Papers

Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distribution differs from the training distribution and ask: under what assumptions on the target function or operator is stable extrapolation possible, and how far beyond the training domain can one extrapolate? Existing theory controls the test error through additive penalties measuring the discrepancy between the training and test distributions. Such guarantees show robustness to small distribution shifts, but can be very pessimistic in comparison to OOD performance observed empirically. We identify classes of holomorphic functions and operators for which the OOD generalization error converges at algebraic rates even in the presence of large distribution shifts. This phenomenon stems from the increasing smoothness of higher-index coordinates, leading to what we term a `blessing of high dimensionality'. For learning with either polynomials, deep neural networks or deep neural operators, we derive explicit rates for arbitrary test measures supported on suitable domains and quantify how the admissible domain depends on the underlying regularity of the function or operator. Our extrapolation guarantees are independent of the test distribution, depending only on its support. We also present a series of numerical experiments across a range of functions and operators that support the main theoretical findings.

Modern learning systems often acquire supervision at multiple resolutions, trading annotation cost against information content. We study cost-aware two-resolution learning, where expensive fine labels reveal a vector response and cheaper coarse labels reveal a scalar aggregate formed with unknown weights, while the target remains the full response. The challenge is that unknown aggregation changes which directions coarse data can identify, so the value of coarse supervision depends jointly on cost, noise, and identification. We characterize this information geometry and develop an estimate-and-track policy that learns the aggregation rule and tracks the optimal resolution mix. We derive a closed-form break-even condition for coarse supervision and prove that the online policy attains the optimal leading cumulative-risk coefficient, with a matching local asymptotic minimax lower bound. Synthetic experiments support the predicted all-fine/mixed transition, show the online learner approaching the oracle-share benchmark, and demonstrate a finite-budget gain over all-fine acquisition when coarse supervision is sufficiently favorable. Our results provide a principled way to balance information and annotation cost across supervision resolutions.

To reduce the number of parameters and cache memory requirements of transformers we introduce dual-headed transformers instead of three heads. We studied Walsh-Hadamard Transform (WHT), Discrete Cosine Transform (DCT), Discrete Fourier Transform, filterbank based Shearlet Transform, and Multiplication-Avoiding (MA) operators to construct dual heads. We combine spatial patches and their orthogonal transforms (or Shearlet and MA operators) in a structure similar to the attention block. We obtained better results than triple headed transformers in ImageNet. Extensive simulation examples are presented.

Self-distillation turns knowledge distillation into a closed learning loop and offers a path toward recursive self-improvement. Without an external teacher, however, the model must determine both what information can improve its supervision and which induced changes should be learned. Existing methods typically improve teacher-generated data or select training examples in isolation, leaving the information transferred between these stages unmeasured. We introduce InFlow, a retrieval-guided on-policy self-distillation framework that models this process as potential-to-realized information flow. InFlow first retrieves potentially informative sources using certainty-calibrated hidden-state trajectories, then measures their realized effect through the Jensen–Shannon divergence between the teacher's initial and retrieval-conditioned answer beliefs. Examples with larger belief shifts are selected for on-policy distillation. Our analysis formalizes the information optimized by retrieval and selection and relates the answer-level shift to the teacher–student distillation gap. Across four open-weight language models and three knowledge domains, InFlow achieves the strongest cross-model average among the compared selection methods, with ablations supporting both stages of the framework. Our code is available at https://github.com/1240148048/INFLOW.

