Random

We demonstrate that widely deployed Large Language Model (LLM) inference stacks harbor a steganographic channel that requires no modification to model weights, sampling code, or output distributions. The channel exploits a structural property of deterministic decoding: pseudo-random number generators (PRNGs) used in inverse-transform sampling produce a seed-dependent sequence of token-level probability intervals that can be reconstructed from the generated text alone. A sender encodes a secret message in the PRNG seed before generation; a receiver reconstructs the intervals and recovers the seed, and thus the hidden payload, by exhaustive search over the seed space. We formalize two operational modes. In the known-prompt setting, sender and receiver share the prompt, enabling exact interval reconstruction and perfect seed recovery via forced alignment. In the unknown-prompt setting, only the generated text is available; approximate interval reconstruction combined with a maximum-hit-count scoring strategy still permits reliable recovery from sufficiently long outputs. Extensive experiments across six model families and five heterogeneous text domains show that, in the known-prompt setting, full 32-bit seed recovery from the complete 2^32 candidate space achieves up to 100% accuracy, depending on model and text domain, within 300 tokens and under 35 seconds on a single GPU. In the unknown-prompt setting, recovery reaches near-perfect accuracy at 600-800 tokens in about 12 seconds. We further analyze the influence of prompting strategies, tokenization ambiguities, and sampling hyperparameters on channel reliability. Moreover, we discuss several applications of our results: First, it allows for the steganographic transmission of 32 bits, but also shows that ignorance of the prompt is not a valid security assumption.

Raw numerical datasets remain less systematically examined in integrity screening than images, plagiarism, or summary-statistic inconsistencies. We developed the Fabrication-risk Digit Randomness Screening model (FDRS), a statistical and machine-learning framework for detecting non-random digit-pattern irregularities in numerical research data. FDRS integrates single- and joint-decimal-digit tests, Cramer's V, entropy metrics, Kullback-Leibler divergence, digit-preference indices, progressive subsampling, and semi-supervised risk scoring. It was evaluated using an instrument-derived enzymatic absorbance dataset (RawData, n=253) and a blinded manually simulated irregular dataset (ErrData, n=255). RawData showed no significant deviation in single third-decimal-digit analysis, whereas ErrData showed a significant deviation. In joint third-fourth decimal digit analysis, ErrData showed higher Cramer's V, lower normalized entropy, higher KL divergence, and a more persistent progressive-subsampling deviation signal. In internal validation, Elastic-net Logistic Regression achieved the highest AUC (0.98395) and lowest Brier score (0.048439), while Random Forest achieved the highest accuracy (0.926667) and balanced accuracy (0.935). RawData received a low ensemble risk score of 0.124627 and was classified as Grade 0; ErrData received a score of 0.740760 and was classified as Grade 3. External real-world benchmarks supported graded risk stratification: three datasets without identified public post-publication concerns were classified as Grade 0 or 1, whereas two datasets from publicly questioned or institutionally handled articles were classified as Grade 2 or 3. FDRS can prioritize raw numerical datasets for further review by integrating interpretable statistical and machine-learning features. It is an auxiliary digit-structure screening tool, not standalone evidence of fabrication or misconduct.

Current evaluations for Multimodal Large Language Models (MLLMs) overwhelmingly focus on utility-driven objectives, leaving model behavior under logic-neutral scenarios largely underexplored. Stochasticity is essential in scenarios where multiple actions are equally valid, such as recommending travel itineraries or daily schedules where multiple options have similar utility. In such settings, deterministic policies may lead to repetitive behaviors and reduced coverage of valid alternatives. To bridge this gap, we propose RandomBench, a benchmark designed to evaluate whether MLLMs can maintain distributionally neutral behavior when selecting among equivalent options. We further introduce three metrics, including RI, BCI, BII, to quantify entropy and distributional bias. Experiments reveal a pervasive phenomenon termed Stochastic Collapse, where MLLMs fail to maintain uniform randomness under explicit random instructions, with top-1 probabilities reaching 97% from the ideal one quarter baseline and RI dropping to 0.068 in Claude Sonnet 4.6. Extensive ablation studies further demonstrate that these deviations persist across languages and representation formats, highlighting the robustness of distributional collapse in logic-neutral decision settings.

Retrieval-augmented QA pipelines often route retrieved passages through an LLM \emph{rewriter} before a smaller reader, lifting F1 by tens of points on multi-hop benchmarks; this gain is typically credited to improved evidence quality. We ask whether that lift is causally driven by the gold answer string appearing in the rewritten context rather than by curation per se, using a controlled intervention audit. For each rewritten context we re-run the reader after one of four controlled edits to the compile output: removing the gold answer span, replacing a length-matched random non-answer span (placebo), or injecting the gold into rewrites where it was absent (at the prefix or at a midpoint sentence boundary). Across twelve completed (cell, baseline) intervention runs spanning three reader families (Qwen2.5-7B, Qwen3.5-35B, GLM-4.7), two datasets (HotpotQA, 2WikiMultihopQA), and three compiler arrangements (MA-only, MB-only, MA$+$verify), removing the gold answer drops reader F1 by $28$ to $64$ points beyond the length-matched placebo on paired \texttt{answer-in-compile} strata, and prepending the gold into rewrites that lacked it raises F1 by $+0.7$ to $+9.7$ points in $10$ of $12$ (cell, baseline) combinations. A companion five-sentinel audit shows the conventional single-\texttt{[MASK]} probe is itself sentinel-fragile: on 2Wiki it reports a $+4.12$~F1 ``non-leakage residual'' that flips to $-3.33$ to $-7.81$~F1 under four alternative sentinels and fails an equivalence test for three of those four ($1/4$~pass). We do not propose a new rewriter or mitigation; we release the intervention runner and the sentinel panel so that other rewriter-gain claims can be tested against the same standard.

