabilistic random-walk ensembles. However, larger relation graphs mean more messages, and more walks mean more sequences to encode, so they improve performance at higher training and inference cost. This cost hinders their use in more complex reasoning tasks, such as complex query answering. To reverse this trend, we design MERIT, the first KGFM with a transformer relation encoder: every relation name attends to every other, and the motifs enter as a soft prior rather than as edges. Over 56 benchmarks, MERIT matches the zero-shot MRR of SoTA KGFMs while being 6x faster than TRIX and over 100x faster than FLOCK at inference. Fine-tuned for complex query answering like UltraQuery, MERITQuery improves over it at matched cost.

Choosing a mixed-precision configuration for large language model (LLM) serving trades speed against accuracy. Allocators that use average bit-width or a memory budget as a speed proxy can miss changes in the resource that limits execution. We argue that served speed can be limited by compute, weight loading, or key-value (KV) cache access, depending on the phase, batch size, and context length. A byte-based proxy does not capture all of these costs, so fewer bits do not always mean faster serving. To address this gap, we build a cost model that accounts for the binding resource and use it in two ways. First, as a predictor: given a configuration and operating point, it estimates serving latency using constants calibrated for the model, GPU, and serving stack. We evaluate its accuracy across three hardware classes. Second, as an allocator: we combine modeled time costs with measured per-tensor accuracy costs and use a dynamic program to select a configuration under a latency or accuracy budget. We compare its configurations against byte-aware and sensitivity-only allocation.

Deep learning is now central to radiology, helping detect changes on X-rays, CTs, and MRIs. However, these systems are highly vulnerable to adversarial attacks - small, crafted perturbations that mislead models while appearing unchanged to humans. Such errors risk missed cancers or false positives. Studies show over 90% attack success on medical scans. Almost 30% of US hospitals use AI in imaging in 2023. Thus, an effective method of detecting such attacks and their directionality is crucial to ensure the credibility and reliability of medical systems based on DNNs. We propose a novel detection framework that leverages subsequent attacks using random noise to identify adversarial perturbations. Our approach uses the analysis of variations in the Sigmoid function to distinguish genuine medical images from adversarially manipulated ones. Specifically, we compare prediction differences between clean and attacked images, as well as between different adversarially altered versions, to improve detection accuracy. We evaluated our method on three popular medical datasets including 'Chest X-Ray Images for Classification', 'Retinal Fundus Multi-disease Image Dataset' and 'Brain Tumor Dataset' under various attack scenarios, including random noise. Our framework achieved up to 99.8% ACC in identifying adversarial directional attacks, significantly outperforming existing defense mechanisms. It consistently identified adversarial samples across varying attack strengths while keeping false positives low, showing strong reliability and potential for clinical use. Furthermore, our proposal highlights its potential for real-world deployment.

Hybrid federated semantic communication enables user equipment (UEs) to contribute model updates or semantic features under a shared training framework. However, heterogeneous role costs and the interaction between model aggregation and feature reconstruction (FR) remain key challenges in practical radio access network (RAN) deployment. To address these issues, we propose ARC-FedSC, a RAN-aware framework that coordinates UE role assignment and server-side controlled FR under a fixed communication budget. Within ARC-FedSC, RAN Aware Role-Bandit learns the historical contribution of UEs in different roles together with current uplink conditions, while Temporal Consistency Alignment (TCA) regulates FR according to recent model aggregation directions. Experiments on CIFAR-10 with time-varying RAN channels show that ARC-FedSC outperforms baselines across all five tested role configurations in the later training stage, with the best configurations achieving about 24.17 dB average PSNR over the last 20 rounds. Component level results further show that Role-Bandit maintains an average rolling UE coverage of 85.3%, compared with about 65.7% for baseline, while TCA reduces the probability of harmful FR events from 0.245 to 0.093, corresponding to a 62.0% reduction. Ablation and sensitivity studies further support the effectiveness and robustness of the proposed design.