Matrix optimizers have emerged as a promising direction, with Muon standing out as a prominent design. Revisiting Muon through its full-Gram representation, we observe that it jointly processes marginal-scale and interaction information. This opens an alternative way to organize geometric information hierarchically, motivating the Normalize-Then-Precondition framework. Specifically, it first uses diagonal-Gram information to construct a marginally normalized update, then applies spectral preconditioning to its directional interaction geometry. Building on this framework, we develop NormPre with NormPre-G and NormPre-L adopting global and localized spectral preconditioning, grounded in spectral-norm steepest descent and a regularized formulation followed by leading mode selection, respectively. To enable large-scale training, NormPre-G uses Newton-Schulz iterations and NormPre-L employs randomized sketching to approximate the leading interaction eigenspace. Theoretically, we establish $\mathcal{O}(T^{-1/2})$ convergence guarantees for simplified versions of NormPre. Across extensive pretraining experiments on GPT-2 Small, LLaMA and Qwen3, both variants consistently outperform AdamW, Muon and MANO under matched training budgets. Further efficiency and spectral analyses reveal the complementary strengths of two variants and characterize their performance-efficiency trade-off. We open-source our code through a GitHub repository at https://github.com/zx-gong/NormPre.

Large language models have achieved significant progress in event forecasting, yet their probability outputs exhibit systematic calibration bias that varies heterogeneously across different domains and question types, undermining the trustworthiness of probabilistic outputs for decision-making under uncertainty. However, existing calibration methods typically correct probability outputs after prediction is complete, without modeling the structural sources of bias within the prediction process itself. To address this challenge, we decompose probabilistic prediction over causal-temporal hypergraphs into three stages, evidence weighting, evidence aggregation, and source fusion, and propose CHAIN, which designs stage-specific mechanisms to mitigate bias at each stage: (i) modulating the temporal decay function by causal topological distance, (ii) aggregating approximately independent causal chains via Noisy-OR after direction-aware deduplication, and (iii) driving adaptive fusion by causal coverage and directional balance. Experimental results on cross-domain forecasting benchmarks show CHAIN outperforms existing methods in expected calibration error, Brier score, and accuracy. Our project is available at https://github.com/QwenQKing/Chain.

Identifying the root cause of an anomaly among hundreds of sensors is critical for preventing safety incidents and costly downtime in complex monitored systems. Existing studies evaluate root cause analysis (RCA) methods using top@k accuracy. We show that this metric has a fundamental blind spot: it conflates two failure modes, retrieval failure, where the true cause is never considered, and reranking failure, where it is considered but ranked too low. In this work, we introduce a retrieval-reranking decomposition and audit four well-known benchmarks to expose this blind spot. Our experiments show that, on benchmarks with complex faults, statistical baselines mis-rank the true cause 79-100% of the time, and graph-based methods never clearly beat the best statistical baseline, whether their causal graphs are learned on short fault windows, on retrieved candidate pools guaranteed to contain the cause, or on multi-day normal-operation data. Meanwhile, on simple benchmarks where faults manifest significantly at their origin, retrieval is nearly solved (98-100%). Guided by the decomposition, we build a two-stage pipeline combining a multi-signal retriever with an LLM reranker that, as one fixed configuration, matches or exceeds the best baseline's top@1 accuracy on all six benchmark suites (by up to +12 points), with no causal graph or labeled data required. When all methods rank the same retrieved candidates with the true cause guaranteed present, adding a short system-description document lets the reranker lead the best baseline by +7 to +18 points on every benchmark. Code is available at https://github.com/cruiseresearchgroup/DecompRCA.

Molecular optimization is inherently iterative: a candidate is proposed, evaluated against several objectives, and revised while preserving a relationship to the source molecule. Most instruction-following models instead emit one edited molecule, forcing validity, property improvement, and similarity control into a single response. We introduce MARCO, an evaluator-grounded reinforcement-learning framework that trains molecular editors on bounded proposal–feedback–revision trajectories. MARCO aggregates shaped turn rewards into an undiscounted trajectory return for group-relative policy optimization. We evaluate two consequences of this training: Same-1 tests the trained policy under a one-response budget, while Same-5 tests whether the same policy can use verifier feedback when up to five responses are available. Across the three-objective MuMOInstruct benchmark, three Qwen backbones, and seen/unseen instruction splits, SFT-initialized MARCO obtains the highest product of property success rate and similarity in every reported primary setting. Same-5 further improves the observed score under the tested budget, while four-objective and public-checkpoint experiments test transfer across constraint sets and initialization regimes.