Diffusion Models (DM) have revolutionized text-driven generation by enabling the synthesis of high-quality, photorealistic visual content from user prompts. Whereas prior advances in visual generation such as VAEs and GANs were primarily evaluated on perceptual or visual similarity metrics such as FID PSNR, DM advances have fostered the development of more advanced Human Preference Metrics (HPM) that model and quantify human judgment as scalar values. However, DMs synthesize content using an inherently stochastic process where random noise seeds generation. The initial random noise directly affects the quality of generated outputs, both qualitatively and quantitatively. This influence is pronounced in smaller models for local deployment scenarios. Given this phenomenon, we first investigate to what extent we can predict scalar HPM scores prior to committing compute resources for generation. Further, we then investigate to what extent we can leverage such prediction to improve the quality of generated images, and also study which HPMs are best suited for this task. Our investigation reveals that not only is this possible, but that it is feasible to achieve negligible hardware overhead.

We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data. We prove matching low-degree upper and lower bounds for counting communities in the planted submatrix and planted dense subgraph models. The resulting testing threshold coincides, down to the sharp constant, with the known low-degree recovery threshold. In contrast, the task of weak testing, where the goal is to outperform random guessing, does not have a sharp threshold but rather a smooth transition, which we identify. To prove our results, we develop a framework for planted-vs-planted testing that builds on a latent-variable expansion originating in low-degree recovery and employs new methods to identify and prune non-signal contributions.

File-type classification underlies many workflows like malware triage, forensic carving, packet inspection, and storage indexing. Learned systems such as Google's Magika assume whole-file access at a known offset, so they break on the inputs many of these tasks actually produce, like a single packet payload, a header-less carved fragment, a random disk block, or a chunked upload. We introduce MimeLens, a family of small BERT-style encoders pretrained on binary content from windows sampled at a uniformly random offset within each file, with no privileged head-of-file position, in standard- and short-context variants. A byte chunk goes in from anywhere in a file, no header needed and no fixed size; out comes one of libmagic's 125 MIME labels. On the clean head of complete files, MimeLens beats Magika v1.1 by +10.7 pp top-1 on libmagic-labeled data, and it keeps classifying where Magika cannot: from a single mid-stream UDP packet, and more than twice as accurately as libmagic and Magika on random mid-file disk blocks. The cost is latency: MimeLens runs roughly one to two orders of magnitude slower per sample on CPU than Magika, though it matches on consumer GPUs or in batch. All trained checkpoints are released on Hugging Face (mjbommar/mimelens-001-*).

Physical systems do not merely add noise to search processes; they impose constraints that generate structured correlations. We propose a principle of constraint-enhanced physical search in which temporal correlations in exploration are matched to constraint-induced spatial correlations in the update dynamics. Using a minimal tug-of-war bandit model (TOW), we show that a conservation law converts local observations into differential evidence across alternatives, while a temporally correlated drive controls the order of exploration. Search efficiency is improved not by stronger randomness or by maximal anti-correlation, but by matching the temporal correlation to the physical update scale that converts feedback into evidence. A scaling estimate identifies the update-noise-to-contrast ratio as the leading parameter that limits how strongly temporal anti-correlation can be used. The results suggest a general organizing principle for physical search: constraints and fluctuations can generate structured spatiotemporal correlations, and efficient exploration emerges when these correlations are matched to the update dynamics.

Training modern machine learning models increasingly requires computation to be distributed across many accelerators. Data parallelism remains the default choice and is often paired with tensor-parallel sharding, but model parallelism becomes unavoidable once parameters, activations, or optimizer states no longer fit on a single device. This paper studies pipeline model parallelism through the lens of PipeDream (PD) (Harlap et al., 2018). Our first contribution is theoretical: we introduce Randomized PipeDream (RPD), a stale block-SGD abstraction that yields, to our knowledge, the first clean nonconvex convergence guarantee for a PD-style method. Our second contribution is a scaling diagnosis: we prove that the delay induced by steady-state PD grows as $S^2 - S/2 + O(1)$ for $S$ stages, so the stale-read contribution in the convergence theorem scales as $Θ(γ^2 S^4)$, equivalently as $Θ(S^4/K)$ in the tuned-rate form. Our third contribution is a comparison with LocalSGD, whose periodic model averaging trades weight staleness for synchronization bubbles. In our reported simulated-time experiments, the better-performing method depends on the objective: PD performs better on the quadratic objective and on a small language-modeling training-loss task, while for logistic regression LocalSGD becomes superior as the number of stages increases.

Randomized smoothing (RS) uses a smoothed classifier to provide architecture-agnostic certificates of $\ell_2$ classification robustness, but its dependence on per-input Monte Carlo (MC) sampling undermines its use in real-time systems. We argue that this cost is structural rather than fundamental, such that it can be significantly reduced by sharing information across the deployment stream. We introduce RRISE, an RS framework that compresses certification into a single forward pass through a learned surrogate. RRISE trains the surrogate against precomputed MC class-count targets via a soft-label cross-entropy loss and converts surrogate predictions into provably conservative certified radii through a one-time conformal calibration step. The resulting certificate is deployment-verifiable: whenever the calibrated radius is positive, the surrogate's prediction provably matches the smoothed classifier's and the smoothed classifier is constant on a ball of that radius around the input. Across image classification benchmarks, RRISE matches fixed-budget MC certified accuracy within $0.84$ percentage points while replacing up to $10^4$ noisy base-model evaluations per query with a single surrogate forward pass, recouping MC training cost after $\approx 10^5$ deployment queries. On CIFAR-100 and Tiny ImageNet, where the only prior offline-surrogate method collapses, RRISE achieves $1.23$ to $1.91\times$ higher certified accuracy, establishing efficient randomized smoothing as a practical path to certified robustness in repeated-deployment settings.

