Silicon sampling generates survey respondents by having a large language model (LLM) answer a survey as a person with given demographic attributes, and the resulting synthetic populations are increasingly used in place of human ones. Existing evaluations focus on individual-answer accuracy, per-question answer distributions, and correlations across questions. None of these compares the respondents themselves, so a generator whose respondents have combinations of answers found in no human respondent can still score well if it reproduces every answer distribution. We propose the respondent coverage gap (RCG), which represents each respondent as a point defined by their complete answer profile and measures how far each human respondent is from the nearest generated one, relative to the distance between human samples. On two US social surveys, all six LLMs we evaluate leave human respondents uncovered, and under our main settings, they fall behind a baseline that samples each answer independently from the human marginals. Across the prompting and inference settings we test, every LLM has a higher RCG than a Gaussian copula fitted to the human data.

Recommender systems typically serve one user at a time. However, in households, members share a finite pantry and follow different dietary rules, making independent recommendations prone to resource conflicts and dietary violations. We formulate household food recommendation as constrained fair division and present FairFRESH, a neuro-symbolic framework that learns per-member utilities, allocates foods under explicit welfare objectives, enforces dietary rules through a deterministic filter, and explains recommendations using Shapley and Banzhaf attributions. Theoretically, we show that no finite penalty guarantees compliance near a dietary-rule threshold, establish approximation guarantees for greedy allocation under utilitarian and smoothed Nash objectives in the stock-free model before filtering, and characterize the scale invariance of Nash welfare. We also use the minimax theorem to analyze rotating shared meals. On NHANES-derived data, the learned utility model achieves Recall@20 of 0.293, outperforming five learned recommenders (at most 0.244) but not a previous-day repetition heuristic (0.321). On held-out four-person households, Nash allocation reduces Gini disparity by 42% relative to conflict resolution while improving Recall@20 from 0.180 to 0.197. It comes within 2% of an upper bound on the smoothed Nash optimum, and rescaling one member's utilities changes at most 1.5% of assignments. All recommendations satisfy the encoded dietary rules, while attribution scores correlate with utility loss upon component removal (r = 0.76). In simulation, shared meals reduce pantry use by about one-third, and weekly rotation increases the worst-off member's utility by 38% over the best fixed meal.

Understanding catastrophic forgetting, in which learning new tasks degrades performance on previously learned tasks, remains a fundamental challenge in continual learning (CL). Existing theoretical analyses often rely on specific model or task structures and offer limited insight into how iterative optimization affects forgetting. To address this gap, we develop an algorithmic stability framework for expected population forgetting under SGD without prescribing a particular model architecture. Specifically, we decompose forgetting into intra-task and cross-task generalization gaps and empirical forgetting. To bound the generalization gaps, we track how a sample perturbation affects updates within a task and propagates through subsequent tasks. We consider constant, intra-task decaying, and continuously decaying learning-rate schedules. Comparing the two decaying schedules allows us to characterize how restarting learning-rate decay at task boundaries affects the propagation of historical sample perturbations. For empirical forgetting, we derive bounds for all three schedules by retaining cumulative gradient alignment along the optimization trajectory, without requiring convexity. Combining these results yields upper bounds on expected forgetting that capture the effects of training set size, the number of updates per task, the total number of tasks, learning-rate schedules, and cumulative gradient alignment. Finally, we conduct experiments on Split CIFAR-100 and Split MiniImageNet to examine the empirical implications of our theoretical findings.

We consider differentially private (DP) optimization in the federated setting, where a DP estimate of the feature covariance matrix serves as a Hessian approximation for generalized linear models. Existing central DP methods for covariance estimation have communication cost that grows quadratically in the data dimension, while existing baselines with linear communication cost are only locally private and degrade as the number of clients increases. As a remedy, we propose a federated DP-PCA framework that achieves linear communication cost while providing central DP guarantees under secure aggregation. It consists of a DP rank selection step, a DP power method, and a noisy release of the covariance projected onto the selected low-dimensional subspace. We give error bounds for this covariance estimate and for the resulting low-communication preconditioned DP gradient descent. Empirically, our proposed DP optimization method matches a centralized baseline with quadratic communication cost at a fraction of the communication.