Private Evolution (PE) is a differentially private algorithm for synthetic data generation. While it can be viewed as a Wasserstein learning algorithm, it performs much better in practice than worst-case Wasserstein analyses would predict. We recast PE as generative model-augmented Wasserstein learning. We show theoretically that when we take into account the use of a generative model that is able to capture something about the true distribution, then we can obtain much better performance bounds. For example, if the generator gives samples in the same low-dimensional space as the distribution, then sample complexity depends on intrinsic, not ambient, dimension. We also show that standard variants of PE can fail to converge on simple well-clustered instances, and propose a new geometry-aware version of PE with provable convergence on such instances. Experimentally, we show that our new algorithm is competitive with standard baselines and can improve recall.

Efficient exploration in high-dimensional decision spaces remains a central challenge for decision-making systems. Humans, in contrast, can navigate large decision spaces with remarkable efficiency. Recent behavioral studies suggest that humans reduce dimensionality in large decision spaces by probing candidate feature dimensions, identifying reward-relevant ones, and restricting the effective decision space. Inspired by this mechanism, we propose TDGE (Task-Dimension-Guided Exploration), a human-inspired, model-agnostic algorithm with an automatically constructed task-dimension–feature–item hierarchy. TDGE follows a top-down exploration strategy: it first selects task-relevant feature dimensions, then identifies informative features within those dimensions, and finally recommends concrete items based on the selected features. Experiments on MovieLens-20M, LastFM, and Amazon recommendation datasets show that TDGE substantially improves exploration efficiency and cold-start adaptation over baseline algorithms. Comparisons with other structured algorithms and ablation studies attribute these gains to TDGE's hierarchical structure and semantic feature-space exploration, with robust results across clustering methods and hierarchy depths. Recommendation-trajectory visualizations also show exploration patterns similar to human dimension-guided behavior.

Polyak step size (PS) and Armijo line search (ALS) have received increasing attention in stochastic optimization, with encouraging empirical performance and theoretical guarantees. However, their convergence theory for stochastic heavy ball (SHB) methods remains limited. In this work, we develop a unified convergence analysis for SHB equipped with PS and ALS. To this end, we introduce a modified Armijo rule that closely parallels the Polyak step size, together with a decoupling analysis that isolates the historical dependence induced by momentum. For SHB with standard PS and ALS, we establish expected convergence for strongly convex, convex, and non-convex objectives without interpolation or restrictive conditions on the momentum parameter. Under interpolation or strong growth, we further strengthen the results to almost sure rates and last-iterate convergence. Moreover, for general settings beyond interpolation, we prove almost sure convergence to the exact optimum or to stationarity for SHB with diminishing variants of PS and ALS. These results provide a more comprehensive theoretical view of Polyak step size and Armijo line search for stochastic heavy ball methods.

We present GenLimitLib, a source-aligned Lean 4 library for language generation in the limit. Introduced by Kleinberg and Mullainathan at NeurIPS 2024, language generation in the limit studies a theoretical question motivated by LLMs: how to generate valid new strings from observed examples. This young and rapidly evolving field offers a natural testbed for studying large-scale formalization. GenLimitLib contains formal developments for 30 papers. It extracts shared definitions and reusable proof components while preserving paper-specific assumptions and statements, and records relationships across papers. In this way, GenLimitLib provides a concrete and structured view of the literature. We show through mathematical case studies and LLM experiments how our library can support both human mathematical research and AI-assisted research. Our Library: https://github.com/pengzhang91/generation-in-the-limit-lib.