Watermarking should identify language-model output without degrading quality or limiting verification to the model provider. Multilingual deployment makes this harder because morphology, segmentation, and script change where watermark evidence can enter naturally. We introduce LUNA, a linguistically adaptive watermark that combines model-free detection with single-token non-distortion under the standard random-key model. LUNA estimates normalized next-tag entropy from part-of-speech contexts in an external corpus and uses it to set the depth of a non-distortionary binary tournament sampler; the detector reconstructs the same schedule from text, a tokenizer, a tagger, and a secret key. We evaluate six typologically diverse languages and two domains against eight primary baselines. LUNA attains an AUROC of 0.9959 and the lowest mean absolute median perplexity shift of 0.045 across the twelve settings; its 95% bootstrap interval [0.022, 0.073] lies below all baseline intervals. LUNA also records the lowest mean Self-BLEU, Distinct-1, surprisal, and entropy shifts. It is the only method that simultaneously achieves AUROC > 0.99 and an absolute median perplexity shift below 0.1 in a majority of settings, reaching this regime in 9 of the 12 settings while no baseline reaches it in more than 2. Our code is available at: https://github.com/Shinwoo-Park/luna_watermark

Masked diffusion language models (MDMs) uniquely support any-order generation, with confidence-based decoding currently serving as the de facto standard inference policy. To optimize for this, recent training schemes attempt to align training mask patterns directly with those observed during generation. However, we argue that confidence-based decoding is inherently misaligned with the logical-flow trajectories required for complex reasoning, and that confidence-aligned training actively entrenches this misalignment. We make this concrete using multi-digit addition, where the decoding strategy prematurely predicts locally easy digits before resolving their long-range dependencies, producing high-confidence errors on challenging inputs. While traditional random masking keeps the failure rate low on this challenging tail, confidence-aligned training amplifies the error rate by an order of magnitude. Across five distinct reasoning tasks, this same pattern emerges with task-dependent severity: confidence-based decoding induces failures on highly complex inputs, and confidence-aligned training exacerbates them. In contrast, random masking -- despite its perceived inefficiency -- robustly preserves the reasoning-trajectory conditionals essential for solving the challenging tail.

Cryptographic watermarking is a leading defense for attributing text generated by large language models (LLMs). Existing schemes, including KGW, Unigram, and DipMark, derive their security guarantees from the assumption that the underlying pseudo-random number generator (PRNG) is trustworthy. This work introduces SeedHijack, the first supply-chain attack on LLM watermarking that is simultaneously (i) blind -- requiring no knowledge of the watermark key, detector, or model logits, (ii) integrity-preserving -- amplifying rather than erasing the watermark signal, and (iii) orthogonal to detection -- the attack-induced bias is statistically independent of all content-side detector statistics, ensuring that amplification and evasion coexist without trade-off. Rather than perturbing generated text, SeedHijack replaces the PRNG at the supply-chain layer, biasing green-list selection without altering output tokens or degrading text quality. Across three watermarking schemes and three open-source LLMs, the attack triggers 0/6 state-of-the-art content-side statistical detectors while inflating the watermark z-score up to 2.42x (system-level defenses such as entropy-source attestation remain orthogonal and complementary). A quantum random number generator (QRNG) countermeasure is shown to fully neutralize the attack while preserving benign watermarking utility. These findings establish PRNG integrity as a first-class security requirement for cryptographic content-provenance systems.

An effective method of teaching across disciplines is to provide examples of high-quality work. However, an example may be significantly different from a student's current work, making it challenging for them to emulate. An ideal learning demonstration is a counterfactual version of the student work, an improved version that is still similar to their own. Existing automated approaches for counterfactual text generation using Large Language Models (LLMs) result in domain-specific systems that are difficult to translate into practical applications. We present the Gumbel Machine, a flexible, modular approach to generating counterfactuals that leverages LLM instruction-following capabilities while encouraging similarity to a reference factual text. Central to our approach is a novel, controlled decoding algorithm, $β$-Hindsight control, which uses latent randomness as a tunable similarity control mechanism during counterfactual generation. Experiments on datasets of student writing, scored on various criteria, demonstrate the effectiveness of our approach at generating counterfactuals both rubric-consistent and similar to a reference.

CART random forests are among the most widely used modern predictive methods, with well-documented empirical success. Yet, at the mechanistic level, the algorithm is often treated as a black box because of its complexity. In this paper, we develop a stochastic-control perspective on feature-subsampled CART random forests, named CART random opportunity-set allocation (CART-ROSA). At each node, the random subset of features is interpreted as a random feasible action set, and the CART split rule as a masked-action allocation policy. This policy induces a controlled stochastic process over informative split-count states, whose terminal law determines both single-tree error and cross-tree interaction terms in the forest mean squared error (MSE). Such representation opens the black box of CART-forests by separating two design levers: the informative-opportunity rate induced by feature subsampling, and the contraction strength from the within-mask split policy. We establish that the CART policy is locally stabilizing: it contracts imbalances in informative split allocations and concentrates terminal tree geometry. At the system level, however, it can be globally suboptimal for the forest objective. Specializing to the linear model, we derive the MSE risk expansion explicitly. Our results show how an operations-research perspective makes tractable a theoretical gap difficult to access from the standard algorithmic description of CART forests.

Capturing relightable 3D assets from real-world objects is a widely researched problem. Several per-scene optimization-based methods, based on 3D Gaussian splatting (3DGS), support relighting; however, they usually require dense input views, and their overfitting nature makes it difficult to generalize across scenes. Unlike per-scene optimization methods, generalized feed-forward models can directly reconstruct Gaussians from sparse input views. However, the resulting assets have baked-in illumination and cannot be easily used for relighting. In this paper, we present F-RNG, a feed-forward framework that directly generates relightable 3DGS assets from sparse-view inputs. Training such a model from scratch can require massive data and computing resources, and it is especially challenging to generate relightable assets in a feed-forward manner with acceptable cost. We develop F-RNG upon an existing large reconstruction model (LRM) to extract relightable representations, while also utilizing priors from an intrinsic decomposition model (IDM). Specifically, we first introduce a latent-interpolated fine-grained geometry synthesis to enhance the LRM's geometry representation. Second, we propose a prior-guided relightable appearance distillation to extract relightable neural representations by incorporating IDM priors. Finally, a universal neural renderer enables flexible and high-fidelity relighting. F-RNG requires neither re-training nor fine-tuning of the underlying LRMs, thus can automatically benefit from better LRMs and IDMs in the future. With only small networks that can be trained with affordable data and computational resources, F-RNG avoids the repetitive inference of large models under different light conditions. By comparison to the state-of-the-art LRM-based relighting method, F-RNG achieves 25x faster relighting, as well as superior quality (+2.0 dB).