We study episodic linear Markov decision processes with unknown transitions, adversarial losses, and bandit feedback. The state-of-the-art result for this setting (Liu et al., 2024) either achieves $\sqrt{K}$ regret with a computationally inefficient algorithm or achieves suboptimal $K^{3/4}$ regret, where $K$ is the number of episodes. Our work gives the first $\sqrt{K}$ regret with a polynomial-time algorithm. Our method reduces adversarial linear MDPs to adversarial linear bandits whose action set consists of policies' expected feature vectors. The central challenge is that this action set is unknown and can be estimated only through exploration. We address this challenge by constructing an approximate separation oracle for the action set that either generates executable policies from queried features, or refines an outer approximation of the action set. This approach draws inspiration from the reduction of van Erven et al. (2025) for linear contextual bandits and the oracle-efficient linear bandit algorithm of Ito et al. (2019), but additionally deals with the imprecision of the oracle. The resulting algorithm requires only aggregate loss feedback, and to our knowledge. This is the first polynomial-time algorithm for adversarial MDPs with aggregate feedback beyond the tabular case.

Cyberbullying involves behavioral and contextual patterns beyond isolated abusive messages. However, existing approaches remain fragmented across content detection, semantic representation, and network analysis, with limited interpretable perpetrator representations, multi-scale structural modeling, and explanations of behavior-driven similarity and influence propagation. These limitations hinder the identification of persistent perpetrators, characterization of behavioral communities, and assessment of potentially influential users. This paper proposes Ontology-Driven Cyberbullying Behavior and Network Analysis (ODCBNA), a perpetrator-centric framework integrating requirements-driven ontology design, knowledge graph construction, behavioral modeling, community analysis, and influence modeling. Using the Bengali Contextual and Diverse Cyberbullying (BenCoDiC) corpus as a use case, ODCBNA identifies $1{,}063$ users with at least three bullying comments or replies as perpetrators and represents each through a $64$-dimensional behavioral and contextual feature vector. Cosine similarity and $k$-nearest-neighbor modeling produce a weighted network with $27{,}554$ edges. Louvain analysis identifies six communities with a modularity of approximately $0.495$ and $27$ sub-communities. Feature-contribution analysis identifies the Video, Impact, and User Profile groups as the strongest contributors to behavioral similarity and community separation, while contextual dimensions support interpretation. Community-constrained influence analysis shows that IM Greedy achieves small positive gains in all six communities, although different seed-selection methods produce comparable diffusion spreads despite limited seed overlap. These findings provide an interpretable basis for understanding perpetrator behavior, community organization, and potential influence patterns in Bengali online environments.

Large language models increasingly act as controllers in structured decision pipelines, yet their decisions are still executed by autoregressive text decoding. Hierarchical RAG is one such setting: at each frontier of a document tree, an LLM commits to $b$ of $k$ sections under an input-dependent action grammar, executed as either failure-prone free-form JSON or reliable but strictly serial grammar-constrained generation. We show that this serialization is unnecessary for bounded-horizon control: the reachable future forms a shallow action-prefix tree, which we compile --- one root prefill plus one tree-causal probe evaluate every prefix-conditioned action distribution with serial decoding's tokens, positions, and causal ancestry. A prefix-state lemma makes compiled control policy-exact in exact arithmetic: the same policy with a two-forward critical path and zero output tokens. One further probe pass certifies the exact order-marginalized MAP set. Across four document-disjoint splits and two scales on the primary MetaX device, compiled control matches the serial policy on $84$--$89\%$ of questions --- every instrumented divergence a floating-point near-tie --- and cuts control latency by $35$--$47\%$ versus token-wise serial decoding and $6$--$7\%$ versus an idealized chunked engine; an H800 repetition preserves the ordering.