The pre-training of Large Language Models (LLMs) is increasingly conducted across multiple data centers. As training scales to a larger number of accelerators, the fraction of time spent on computation decreases, while the fraction spent on communication increases. Therefore, frequent synchronization becomes a growing bottleneck. Local update methods reduce this cost by allowing workers to perform several optimizer steps between synchronizations. Most local update methods set the number of local optimizer steps between synchronizations before training and keep this interval fixed throughout the run. However, the best interval can change during the entire train process. If the interval and optimizer are adapted to the current training state, the communication frequency is reduced while maintaining the training performance. In this work, we introduce AutoLoCo, an adaptive training framework to reduce communication in LLM training. It adapts the local interval using scalar training statistics and corrects each outer update. Our method is motivated by two observations: 1) the appropriate local interval varies across training stages, and 2) changing the number of inner steps per interval creates a mismatch with an unchanged outer optimizer, requiring a correction to the outer update. We optimize this mismatch by correction of the outer optimizer for the momentum and the learning rate using the accumulated inner learning rate. Our experiments under communication constraints demonstrate that AutoLoCo reduces communication frequency by 27% relative to DiLoCo while maintaining training performance.

We study federated learning (FL) with adversarial clients, where the goal is to minimize the average loss of the honest (non-adversarial) clients without knowing their identity. Under heterogeneity, a single shared model parameter is statistically inappropriate: it cannot capture the distinct data-generating processes across clients, incurring an irreducible model-heterogeneity bias and severely limiting robustness to adversarial clients (a.k.a. Byzantine-robustness). We address this problem through representation learning, where each client learns a personalized linear head, while collaboratively estimating a shared nonlinear representation through Byzantine-robust aggregation. We demonstrate that the heterogeneity among honest representation gradients is controlled by the representation error and statistical errors that decay either with the number of data samples per client ($\tau$) or the number of iterations ($T$). In particular, our non-asymptotic parameter recovery error bound reveals three terms: (i) an initialization-dependent error that goes away with $T$, (ii) finite-sample noise terms that decreases with $\tau$ and the number of honest clients, and (iii) a stochastic gradient variance term that also reduces with $T$. Importantly, with no irreducible model-heterogeneity bias in our bounds. We extend the regression analysis to multiclass classification, and empirically validate it on CIFAR-10, FEMNIST, and School Exam Score datasets.

The strong generalization performance of on-policy post-training paradigms has motivated studies of their parameter update behaviors. However, these studies treat the observed behaviors only as byproducts in on-policy training, overlooking their potential to serve as optimization principles for improving the generalization of other paradigms such as supervised fine-tuning (SFT). To address this limitation, we investigate whether there exists a specific on-policy update behavior that can achieve such improvements. First, our analyses reveal that SFT updates parameters along consistent directions, while the on-policy paradigm continuously adjusts the direction during training. This difference inspires us to focus on the cumulative update direction of each parameter as a promising behavior. Then, we evaluate its effectiveness for improving generalization by proposing On-Policy direction-constrained Supervised Fine-Tuning (OPSFT), which constrains SFT updates to the direction identified by on-policy paradigms. The strong performance of OPSFT indicates that the generalization advantage of on-policy paradigms can be transferred to SFT through the parameter update direction. Once such a direction is identified, even SFT can generalize with its updates constrained to this direction. This finding offers two practical benefits by combining the strong generalization of on-policy paradigms with the advantages of SFT, including the high training efficiency and ability to leverage high-quality trajectories. For efficiency, we identify update directions that support strong generalization using a few on-policy training steps, and subsequently apply OPSFT to achieve high training efficiency. For leveraging high-quality trajectories, OPSFT can utilize these trajectories to continue improving a post-trained model along its update direction without disrupting the ability learned from on-policy training.

Training models to act in accordance with an explicitly defined set of principles, or "constitution," has shown promise as a robust and transparent mechanism for AI alignment. However, the generality and flexibility of such methods remain unclear. Here, we show that constitution-consistent behavior can be distilled from synthetic corpora into lightweight objects (low-rank adapters and steering vectors). Despite never seeing a harmful request or jailbreak during training, such objects increase jailbreak defense success and measured alignment – particularly at long context lengths and against multi-turn attacks, where they outperform both prompted and steered baselines. Subtracting control-trained from constitution-trained objects further accentuates these effects, yielding defenses we call "constitutional adapters" (CAs). CAs can be trained on a base model, transferred zero-shot to its post-trained checkpoint, and scaled at inference time to predictably trade off defense for benign compliance. Taken together, these results recommend CAs as a lightweight, portable, and tunable lever for mitigating misalignment and misuse in API deployments.