Missing data frequently arises across diverse domains, including time-series and image domains. In the real world, missing occurrences often depend on the unobservable values themselves, which are referred to as Missing Not at Random (MNAR). In this work, we introduce the Missing Pattern Recognized Diffusion Imputation Model (PRDIM), a novel framework that explicitly captures the missing pattern and precisely imputes unobserved values. PRDIM iteratively maximizes the likelihood of the joint distribution for observed values and missing mask under an Expectation-Maximization (EM) algorithm. In this sense, we first employ a pattern recognizer, which approximates the underlying missing pattern and provides guidance during every inference toward more plausible imputations with respect to the missing information. Through extensive experiments, we demonstrate that PRDIM consistently achieves strong imputation performance under MNAR settings across multiple data modalities.

Public service programs often allocate limited resources under uncertainty about their benefits, creating a need for randomization to support credible evaluation. In practice, however, applicants commonly enter waitlists where resources are prioritized toward individuals judged to have higher need through tiered priority queues, making direct randomization difficult. Motivated by this, we develop an experimental design framework for learning treatment effects while treating those most in need where incoming applicants are randomized into priority queues based on their assessed risk scores. Treatments are then provided across queues in priority order and first-in-first-out within queue as budget becomes available. Our contributions are two-fold. First, we characterize what causal effects are identified under this priority-queue allocation. When arrivals are exogenous, treatments are conditionally randomized, and hence standard estimands are identified; when arrivals are endogenous, queue randomization instead provides an instrument for treatment, identifying local treatment effects induced by the queuing process. Second, we develop optimized queue-assignment designs that trade off statistical efficiency against prioritizing higher-need applicants. We show in the process that, despite dependence in treatment assignments induced by the design, usual iid efficiency bounds remain well-justified design objectives. We illustrate the proposed designs using data from a housing allocation program in a large U.S. county.

Bayesian optimization is widely employed for optimizing complex black-box functions but struggles with the curse of dimensionality. Random embedding, as a dimension reduction strategy, simplifies tasks that possess the effective dimension by optimizing within a low-dimensional subspace. However, determining the effective dimension of a task in advance remains a significant challenge, which influences the selection of the subspace dimensionality and the optimization performance. Traditional methods use fixed subspace dimensions provided by experts or rely on trial and error to estimate subspace dimensions with resources consumed. To this end, this paper proposes an automated random embedding for high-dimensional Bayesian optimization with unknown effective dimension, called Dynamic Shared Embedding Bayesian Optimization (DSEBO). DSEBO starts with a low dimension and switches to a higher subspace if the solutions in the current subspace show preliminary convergence. DSEBO dynamically determines the dimension of the next subspace based on the quality of the solutions in different subspaces and shares the queried solutions with the new subspace for a better initialization. Theoretically, we derive a regret bound for DSEBO and demonstrate that DSEBO can better balance approximation and optimization errors. Extensive experiments on functions with dimensionality of varying magnitudes and real-world tasks with unknown effective dimensions reveal that, compared with state-of-the-art methods, alternating optimization across different subspaces results in significant improvements in high-dimensional optimization, both in terms of optimization regret and time.

Many novel unsupervised feature selection methods are proposed each year, yet their empirical evaluation is limited to supervised and unsupervised evaluation metrics computed on selected datasets, along with comparisons to existing methods. However, in the absence of an established evaluation baseline, it is difficult to determine the value added to the existing literature by each of these methods, and how effective their underlying approaches are. We propose using random feature selection as a baseline for evaluating the unsupervised feature selection methods. We empirically show that many of the state-of-the-art methods in unsupervised feature selection are outperformed by random feature selection in both performance and efficiency. Accordingly, we emphasize on the strict requirement of considering random feature selection as a baseline in the development process of novel unsupervised feature selection methods to ensure a consistent improvement over random feature selection.

Multi-center survival prediction can improve robustness and generalizability, yet privacy regulations and institutional governance often prevent pooling patient-level clinical and genomic data across institutions. In practice, deployment is further complicated by feature-space heterogeneity, in which sites collect different covariates or use different sequencing panels, resulting in only partially overlapping feature sets. We present FederatedRSF, a Python package that implements federated random survival forests, aggregating locally trained survival trees and redistributing only feature-compatible trees to each site, enabling inference with partial overlap without sharing raw data. We evaluate FederatedRSF on the GBSG2 breast cancer cohort distributed with the scikit-survival package, simulating feature heterogeneity across clients by withholding subsets of features, and assessing discrimination using Harrell's concordance index (C-Index) under repeated cross-validation and site-splits. The results demonstrated that the federated model can achieve performance comparable to that of the centralized training setting.

Random forests are widely used in fields involving sensitive tabular data, but existing approaches to enforcing differential privacy (DP) typically degrade performance to the point of impracticality. In this paper, we introduce Lumberjack, a differentially private random forest algorithm that achieves substantially higher utility by constructing large random decision trees and then applying aggressive, privacy-preserving pruning to retain only sufficiently populated nodes. A key component of our approach is a novel $(\varepsilon,δ)$-DP heavy hitter detection algorithm for hierarchical data, whose error is $O_{\varepsilon,δ}(\sqrt{\log h})$ for trees of height $h$ and may be of independent interest. This favorable scaling enables the use of significantly deeper trees than in prior work, leading to improved expressiveness under privacy constraints. Our empirical evaluation on benchmark datasets shows that Lumberjack consistently outperforms prior DP random forest methods, establishing a new state of the art. In particular, our approach yields substantial improvements in the privacy-utility trade-off for practical privacy budgets. Our findings suggest that carefully designed DP random forests can close much of the utility gap, highlighting a promising and underexplored direction for future research.