Enthymemes are arguments that leave a premise or conclusion unstated, and they are a common persuasion device on social media. Because readers must fill in the missing part themselves, they often disagree on whether a text contains one. This paper asks how to detect and evaluate enthymemes when such disagreement is part of the task. On tweets about vaccination and immigration, each labeled by five annotators, F1 stalls around 0.67 for every fine-tuned model we train, regardless of data size, added features or label type. We therefore ask how these models should be evaluated instead, and propose metrics that compare predictions with the full distribution of annotator votes, together with a model that predicts this distribution directly and captures disagreement better at no cost in F1. We then ask what role discourse structure plays. Models learn to rely on explicit argumentative structure: they reliably recognize tweets without an enthymeme but rarely commit on tweets that contain one. Both the models and a discourse parser miss arguments whose links are left implicit and must be inferred by the reader. Finally, we discuss what these blind spots mean for content moderation systems trained on majority labels.

Real-world deployment of personalized federated learning (PFL) requires adapting to heterogeneous clients while preserving recognition performance beyond local distributions. However, high local accuracy can conceal failures on locally rare or absent classes. Effective personalization should therefore strengthen global recognition while raising the personalization floor. We propose an evaluation protocol that complements local accuracy with global, rare-class, and unseen-class evaluations to reveal generalization obscured by local scores, and assesses personalization floors among the worst-performing clients to expose weaknesses hidden by aggregate performance. To meet these deployment challenges, we propose FedGRC, a unified PFL framework integrating generalization and personalization through (i) Consensus-Guided Representation Learning (CGRL), which learns discriminative representations through shared directional and magnitude guidance; (ii) Multilayer Metric Synthesis (MMS), which constructs a shared covariance metric from these multilayer representations for statistical classification; and (iii) Support-Adaptive Shrinkage Personalization (SASP), which adapts class means within this metric by shrinking local estimates toward shared means according to local sample support, enabling adaptation while retaining shared knowledge. Extensive experiments, including benchmarking against 21 methods across 5 heterogeneity settings on 3 datasets and comprehensive ablation studies, validate the effectiveness of FedGRC. On CIFAR-10 and CIFAR-100, FedGRC surpasses state-of-the-art (SOTA) baselines in global recognition and personalization floors by at least 2.17% and 2.13%, respectively. On the real-world heterogeneous FedRS dataset, it outperforms the respective best baselines by 2.15%, 3.30%, and 4.61% in local adaptation, global recognition, and the personalization floor.

We construct a continuous function on $[-1,1]^2$ for which the infimum of the $L^2$-approximation error over the class of ReLU networks with two hidden layers and architecture $(2,2,1,1)$ is not attained. This counterexample shows that deep ReLU networks do not satisfy the best approximation property in general, even for continuous target functions. Our findings contrast with existing results for shallow neural networks, where ReLU is one of the few activation functions that guarantee the existence of global minima in typical regression tasks. The proof is based on the fact that the breaklines for neurons in the second hidden layer can bend, which breaks the symmetry arguments used in the one-hidden-layer case.

Our previous analysis found that a model's native hashed N-gram table is where continual updates disturb the base least, but its writes needed backpropagation and changed the pretrained table. We present Delta N-gram, a forward-only write path into that table. The pretrained table T^0 is never modified. Evidence is written into a sparse patch \Delta on the rows it addresses: a 4.1M-parameter writer emits a target and a gate per (position, hash head) event, and a block-averaged delta rule keeps each row a convex combination of its old value and the gated targets. The writer is trained offline on raw text with the pretraining objective; at use time writing takes forward passes only, and clearing \Delta restores the original model. A 0.6B prototype trained to answer questions keeps 16/16 facts after a second write; online gradient writes keep 2--4/16. We study two writers: a plain writer that encodes evidence with the T^0-only model, and a delta writer that reads its current memory while encoding. On Qwen3.8-Flash-Next, the plain writer's memory is document-specific: on 64 held-out news events it lowers continuation NLL by 0.068 nats/token against empty memory and by 0.024 against another document's memory, and 0.063 and 0.013 after 16 intervening articles. The delta writer's memory is more document-specific and keeps more of it under distraction (70% vs 54%). Over 35,000 writes on our previous seven-task chain both writers stay stable and the delta writer drifts less (layer-2 math drift 176% vs 188%); later accuracy changes by -0.26/-0.52pp (-7.29pp for gradient updates) and small-k_i drift is 17.9/17.5% (39.2%). Acquisition is negative, and general-input drift reaches 32.8% (20.75%): format rows read by every example grow to 4--12 times their pretrained norm. Zeroing eight such rows removes over 98% of layer-2 drift on math inputs, together with their NLL gain.