Recursive synthetic-data training can degrade a fitted model, but its effects on the variable-screening stage that precedes model fitting are less understood. When each generation labels data for the next, a marginal screener ranks variables against the current pseudo-label target rather than the original response. Across generations, this target drift can erode or reverse the active–inactive score margin and cause screening to discard variables that clean-label screening would retain. We call this process screening collapse. In a Gaussian linear model with minimum-norm recursive generators, we establish finite-sample screening bounds, characterize a late-generation information-loss limit, and derive a minimax impossibility result. Screening collapse can precede and compound ordinary model collapse: omitted variables incur a covariance-weighted loss that no refit restricted to the selected variables can eliminate, while recursive labels further degrade estimation on the retained variables. We also examine two approaches to mitigating screening collapse. Fixed-fraction real-label retention preserves a clean-label component but leaves resolution fixed, whereas data accumulation can avoid screening collapse if the pooled target preserves a positive margin and the growing sample resolves it. Numerical experiments on gene-expression data support the theoretical findings.

Multi-label learning typically pursues model construction through the joint optimization of label fitting, correlation modeling, and structural regularization. While empirically effective, such a coupled paradigm imposes multiple learning objectives on a single predictive parameter matrix, forcing it to simultaneously fit observed labels and encode structural priors. This coupling may induce ill-conditioned optimization geometry, increase hyper-parameter sensitivity, and complicate capacity control. To address the these issues, this paper proposes a Progressive Multi-Label Learning (ProML) framework, which decouples direct label fitting from predictor learning via the introduction of an auxiliary predictive variable. This auxiliary variable admits a closed-form solution, yielding an equivalent profiled objective in which the supervised fitting term is scaled by a trade-off parameter. This result provides a unified view of ProML and conventional coupled learning, with the latter recovered as a limiting case. We theoretically analyze the optimization geometry of ProML and show that, under quadratic positive semidefinite structural regularization, ProML attenuates the dominant curvature of the fitting term, enlarges the stable learning rate range, and provides a controllable fidelity-regularization trade-off. Further, we instantiate the ProML for multi-label feature selection task by integrating global-local label priors and row-sparse regularization. Extensive experiments and controlled optimization analyses on 12 benchmark datasets empirically corroborate the theoretical analysis and demonstrate the robust and competitive performance of the proposed method.

Effective unsupervised domain adaptation (UDA) requires a representation that captures transferable structure from both the labeled source domain and the unlabeled target domain. We introduce Joint Contrastive-Adversarial Representation Learning (JCAR), a two-stage framework that learns a common representation from the union of unlabeled source and target samples by combining contrastive learning with adversarial domain alignment, and then freezes the representation to fit a source-supervised predictor. We establish a non-asymptotic excess-risk bound for this procedure that couples representation and domain-discriminator estimation while separating downstream prediction, with explicit neural-network approximation errors. Under the stated assumptions and common Hölder smoothness $\beta\geq1$, the bound identifies a sufficiently large unlabeled-sample regime in which the downstream rate is $\widetilde{\mathcal{O}}(m^{-\beta/(2\beta+d)})$, where $m$ counts labeled source samples and logarithmic factors are suppressed. The labeled-sample exponent is governed by the latent dimension $d$ rather than the ambient dimension $p$, which enters the pretraining cost. Experiments on Office-31, Office-Home, and DomainNet demonstrate clear transfer gains across diverse domain shifts, with particularly strong performance when representations are learned from scratch.