Our preliminary experiments on gym-DSSAT maize irrigation tasks revealed that +/-2 degrees C temperature noise causes an 11.9% reduction in economic returns for PPO policies trained under clean conditions - a systematic robustness deficit that existing research has not adequately addressed. This paper tackles three interconnected limitations impeding practical deployment of agricultural RL systems: the trade-off between early-stage learning efficiency and late-stage generalization capability; the naive additive combination of intrinsic and extrinsic rewards in exploration-augmented PPO; and uniform measurement noise injection strategies that disregard empirically validated differential sensitivity across agricultural state variables. We introduce three systematic innovations: Progressive Generalization Augmentation (PGA) implementing a three-phase curriculum (clean training 0-800 episodes, progressive 800-1200, full augmentation 1200-2000); a deeply coupled RND-PPO architecture with dual-channel GAE normalization, progress-decayed intrinsic coefficients, and semantic discretization; and domain-prioritized noise injection with hierarchical activation. Our experimental evaluation demonstrates: 8.43% yield improvement and 16.42% nitrogen use efficiency improvement over SOTA BERT-DQN in Florida; 5.61% yield improvement in Zaragoza (though 3.67% lower economic score due to challenging Mediterranean climate); and 94.4% vs 80.0% performance retention under combined perturbations. All experiments used 5 random seeds on NVIDIA A100 GPUs with 4.2+/-0.3 hours per run (2000 episodes, 2048-step buffer, 64 mini-batch size).

Achieving human-level manipulation requires dexterous robotic hands capable of complex object interactions. Advancing such capabilities further demands standardized benchmarks for systematic evaluation. However, prior work does not focus on task-oriented dexterous manipulation. Existing benchmarks also often lack high quality human demonstrations and an easy-to-use evaluation pipeline. In this paper, we present DexJoCo, a benchmark and toolkit for task-oriented dexterous manipulation, comprising 11 functionally grounded tasks that evaluate tool-use, bimanual coordination, long-horizon execution, and reasoning. We develop a low-cost data collection system and collect 1.1K trajectories across these tasks, with support for domain randomization to assess robustness. We benchmark modern models under diverse settings, including visual and dynamics randomization, multi-task training, and action-head adaptation. Through extensive empirical analysis, we identify several important insights and common limitations of current policies in dexterous manipulation, highlighting key challenges for future research in dexterous hand robot learning. Code is available at: https://dexjoco.github.io

We introduce a dynamics-level approach to watermarking generative models. Rather than embedding signals into model weights or outputs, we embed the watermark directly into the learned continuous dynamics -- the velocity field of a flow matching model. We formulate this as random coding over a continuous channel: a key-dependent perturbation is added during training, and the message is recovered at detection time from black-box queries. The perturbation is designed to leave the generated distribution unchanged. Experiments on MNIST and CIFAR-10 across different architectures confirm reliable message recovery, preserved generation quality, and chance-level decoding accuracy without the secret key.

For most of the history of information retrieval (IR), search results were designed for human consumers who could scan, filter, and discard irrelevant information on their own. This shaped retrieval systems to optimize for finding and ranking more relevant documents, but not keeping results clean and minimal, as the human was the final filter. However, LLMs have changed that by lacking this filtering ability. To address this, we introduce Bits-over-Random (BoR), a chance-corrected measure of retrieval selectivity that reveals when high success rates mask random-level performance. We measure selectivity as $BoR = \log_{2}\left(\frac{\mathrm{P}_{obs}}{\mathrm{P}_{rand}}\right)$, where $\mathrm{P}_{rand}$ is the hypergeometric baseline for the chosen success rule (here, coverage: $\geq1$ relevant in top-$K$). On the 20 Newsgroups dataset, BM25 and SPLADE both report $>99$% success at $K=100$ (coverage), yet $BoR \approx 0$, indicating random-level selectivity at that depth. When the expected coverage ratio $\left(\frac{K \cdot \bar{R}_{q}}{N}\right)$ exceeds 3-5, the baseline dominates and selectivity collapses. Downstream retrieval-augmented generation (RAG) evaluation confirms this pattern: LLM accuracy can degrade substantially at $K=100$, consistent with the near-zero BoR ceiling. In contrast, BoR remains positive on BEIR/SciFact and on MS MARCO (where 41 systems cluster within 0.2 bits of the theoretical ceiling despite a 13-point recall gap), confirming baseline predictions across sparse and large-scale settings. We further show that the collapse boundary applies to LLM agent tool selection, where small catalog sizes cause selectivity to vanish even with perfect selectors. These findings suggest reporting BoR alongside traditional metrics and reconsidering depth choices when additional retrieval provides negligible selectivity gains while inflating computational costs.

Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random rotations yield clean theoretical guarantees, they require $Θ(d^2)$ time. The randomized Hadamard transform $HD$ reduces this cost to $O(d \log d)$, but its discrete structure complicates analysis and leads to weaker or purely empirical compression guarantees. In this work, we study a variant of this approach: dithered quantization with a single randomized Hadamard transform. Specifically, the quantizer applies $HD$ to the input vector and subtracts a random scalar offset before quantizing, injecting additional randomness at negligible cost. We prove that this approach is unbiased and provides mean squared error bounds that asymptotically match those achievable with truly random rotation matrices. In particular, we prove that a dithered version of TurboQuant achieves mean squared error $\bigl(π\sqrt{3}/2 + o(1)\bigr) \cdot 4^{-b}$ at $b$ bits per coordinate, where the $o(1)$ term vanishes uniformly over all unit vectors and all dimensions as the number of quantization levels grows.

Diffusion models depend on pseudo-random number generators (PRNGs) for latent noise sampling. We present DiffusionHijack, a supply-chain backdoor attack that hijacks the PRNG to deterministically control generated images. A malicious PRNG, injected via compromised packages, forces pixel-perfect reproduction of attacker-chosen content (SSIM = 1.00, N = 100 trials) on Stable Diffusion v1.4, v1.5, and SDXL -- without modifying model weights. The attack is inherently undetectable by existing model auditing and content moderation mechanisms, as it operates entirely outside the neural network computation graph. The attack remains effective under stochastic sampling (eta > 0), bypasses CLIP-based safety checkers (98-100% success), and operates independently of the user's prompt. As a countermeasure, we replace the PRNG with a quantum random number generator (QRNG), which provides information-theoretic unpredictability. Across N = 100 prompt-model combinations, QRNG defense completely neutralizes the attack, reducing output similarity to random baseline levels (SSIM < 0.20 for SD 1.x models, < 0.45 for SDXL). This work exposes a previously overlooked supply-chain vulnerability and offers a hardware-level fundamental mitigation for generative AI systems.