Offline contextual pricing often relies on logged observational data, but faces challenges from distributional shifts between training and deployment environments. Distributionally robust optimization (DRO) provides a principled approach to off-policy evaluation and learning (OPE/L). However, existing methods are mostly limited to discrete actions. Recent work has explored DRO for continuous treatments using inverse propensity weighting (IPW), while such IPW-based estimators can be sensitive to the convergence rate of propensity score estimates, particularly when estimated nonparametrically, which may lead to larger estimation errors and regret. In this work, we develop a doubly robust (DR) framework for distributionally robust OPE/L in continuous pricing settings. For evaluation, we propose a localized DR estimator that addresses the computational challenges of worst-case expectations by fitting only a small number of regressions, comparable to standard non-robust DR, while achieving semiparametric efficiency under mild product rate conditions. For learning, we leverage the inherent smoothness of demand noise to handle pricing-specific discontinuities in revenue outcomes (e.g., threshold-based purchase decisions), establishing a finite-sample regret bound of $\tilde{\mathcal{O}}_p(T^{-s/(2s+1)})$ for smoothness orders $s=1,2$. This bound improves upon existing regret rates in existing DRO-based off-policy learning (OPL) for continuous treatments. Extensive experiments under various levels of distribution shift validate our proposed framework.

Deep learning (DL) methods have substantially improved predictive performance across a wide range of downstream prediction tasks, enabling new discoveries in multiple domains. However, principled DL methods for non-Euclidean random objects remain relatively scarce, despite the growing importance of modern biomedical outcomes taking the form of probability distributions, random graphs, functions, and other random objects in metric spaces. Motivated by a new generation of digital and clinical biomarkers, we propose a deep learning framework for regression with random objects in metric spaces. Our approach operates directly on the metric structure of the response space, avoiding restrictive manifold or Euclidean embedding assumptions imposed by many existing methods. At the same time, it retains modern statistical guarantees under the stated statistical assumptions. We establish statistical consistency and convergence rates for the proposed estimator, and characterize conditions under which it can mitigate the curse of dimensionality for hierarchically compositional regression functions. Extensive simulation studies demonstrate competitive predictive performance, with gains over several competing approaches in multiple Euclidean and non-Euclidean configurations. Finally, we demonstrate the practical utility of the proposed framework in two digital health case studies with distribution-valued outcomes in Wasserstein spaces, using high-resolution accelerometry and continuous glucose monitoring data. Embedding-based deep-learning methods may be less suitable when no informative low-dimensional representation exists or when the learned embedding does not adequately preserve the intrinsic geometry of the response space.

Electroencephalography (EEG)-to-language models offer a promising approach for translating complex neural signals into human-readable descriptions. However, generating plausible language does not necessarily demonstrate that a model has learned to interpret the underlying EEG signal. A direct way to assess such interpretation is to probe objectively measurable properties of the signal itself. We therefore construct an EEG-language dataset of 160,781 segments annotated with signal-level question answering (QA) pairs, where each question targets one of five property families and requires a quantitative comparison involving spectral, spatial, temporal, or lateral signal properties. Each segment is also paired with a feature-grounded EEG caption. We further propose a Dual-Domain EEG Encoder that jointly models temporal waveforms and spectral-spatial representations, and introduce EEG-Captioner, a unified EEG-to-language framework trained with both signal-level QA and EEG caption supervision. Experiments show that the proposed encoder achieves the highest overall macro-averaged balanced accuracy (Macro-BA) among the compared EEG encoders, while EEG-Captioner achieves a Macro-BA of 88.81% on signal-level QA and improves caption factual consistency from 82.06% to 83.46% over caption-only language adaptation, demonstrating the complementary benefits of signal-level QA and caption supervision.