Large language models make weight storage and memory traffic major inference costs, motivating low-precision formats that represent each weight with only a few bits. Such formats use a scale to map floating-point values into a small codebook; NVFP4 improves local range utilization by letting every 16 E2M1 weights share an E4M3 block scale. Choosing that scale is difficult in GPTQ because quantizing one column updates those that follow, so evaluating a block independently can misestimate its final reconstruction error. Large models pose a second challenge: full-precision weights, calibration activations, and second-order state cannot all remain on one accelerator, while assigning complete layers to devices leaves each time-consuming layer solve serial. We introduce Schur Replay, a scale-selection algorithm that reproduces the GPTQ updates caused by each block scale and scores the resulting block error after accounting for compensation from unquantized columns. Separately, our execution infrastructure keeps only the active layer resident, tiers activations across device, host, and disk, retires full-precision layers after export, and distributes independent output rows across tensor-parallel ranks. Together, the algorithm and infrastructure attain $99.35\%$ and $100.84\%$ question-weighted recovery from BF16 across seven benchmarks on Qwen3.5-397B-A17B and Llama-3.3-70B-Instruct. On the 397B model, the infrastructure reduces measured per-layer time by $15.17\times$ over ModelOpt and $23.14\times$ over LLM Compressor, with lower memory used per GPU.

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

Language-model agents are usually trained by reinforcement learning from one reward per episode, and privileged self-distillation enriches it by letting the same policy, given a skill, teach its skill-free self through token probabilities. However, we identify two phenomena that question this channel. Invisible Advantage: a skill in context lifts WebShop success from 42.2% to 56.2%, yet changes the probabilities of fewer than a quarter of the sampled tokens. Much to Align: a skill changes the hidden states of over 80% of response tokens, in a way that linear probes can trace back to the specific skill. To exploit this, we propose Privileged Representation On-policy Self-Distillation (PR-OPD). After a GRPO warm start, the policy writes a hindsight skill for each trajectory, re-reads its own responses with that skill as a stop-gradient teacher, and aligns its projected hidden states to the teacher's at every layer alongside the reward objective, with no external skill library, separate teacher, or inference overhead. On ALFWorld and WebShop with two backbones, PR-OPD achieves the best overall results in every setting, improving over GRPO by up to 4.7 points in ALFWorld success and 14.0 points in WebShop accuracy. Code is available at https://github.com/balibata/PR-OPD.

Process reward models (PRMs) have become a key component for LLMs, as their step-level feedback supports both post-training and test-time reasoning. However, training strong PRMs remains costly: human step annotation is difficult to scale, while Monte Carlo estimation is computationally expensive and can drift from the intrinsic correctness of steps. To get effective PRMs at low cost, we introduce TIPS (Thinking-Induced Process Supervision), an outcome-only reinforcement learning (RL) framework for training generative PRMs. In TIPS, the model generates a chain-of-thought (CoT) followed by step-level labels and an outcome label. The reward depends solely on whether the predicted outcome matches the ground truth, and the resulting group-relative advantage is used to optimize the entire generated response. Intuitively, when checking intermediate steps helps determine the outcome, more accurate checks can lead to better outcome judgments and higher rewards. Outcome-only RL can therefore reinforce step-level verification without explicit process supervision. We validate the effectiveness of TIPS across math and agent benchmarks and four backbone families. Notably, TIPS-Qwen3-4B-Thinking-2507 reaches 85.2 F1 on ProcessBench with only 3.2K outcome-labeled trajectories, surpassing all evaluated trained PRMs and strong prompt-only judges such as GPT-5.4-Instruct and Claude-4.7-Opus, while still trailing o1-mini. Code and data are available at https://github.com/RUCBM/TIPS.