The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear minimization oracle (LMO) theory. In this paper, we challenge this geometric narrative through three contributions, demonstrating that precise geometric structure is not the key factor affecting optimization performance. First, we introduce Freon, a family of optimizers based on Schatten (quasi-)norms, powered by a novel, provably optimal QDWH-based iterative approximation. Freon naturally interpolates between SGD and Muon, while smoothly extrapolating into the quasi-norm regime. Empirically, the best-performing Schatten parameters for GPT-2 lie strictly within the quasi-norm regime, and thus cannot be represented by any unitarily invariant LMO. Second, noting that Freon performs well across a wide range of exponents, we introduce Kaon, an absurd optimizer that replaces singular values with random noise. Despite lacking any coherent geometric structure, Kaon matches Muon's performance and retains classical convergence guarantees, proving that strict adherence to a precise geometry is practically irrelevant. Third, having shown that geometry is not the primary driver of performance, we demonstrate it is instead controlled by two local quantities: alignment and descent potential. Ultimately, each optimizer must tune its step size around these two quantities. While their dynamics are difficult to predict a-priori, evaluating them within a stochastic random feature model yields a precise insight: Muon succeeds not by tracking an ideal global geometry, but by guaranteeing step-size optimality.

Data selection studies the problem of identifying high-quality subsets of training data. While some existing works have considered selecting the subset of data with top-$m$ Data Shapley or other semivalues as they account for the interaction among every subset of data, other works argue that Data Shapley can sometimes perform ineffectively in practice and select subsets that are no better than random. This raises the questions: (I) Are there certain "Shapley-informative" settings where Data Shapley consistently works well? (II) Can we strategically utilize these settings to select high-quality subsets consistently and efficiently? In this paper, we propose a novel data selection framework, NASH (Non-linear Aggregation of SHapley-informative components), which (I) decomposes the target utility function (e.g., validation accuracy) into simpler, Shapley-informative component functions, and selects data by optimizing an objective that (II) aggregates these components non-linearly. We demonstrate that NASH substantially boosts the effectiveness of Shapley/semivalue-based data selection with minimal additional runtime cost.

Dexterous manipulation is physics-intensive and highly sensitive to modeling errors and perception noise, making sim-to-real transfer prohibitively challenging. Domain randomization (DR) is commonly used to improve the robustness of learned policies for such tasks, but conventional DR randomizes one instance per episode, offering very limited exposure to the variability of real-world dynamics. To this end, we propose Domain-Randomized Instance Set (DRIS), which represents and propagates a set of randomized instances simultaneously, providing richer approximation of uncertain dynamics and enabling policies to learn actions that account for multiple possible outcomes. Supported by theoretical analysis, we show that DRIS yields more robust policies and alleviates the need for real-world fine-tuning, even with a modest number of instances (e.g., 10). We demonstrate this on a challenging reactive catching task. Unlike traditional catching setups that use end-effectors designed to mechanically stabilize the object (e.g., curved or enclosing surfaces), our system uses a flat plate that offers no passive stabilization, making the task highly sensitive to noise and requiring rapid reactive motions. The learned policies exhibit strong robustness to uncertainties and achieve reliable zero-shot sim-to-real transfer.

Large language models (LLMs) rely on deterministic pseudorandom number generators (PRNGs) for autoregressive sampling, creating a critical supply-chain attack surface overlooked by existing defenses. We present SeedHijack, a backdoor attack that manipulates PRNG outputs to force attacker-specified token selection without altering model logits. In a 540-trial benchmark on GPT-2 (124M), the attack achieves 99.6% exact token injection across 9 sampling configurations; it reaches 100% success on four aligned models (1.5B-7B, RLHF/SFT/reasoning distillation) and bypasses all alignment methods tested in this work. We further propose a defense based on a hardware quantum random number generator (QRNG), which neutralizes the attack in our evaluated threat model with negligible median overhead (+0.6% latency, +7.7 MB memory). Our work identifies a critical sampling-layer vulnerability and provides a practical, deployable QRNG-based defense.

Evaluating a new model on an existing benchmark is often necessary to understand its behavior before deployment. For modern evaluation frameworks, generating and evaluating a response for all queries can be prohibitively expensive. In practice, responses from previously-evaluated models are often cached -- creating a potential opportunity to use this additional information to decrease the number of queries required to accurately evaluate a new model. In this paper, we introduce an approach for predicting benchmark performance that leverages cached model responses based on the Data Kernel Perspective Space (DKPS), a method for quantifying the relationship between models in the black-box setting. Theoretically, we show that DKPS-based methods are query-efficient under certain conditions. Empirically, we demonstrate that DKPS-based methods achieve the same mean absolute error as baselines with a substantially decreased query budget. We conclude by proposing an offline method for selecting a set of queries that maximizes the goodness-of-fit on reference models, improving prediction accuracy over random query selection.

Poisson subsampling is the default sampling scheme in differentially private machine learning, largely because its unstructured randomness yields tractable privacy amplification analyses. Yet this same randomness introduces substantial participation variance: each sample appears in very different numbers of training iterations. In this work, we show that this variance is not merely a practical artifact to be tolerated, but a fundamental source of suboptimal privacy amplification. We prove that Balanced Iteration Subsampling (BIS), a structured scheme in which each sample participates in exactly a fixed number of iterations, achieves stronger privacy amplification than Poisson subsampling and is optimal at both extremes of the noise spectrum ($σ\to 0$ and $σ\to \infty$). Our analysis reveals that the privacy-noise tradeoff is governed not by maximizing randomness, but by eliminating participation variance while preserving uniform marginal participation across iterations. To translate this asymptotic theory into finite-noise guarantees, we introduce a practical near-exact Monte Carlo accountant for BIS, which removes the analytical slack of existing RDP and composition-based PLD analyses. Evaluations across more than 60 practical DP-SGD configurations show that BIS consistently outperforms Poisson subsampling in the low-noise regimes most relevant for high-utility private training, reducing the required noise multiplier by up to $9.6\%$. These results overturn the common intuition that more sampling randomness necessarily yields stronger privacy amplification: in DP-SGD, structured participation can be both more practical and more private. Our implementation is available at https://github.com/dong-xin-ao-andy/bis-mc-accountant.