Agentic reinforcement learning rewards a complete episode, yet the policy needs credit for every decision inside it. Counterfactual branching estimates this credit by re-running the episode after an alternative decision, but the branch draws its sampling noise independently of the factual episode, so the outcome difference mixes the effect of the decision with the luck of everything that follows. We observe that in agentic search the retriever, the corpus, and the grader are deterministic, so an episode is a deterministic function of the policy's decisions and its sampling noise. Twin worlds are therefore realizable: the same noise, a different decision. We introduce TWICE (TWIn-world Credit Estimation), which keys the Gumbel noise of every token by turn and line, rolls out counterfactual twins that inherit the factual episode's downstream noise, and turns their paired outcome differences into turn-level advantages for policy-gradient updates on actor-sampled trajectories; only the actor is deployed. Twin credit is unbiased for any coupling quality, its variance is that of an independent counterfactual scaled by $1-\rho$, where $\rho$ is the twins' outcome correlation, and under coupling the number of rollouts needed to resolve an advantage of size $\Delta$ falls from $\Theta(\Delta^{-2})$ to $\Theta(\Delta^{-1})$. A square-root rule spends the twin budget where outcomes are predicted to disagree per unit cost. On seven question-answering benchmarks, TWICE improves the average exact match of GRPO by 5.3 and 4.5 points on Qwen2.5-3B and 7B, outperforms tree-search and counterfactual-branching baselines, and uses 68% fewer auxiliary tokens than VinePPO.

Time series foundation models (TSFMs) use self-supervised pretraining to learn reusable representations for downstream tasks such as multivariate time series classification (MTSC). We examine how much pretrained weights contribute beyond the architecture itself by comparing seven publicly released instances from four TSFM families with architecture-matched randomly initialized counterparts on the UEA MTSC archive. For each instance, five random initializations are evaluated using four classifiers on frozen representations: ridge classification, logistic regression, RBF SVM, and random forest. After model-specific exclusions due to computational constraints, the study comprises 183 paired dataset-level comparisons. Pretraining improves mean accuracy for all seven instances, but the gains are modest, ranging from 1.43 to 5.19 percentage points, with an overall average improvement of 2.58 points. Three of seven per-instance Wilcoxon signed-rank tests have raw $p$-values below 0.05, but only NuTime remains significant after Holm correction. A secondary pooled test across all 183 pairs gives $p < 0.001$, while the corrected per-instance tests remain the primary evidence. We also compare with ROCKET, Hydra, and Quant, which remain competitive without requiring large-scale pretraining. These findings suggest that MTSC evaluations should distinguish the effect of pretrained weights from that of the underlying architecture and should include both architecture-matched random initialization and strong non-pretrained baselines.

Scaling embedding capacity alongside Transformer computation is an emerging trend in language models. This trend makes high compression rates increasingly useful. Hence, we study extreme compression of Per-Layer Embeddings (PLE), which follow this trend and account for 35.2% of the parameters of Gemma 4 E4B. At such rates, conventional quantizers give each token-layer vector its own code of only a few bytes. We instead develop OPTIC (Output-Path-fitted, Token-shared Indexed Codes), which stores one quantized code tuple per token and decodes it at every layer with a layer-specific affine decoder. Codes and decoders are fitted to the PLE output path rather than to the stored vectors. At about $100\times$ PLE compression of bfloat16 (BF16) E4B, OPTIC retains an aggregate 97.8% of the uncompressed model's performance across seven benchmarks, whereas product quantization, the strongest of six conventional baselines, retains 66.3%. At $594\times$ and $1,002\times$ PLE compression of BF16 E4B, OPTIC retains 90.5% and 84.1%. On the official E4B release with 4-bit linear weights and 16-bit activations (W4A16), OPTIC retains 96.9% at about $100\times$ PLE compression. During inference at about $100\times$ PLE compression, BF16 E4B uses 29.7% less GPU memory than with uncompressed PLE at the same key-value cache size, while running at most 0.40% slower.