Scanning Tunneling Microscopy (STM) is a widely used tool for characterizing surfaces of materials at the atomic scale, playing a crucial role in discoveries across condensed matter physics and materials science. Despite its extreme spatial resolution, STM is one of the most sensitive microscopy techniques and is highly prone to noise. While existing unsupervised denoising methods are very cheap to train, these are primarily focused on removing the noise with minimal recovery of key physical information. While supervised methods can offer superior performance, the major bottleneck is that a large amount of paired clean-noisy experimental images is required which are impractical to obtain. Thus, we developed a low-cost physics-driven digital toolkit to rapidly generate large volume of realistic STM images. Firstly, we simulate clean images from a chosen material system. Then, with prior knowledge of the physical characteristics of the artifacts and noise present in STM experiments, we formulate several artifact-noise functions such as Gaussian electronic noise, 1/f flicker noise, scan-line noise, background tilt and mechanical drift. These physically informed noise components are then added to the simulated clean images to generate realistic STM images. We demonstrated the capability of the proposed digital toolkit to generate AI-ready data for denoising images of the (111) surfaces of copper and lead, while preserving atoms, defects, and electron waves. We also validated the quality of the downstream image analysis of learning electron wave patterns induced by quantum interference from Cu(111) images. Results show that the supervised models trained on digitally generated AI-ready data can more effectively denoise and learn electron wave patterns on Cu(111) images than benchmarked unsupervised approaches, indicating that the proposed toolkit facilitate scientific discovery.

Text-to-image users often provide concise and underspecified prompts, whereas generative models benefit from detailed textual conditions for reliable instruction following. Existing systems bridge this gap with Prompt Enhancers (PEs) that rewrite raw prompts at inference time, introducing additional latency and leaving prompt elaboration external to the generator. We instead view enhanced prompts as privileged training information and ask whether their benefits can be internalized. We propose Prompt-Enhanced On-Policy Self-Distillation (PE-OPSD) for text-to-image flow-matching models. During training, a raw-prompt student follows its own generation trajectory, while an enhanced-prompt teacher provides vector-field targets at the states visited by the student. This on-policy supervision distills the behavior induced by enhanced prompts into the raw-prompt student without requiring additional text–image pairs. At inference, both the PE and teacher are removed, and the student generates directly from raw prompts. Across multiple model families, PEs, and benchmarks, PE-OPSD achieves the strongest aggregate prompt fidelity among the evaluated baselines, yields positive aggregate visual appeal gains, and retains the base-model inference efficiency.

Looped language models (LoopLMs) increase computational depth through parameter sharing, offering a path to scale inference computation without adding parameters. However, it remains unclear when additional recurrence is beneficial and how architectural choices affect its effectiveness. Through controlled experiments, we systematically examine (1) when recurrence helps, (2) where it should be applied, and (3) how its conditioning affects performance. Our evaluation covers inference budgets below, within, and beyond the training horizon under knowledge and reasoning tasks. (1) We find that recurrence can improve reasoning beyond the training horizon while degrading knowledge performance, but harder reasoning instances do not consistently benefit more. (2) Performance also depends on how distinct layers and recurrent iterations are allocated, showing that effective depth alone is insufficient to predict behavior. Non-recurrent output layers improve robustness to under-unrolling, while the preferred placement of input and output layers varies with inference budget. (3) Finally, we find that conventional initial-state injection offers limited robustness to varying recurrence depth. We therefore propose history-state injection as an alternative, and show that channel-wise history-state injection combined with timestep conditioning offers a low-cost and more effective design, better preserving knowledge under extended unrolling while improving robustness across inference budgets. Overall, our results clarify when recurrent computation helps, where it fails, and offer practical guidelines for designing LoopLMs across variable inference budgets.