Full parameter sharing is standard in cooperative multi-agent reinforcement learning (MARL) for homogeneous agents. Under permutation-symmetric observations, however, a shared deterministic policy outputs identical action distributions for every agent, making role differentiation impossible. This failure can theoretically be resolved using symmetry breaking among anonymous identical processors, which requires randomness. We propose Diamond Attention, a cross-attention architecture in which each agent samples a scalar random number per timestep, inducing a transient rank ordering that masks lower-ranked peers from agent-to-agent attention while leaving task attention fully unmasked. This realizes a random-bit coordination protocol in a single broadcast round, and the set-based attention enables zero-shot deployment to teams of different sizes. We evaluate across three regimes that isolate when structured randomness matters. On the perfectly symmetric XOR game, our method achieves $1.0$ success while all deterministic baselines plateau near $0.5$. On control coordination tasks, a policy trained on $N=4$ generalizes zero-shot to $N \in [2,8]$. On SMACLite cross-scenario transfer, we achieve zero-shot transfer where standard baselines cannot transfer due to structural limitations. Furthermore, replacing the structured mask with standard dropout-based randomness results in a 0% win rate, confirming that protocol-space structure, not stochastic noise, is the operative ingredient. https://anonymous.4open.science/r/randomness-137A/

In many scientific domains, including experimentation, researchers rely on measurements of proxy outcomes to achieve faster and more frequent reads, especially when the primary outcome of interest is challenging to measure directly. While proxies offer a more readily accessible observation for inference, the ultimate goal is to draw statistical inferences about the primary outcome parameter and proxy data are typically imperfect in some ways. To correct for these imperfections, current statistical inference methods often depend on strict identifying assumptions (such as surrogacy, covariate/label shift, or missingness assumptions). These assumptions can be difficult to validate and may be violated by various additional sources of distribution shift, potentially leading to biased parameter estimates and miscalibrated uncertainty quantification. We introduce an estimate-level framework, inspired by domain adaptation techniques, to empirically calibrate proxy-based inference. This framework models the proxy-primary metric discrepancy as a random effect at the parameter level, estimating its distribution from aggregated historical observations across past domains (e.g., experiments, time periods, or distinct segments). This method avoids the requirement for retaining individual-level response data. Additionally, this adjustment can be layered on top of existing proxy-correction methods (such as prediction-powered inference or importance weighting) to account for additional biases not addressed by those corrections. To manage uncertainty when the number of historical domains is limited, we provide both a method-of-moments estimator and a domain bootstrap procedure. We further validate this approach using publicly available datasets and real-world experiments.

Random directed acyclic graphs (DAGs) based on imposing an order on Erdős-Rényi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.

We study budget-constrained contextual bandits with adversarial contexts, where each action yields a random reward and incurs a random cost. We adopt the standard realizability assumption: conditioned on the observed context, rewards and costs are drawn independently from fixed distributions whose expectations belong to known function classes. We focus on the continuing setting, in which the algorithm operates over the entire horizon even after the budget for cumulative cost is exhausted. In this setting, the objective is to simultaneously control regret and the violation of the budget constraint. Building on the seminal $\mathsf{SquareCB}$ framework of Foster et al. [2018], we propose a simple and modular framework that leverages online regression oracles to reduce the constrained problem to a standard unconstrained contextual bandit problem with adaptively defined surrogate reward functions. In contrast to prior works, which focus on stochastic contexts, our reduction yields improved guarantees for more general adversarial contexts, together with an efficient algorithm with a compact and transparent analysis.

This study presents a novel deterministic optimization algorithm based on a special variant of the Linear Congruential Generator (LCG). While conventional algorithms generally operate within the search space, the introduced technique follows a two-level architecture. In particular, an external loop that adaptively balances between exploration and exploitation, while the internal loop evaluates solutions. It is motivated by the intrinsic structure of the generator, the reason behind naming it the Structured Linear Congruential Generator (S- LCG). which enjoys a number of unique characteristics as follows: 1) a memoryless scheme, which ensures non-overlapping sequences based on distinct seeds, thus ensuring no evaluation redundancy; 2) bit splitting representation, which converts LCG states into multi-dimensional points to overcome the Marsaglia lattice effect; 3) adaptive exploration-exploitation of the generator space, which leads to implicit optimization of the surrogate smooth objective function; and 4) constant information gathering speed to avoid the problem of premature convergence. Extensive testing on 26 benchmark functions across dimensions d = 2 to 30 demonstrates that S-LCG comes within 1% of the global optimum in 83.3% of 138 cases (100% at d = 2, 81.2% at d = 30) while the nearest competitor GA achieved 75.4%. Statistical validation shows that S-LCG outperforms eight cutting-edge binary algorithms. Furthermore, its practical value is confirmed by validation on three constrained engineering design problems. In the end, S-LCG offers an optimization framework that is strictly reproducible and requires only one sensitive parameter to be tuned.

Simulation-based planning with rollouts is a widely-deployed technique for decision making in stochastic environments. The primary instrument of simulation-based planning is a sampling model, which is repeatedly called to generate trajectories and estimate the utilities of available actions. Among the actions thus explored, one with the maximum estimated utility is then executed. In this paper, we examine the effect of using common random numbers in the simulation process. We obtain a simple recipe for (provably) reducing variance in relative utility when simulations invoke a rollout policy beyond some depth. Experiments on synthetic tasks confirm that our scheme improves task performance. The broader significance of our innovation is apparent from two practical applications: (1) single-step lookahead planning in a pension-disbursement task, and (2) a deployment of the well-known UCT algorithm for the game of Ludo.