Wrong automatic routing of an IT support ticket can cost more than human triage. We evaluate cost-aware abstention as an offline, cost-conditional readiness assessment: select a routing policy on calibration data under explicit costs, then evaluate that frozen policy once on held-out test data. On a public 47,837-ticket, eight-class corpus, we compare four trained non-LLM classifiers with four large language models under zero- and few-shot prompting. Under the illustrative cost model (c_ok, c_triage, c_wrong) = (0, 1, 5), TF-IDF with logistic regression and a threshold of 0.60 selected on calibration reduces test cost from 0.763 to 0.472, a 38.1% relative reduction (paired ratio-bootstrap 95% CI [35.7%, 40.4%]), while lowering wrong routes from 15.3% to 3.5%. Frozen calibration-selected policies also beat both always-route and always-defer on held-out test data in 14 of 16 settings in a post-hoc cost-parameter analysis. The strongest prompted configuration reaches 0.477 accuracy on a stratified 1,000-ticket test subset, versus 0.879 for fine-tuned DistilBERT on the same tickets. Isotonic lowers expected calibration error without reliably improving discrimination: GPT-4o-mini few-shot has one confidence value before and after recalibration and correctness AUROC 0.500. We therefore report correctness AUROC and tie-aware risk-coverage area alongside ECE. At the analytically derived break-even probability 0.80, seven prompted configurations defer all tickets; Haiku few-shot routes only 19/1,000. An LLM-only agreement control and margin/entropy rejection baselines further separate calibration from discrimination. The findings are scoped to this dataset, prompt design, model endpoints, and illustrative costs; the work is an evaluation framework, not a new abstention algorithm or universal deployment certification.

Content caching via unmanned aerial vehicles (UAVs) becomes one of the solutions to maintain content delivery when terrestrial infrastructure is unavailable or disrupted. However, existing caching approaches often focus primarily on cache-hit performance or average delivery delay, without jointly addressing spatially heterogeneous and time-varying demand, content-specific deadlines, and uneven communication-energy consumption across UAVs. To address these challenges, we formulate a dynamic deadline- and energy-aware cache placement and replacement problem that jointly considers deadline misses, UAV-side communication energy, and inter-UAV energy imbalance. To achieve this, we first develop deadline- and energy-aware UBAC (DE-UBAC), an interpretable hierarchical rule-based realization that incorporates deadline-aware prioritization, cooperative placement, energy-aware coordination, and cache-update cost. However, predefined priorities and thresholds limit its adaptability under dynamically coupled network conditions. We therefore propose GRU-assisted Deadline- and Energy-aware Proximal Policy Optimization (GRU-DEPPO), which combines local and global GRU-based temporal representations with a centralized PPO actor-critic for adaptive cache placement and replacement. Simulation results show that GRU-DEPPO achieves the lowest deadline-miss rate and total UAV-side communication energy among the considered schemes. Compared with DE-UBAC, GRU-DEPPO reduces the deadline-miss rate by approximately 61% and inter-UAV energy imbalance by approximately 40%.

While functional magnetic resonance imaging (fMRI) decoders reconstruct images and 3D objects, recovering the metric geometry of rooms from a moving viewpoint remains an open challenge. We introduce, to our knowledge for the first time, the task of reconstructing 3D layouts of held-out scenes using only the known camera trajectories and the fMRI signals of participants watching indoor walkthroughs, without any visual frames. The task is hard because of the temporal mismatch between rapid visual changes and blurred fMRI signals. Our method, DRAFT (Decoding and Reconstructing 3D room lAyouts from fMRI and Trajectories), extracts a compact layout representation from the early visual cortex and fuses this neural code with the geometric free space derived from camera motion. To evaluate it, we propose layout r, the Pearson correlation between predicted and ray-cast log depths. On ten held-out scenes (20 participants), DRAFT reaches a layout r of 0.480, outperforming the camera path alone (0.446) and seven fMRI decoders (at most 0.429). DRAFT also works as a plug-in that improves all seven decoders without retraining, raising their layout r from 0.171-0.429 to 0.487-0.493. Brain activity and camera motion can thus recover the metric layout of unseen rooms, a first step toward reconstructing the 3D spaces people see.