In practical engineering and scientific computing, a real physical system can be reduced to a boundary value problem, and the adequate boundary information to determine the interior spatial distribution and evolutionary state of the physical field can be solved with linear equations, alternatively, the the real physical problem can be treated with boundary problems with in adequate information problems in field of machine learning. This paper proposes a deep learning framework for the recovery of missing boundary information using an attention-guided graph neural network (GNN) surrogate. The framework extracts features from the physical information on the discretized boundary into a latent space, and the missing boundary quantities are then predicted by the network. Thus, the nonlinear mapping from known boundary quantities to missing boundary quantities is learned using a variational autoencoder (VAE) architecture, while an attention mechanism is incorporated to better model the correlations among different types of boundary information. Furthermore, the interior physical field can be reconstructed using the conventional boundary element method (BEM) integral formulation. The effectiveness of the GNN-BEM framework is evaluated using numerical examples of the two-dimensional Laplace and Poisson equations, which demonstrate good performance in reconstruction accuracy, local detail preservation, and model stability. The results show that GNN-BEM provides a feasible computational framework for boundary information recovery and fast interior physical field reconstruction for partial differential equations under complex boundary conditions.

Many deployed distillation pipelines show the student a truncated view of the teacher: keep the top-k probabilities, renormalize, and minimize a divergence on what remains. Renormalization is assumed to account for the missing mass. We prove that it removes the visibility of tail mass, not the freedom to move it. The renormalized objective depends only on log-odds among the retained tokens, so at each position its gradient along the directions that control tail mass is exactly zero; on a real teacher that component measures $2$-$3\times10^{-15}$ of the gradient. The full-vocabulary gradient equals the truncated gradient plus a residual weighted by the tail masses, and training acts only on the first term. Without the cross-entropy term, a top-k student's tail mass drifts away from the teacher's while a full-vocabulary control moves slightly toward it; with it, the gap shrinks about fourfold but persists. On seven open-weight teachers, the retained set determines the teacher's distribution only from $k=d+1$ ($d$ the hidden dimension): recovery is exact from there on all seven, and commonly cached sizes sit below it. In our off-policy runs the practical effect is real but smaller than the choice of teacher-student pair. Renormalization is a normalization, not a safeguard. The code is available at https://github.com/KurbanIntelligenceLab/top-k-distillation.

In this work, we propose a transfer learning algorithm for covariate shift, integrating sample reweighting with representation learning. A key feature of our approach is the use of a lower-dimensional latent space for modeling, in contrast to conventional methods that operate directly in the high-dimensional ambient space. Our method estimates the density ratio of learned latent features for downstream weighted prediction. We establish explicit target-domain excess-risk rates with independent data folds for strictly sufficient learned representations with regular learned-space prediction scores and density ratios. We give dimension comparisons under stated smoothness conditions and a variance comparison for true weights and a fixed predictor. General finite-sample inequalities retain representation-quality errors. Experiments on simulated and real-world datasets demonstrate gains from combining learned representations and latent weighting, and reveal sensitivity to initialization and domain choice.

Settling one comparison between two truncation samplers has cost six thousand A100-hours, and nothing says in advance how far apart two samplers can be. We observe that almost every deployed truncation rule keeps a prefix of the probability-sorted vocabulary, so any two such rules are nested at every decoding step. Nesting yields a closed-form per-step distance and a coupling under which both samplers emit identical text until they first disagree. Accumulated over a generation, this gives a separation certificate that bounds the difference between two samplers on any bounded outcome, is computable from logs a comparison already produces, and equals their sequence-level total variation distance exactly when neither rule ever overtakes the other. Two consequences follow without measurement: exactness is fragile, and certifying a small difference requires the two retained masses to agree to very high precision at every step. On six open-weight models over four math and science benchmarks, the certificate for every hyperparameter grid we tested is at least 0.998, so a bound alone rarely settles a comparison, although two members of one family can be far closer. What remains useful is the coupling, which gives an unbiased paired estimator that cuts variance $1.2$-$3.8\times$ against prompt-level pairing. Read against benchmark sizes at the default pair's variance and our point estimate of its between-prompt component, resolving a one-point difference needs 8 to 32 samples per prompt on GSM8K, MATH-500 and GPQA-Diamond and about 210 on AIME 2025; at that component's upper confidence bound GPQA-Diamond needs more than 32 and AIME 2025 cannot be resolved at any sample count. Choosing a truncation sampler is a measurement problem at least as much as a design one. The code is available at https://github.com/KurbanIntelligenceLab/truncation-samplers.