This paper proposes a physics-guided gradient-ascent-based machine unlearning method that couples the forgetting signal with the physical residual of the target cyber-physical systems, ensuring that weight updates during unlearning are steered toward physically feasible regions of the weight space. The physics residual acts as a safety fence during gradient ascent: the model is steered away from the poisoned behavioral basin and simultaneously toward physics-compliant territory, rather than toward an arbitrary alternative that may still violate domain constraints. We evaluate the proposed method against four baselines: naive gradient ascent, exact unlearning, SISA, and full retraining on an IEEE 34-bus distribution system, driven by two physics-informed neural network-based distribution energy resource controllers and validated through high-fidelity OpenDSS power-flow co-simulation. From the evaluation, we found that our proposed physics-guided model simultaneously removes poison and restores physical compliance, which are essential for the safe deployment of safety-critical cyber-physical systems

Polysomnography (PSG) integrates multiple physiological signals to provide a comprehensive characterization of human sleep, yet its heterogeneous channel configurations across centers pose substantial challenges for transferable representation learning. Existing foundation models mainly focus on physiological modeling or temporal learning, while channel identity is often treated as a fixed structural index, overlooking the physiological semantics encoded by signal modality and reference configuration. To this end, we propose SemPSG, a Semantic channel-aware foundation model for heterogeneous PSG analysis. SemPSG explicitly represents the physiological semantics of channel identity and incorporates them into both signal representation learning and channel aggregation, enabling flexible modeling across diverse data configurations. Specifically, a semantic-conditioned time-series encoder captures signal-specific temporal dynamics and cross-signal interactions, while a multi-view image encoder extracts complementary time-frequency and morphological patterns from the same physiological recordings. We evaluate SemPSG on sleep and health-related tasks, including sleep staging, sleep-disorder breathing analysis, disease prediction, cognition and emotion recognition, and demographic estimation. Extensive experiments demonstrate consistent improvements over both general-purpose time series foundation models and PSG-specific foundation models, together with generalization across heterogeneous datasets across diverse channel configurations.

Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, however, their conventional pointwise space–time representation does not explicitly encode temporal dependence, which can hinder accurate prediction. To mitigate this limitation, this work proposes a novel neural architecture termed a causal integral neural network (CinNet). The core module of CinNet is a Volterra-type causal integral term, which aggregates historical features to encode temporal dependence, thereby incorporating temporal causality at the architectural level rather than through training-level modifications as in many existing methods. Building on CinNet, we further develop a causal integral physics-informed neural network (CI-PINN) for solving evolution equations. Extensive numerical experiments on benchmark evolution equations demonstrate that the presented method outperforms various baseline PINN variants in terms of solution accuracy, with pronounced superiority under sparse-collocation scenarios. Additional empirical analyses show that CI-PINN exhibits low sensitivity to hyperparameter choices, while ablation studies confirm the effectiveness of the proposed network components.

A commercial incentive need not enter the final ranking algorithm to affect a shopping assistant's recommendation: it may instead influence which preference question the assistant asks. We make this distinction experimentally observable in a deliberately small, synthetic setting. Each task has two products, three verified numerical attributes, a price limit, and a private fixed preference vector. An honest simulated user answers one pairwise question. A separate recommender receives the products and this answer but not the sponsorship assignment. We contrast a neutral question, a soft commercial instruction, and an explicitly adversarial instruction to ask about the sponsor's advantage while omitting the rival's advantage. Across 40 held-out sponsorship-assignment cases (20 distinct catalog-preference contexts), the soft instruction changes no selections. The targeted instruction raises sponsored selection by 0.30 and reduces mean synthetic utility by 0.0547 relative to neutral questioning (95% context-bootstrap interval [-0.0828, -0.0291]) for one language-model recommender. A fixed Bayesian recommender shows a similar effect; a second model makes the same choices on all 120 frozen question-answer inputs. A terminal-answer consistency judge rates all 20 sampled targeted answers consistent, although five have synthetic regret above 0.05; a separate question-coverage dimension flags their one-sided elicitation. A robust partial-preference certificate remains valid under the stipulated synthetic utility but certifies only 16 of 40 targeted cases and is not better than asking a neutral question directly. These results establish neither typical behavior under advertising incentives nor effects on actual consumers.

Unlearning in large language models (LLMs) is typically evaluated at the output level, where a model appears to suppress sensitive or undesirable content. In this work, we show that such evaluations can create an illusion of forgetting: even when output-level leakage is eliminated, sensitive information can remain encoded in the model's hidden representations. We first provide a theoretical analysis establishing a fundamental separation between output suppression and representational erasure. Specifically, we show that the decoder can be made arbitrarily insensitive to sensitive directions, driving output-level leakage to zero, while the hidden representations retain the underlying information. To empirically validate this phenomenon, we train generative probe decoders on hidden states across transformer layers, enabling layer-wise measurement of information leakage. Across three widely used benchmarks, TOFU, MUSE, and WMDP, and state-of-the-art unlearning methods, we find that substantial sensitive information remains recoverable from hidden representations, even when standard output-level metrics indicate successful unlearning. To address this gap, we propose Probe-Adversarial Representation Suppression (PARS), an unlearning objective that adversarially minimizes the extractable information from hidden representations. PARS directly targets representational leakage and provides significantly stronger guarantees of erasure under adversarial probing and relearning attacks, outperforming all evaluated baselines. Our results highlight a fundamental limitation of existing unlearning paradigms and suggest that true forgetting in LLMs requires controlling not only model outputs, but also the information encoded in hidden representations. Codes are available at https://github.com/OptimAI-Lab/HiddenStateUnlearning.

Agnostic federated learning (AFL) seeks a model that performs reliably across $m$ heterogeneous workers, but communication remains a bottleneck. We improve communication efficiency by reducing the number of synchronization rounds via faster convergence and the communication cost per round via compression. We first propose AFL-BR, which updates the dual weights over workers using online mirror ascent with KL divergence and blockwise restarts. It achieves an $O((\log m)^{1/4}T^{-1/8})$ stationarity rate after $T$ update rounds, reducing the $m$-dependence of the synchronization rounds required for convergence from polynomial to logarithmic order. Building on AFL-BR, we develop AFL-Com by applying bidirectional compression with error feedback (EF). Instead of compressing local gradients, workers apply EF to their dual-weighted gradients, enabling direct control of the aggregated compression error under time-varying weights. We then establish an $O((\delta^{-1}+(\log m)^{1/4})T^{-1/8})$ stationarity rate for AFL-Com under general $\delta$-approximate compressors and improve the $\delta$-dependence from $\delta^{-1}$ to $\delta^{-1/2}$ for additive-and-idempotent compressors with shared randomness (SR). With suitable compression levels, AFL-Com retains the same convergence rate as AFL-BR at a lower per-round communication cost, yielding reductions in total communication complexity by factors of $(\log m)^{1/4}$ with Top-$k$ and $(\log m)^{1/2}$ with Rand-$k$ and SR. Experiments validate the improved synchronization and communication efficiency of our methods.

Electroencephalography (EEG) analysis requires careful choices in preprocessing, statistical modeling, and machine learning because EEG signals are highly susceptible to artifacts, volume conduction, low signal-to-noise ratio, and substantial inter-subject variability. This chapter provides a practical and methodological guide to modern EEG analysis, spanning EEG preprocessing, artifact removal, filtering, bad-channel detection and interpolation, re-referencing, independent component analysis (ICA), and preprocessing of simultaneous EEG-fMRI recordings. We review major approaches for computational EEG analysis, including event-related potentials (ERPs), time-frequency analysis, functional and effective connectivity, source localization, multivariate decoding, permutation testing, and multiple-comparison correction. We then examine machine-learning methods for EEG, from feature-based classifiers to deep learning and emerging EEG foundation models, with emphasis on cross-subject generalization, limited-data regimes, data leakage, evaluation metrics, and fair benchmarking. Reproducibility is treated as a core requirement throughout, including transparent preprocessing, BIDS-EEG data organization, standardized derivatives, preservation of raw data, and FAIR data practices. The chapter is intended as a practical reference for researchers developing reliable, interpretable, and reproducible EEG analysis and machine-learning pipelines.