The dual norm characterisation of weak solutions of second-order linear elliptic partial differential equations is mathematically natural but computationally intractable: evaluating the $H^{-1}$ norm of the residual requires a supremum over an infinite-dimensional test space. We prove that the $H^{-1}$ norm of any functional is equivalent to its expected squared evaluation against a random test function whose probability distribution depends only on the domain. Crucially, realisations of this random test function have negative Sobolev regularity for $d \geq 2$, yet this roughness is not an obstacle: averaging over the distribution exactly recovers the correct weak topology, independently of the differential operator, and no supremum evaluation is necessary. This equivalence introduces the notion of stochastically weak solutions, which coincide with classical weak solutions, and motivates stochastic variational physics-informed neural networks (SV-PINNs): neural networks trained by minimising an empirical approximation of the stochastic norm of the PDE residual. Although instantiated here with neural networks, the underlying principle is independent of the trial space and suggests a broader paradigm for numerical methods based on stochastic rather than deterministic test spaces. The framework extends naturally to higher-order elliptic, parabolic and hyperbolic equations and to abstract operator equations on Hilbert spaces. As a proof of concept, we present numerical experiments on eight challenging second-order linear elliptic problems spanning high-frequency and multi-scale solutions, indefinite operators, variable coefficients, and non-standard domains, in which SV-PINNs consistently and significantly outperform standard PINNs, recovering solutions to within one percent relative error in hundreds of L-BFGS steps.

Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM inference under conditional-i.i.d. calls. One labeled call identifies the mean latent success probability; two labeled calls identify its second moment and hence the same-example correctness correlation that separates stable errors from recoverable call-level randomness. From these two moments, every fixed majority-vote budget has a sharp distribution-free two-call interval. The key technical reduction is that the infinite-dimensional moment problem has three-atom extremizers and quadratic dual certificates for every finite budget, so the bounds are exact rather than discretized or parametric. The first useful budget, three votes, has a closed form, width at most $1/8$, and a certified-improvement criterion. The infinite-vote endpoint is the limit of majority voting as the number of calls tends to infinity; it is also sharply bounded, but remains threshold-sensitive because it depends on latent mass around $q=1/2$. We add maximum-entropy and Latent-difficulty Gaussian-probit point completions, and experiments on LLM calls over QNLI and QQP show that empirical three- and five-vote accuracies are contained in the projected two-call regions while temperature changes and randomized model mixtures can create voting gains not ordered by one-call accuracy.

Domain randomization (DR) is widely used in policy learning to improve robustness to modeling error, but remains underexplored in contact-rich sampling-based predictive control (SPC), where rollout quality is highly sensitive to uncertainty. In this work, we take the first step by studying risk-aware DR in predictive sampling on a simple yet representative Push-T task, comparing average, optimistic, and pessimistic rollout aggregations under randomized model instances. Our initial results suggest that DR affects not only robustness to model error, but also the effective cost landscape seen by the sampling-based optimizer, by reshaping the basin of attraction around contact-producing actions. This opens up potential for exploring better grounded risk-aware contact-rich SPC under model uncertainty. Video: https://youtu.be/f1F0ALXxhSM

Across many scientific disciplines, multiple observations are collected from the same experimental units, and in modern datasets these observations often arise as non-Euclidean random objects. In such settings, the incorporation of random effects is a critical modeling step for efficient estimation and personalized prediction. Although mixed-effects models are well established for scalar outcomes and, more recently, for functional data in Hilbert spaces, general random-effects frameworks for objects in metric spaces remain underdeveloped. In this paper, we propose a nonlinear Fréchet-based algorithm for random-effects modeling of arbitrary random objects defined on a metric space. Using M-estimation theory, we establish conditions under which the proposed metric-space prediction target is consistently estimated under a working random-effects formulation. We then evaluate the empirical performance of the proposed method using both synthetic data and digital health datasets that require practical tools for analyzing random objects in metric spaces, such as multivariate probability distributions and random graphs. We show that, although our method is developed beyond Hilbert spaces, it can outperform existing Hilbert space-based methods.

A predecessor pilot (Cacioli, 2026) found that Llama-3-8B implements prompted sandbagging as positional collapse rather than answer avoidance. However, fixed option ordering in MMLU-Pro left open whether this reflected a model-level position-dominant policy or dataset-level distractor structure. This pre-registered follow-up (3 models, 2,000 MMLU-Pro items, 4 conditions, 24,000 primary trials) added cyclic option-order randomisation as the critical control. The pre-registered item-level same-letter diagnostic did not confirm deterministic position-tracking (same-letter rate 37.3%, below the 50% threshold). However, pre-specified supporting analyses revealed that the response-position distribution under sandbagging was highly stable under complete content rotation (Pearson r = 0.9994; Jensen-Shannon divergence = 0.027, compared to 0.386 between honest and sandbagging conditions). Accuracy spiked to 72.1% when the correct answer coincidentally occupied the preferred position E, and fell to 4.3% at position A. The data provide strong evidence for a soft distributional attractor: under sandbagging instruction, the model enters a low-entropy response-position basin centred on E/F/G that is highly stable and largely content-invariant at the aggregate level. Qwen-2.5-7B served as a negative control (non-compliant, no distributional shift). These results provide evidence, at the 7-9 billion parameter scale, that response-position entropy is a promising black-box behavioural signature of this sandbagging mode.

Even when decoding with temperature $T=0$, large language models (LLMs) can produce divergent outputs for identical inputs. Recent work by Thinking Machines Lab highlights implementation-level sources of nondeterminism, including batch-size variation, kernel non-invariance, and floating-point non-associativity. In this short note we formalize this behavior by introducing the notion of \emph{background temperature} $T_{\mathrm{bg}}$, the effective temperature induced by an implementation-dependent perturbation process observed even when nominal $T=0$. We provide clean definitions, show how $T_{\mathrm{bg}}$ relates to a stochastic perturbation governed by the inference environment $I$, and propose an empirical protocol to estimate $T_{bg}$ via the equivalent temperature $T_n(I)$ of an ideal reference system. We conclude with a set of pilot experiments run on a representative pool from the major LLM providers that demonstrate the idea and outline implications for reproducibility, evaluation, and deployment.

Mixture-of-experts models provide a flexible framework for learning complex probabilistic input-output relationships by combining multiple expert models through an input-dependent gating mechanism. These models have become increasingly prominent in modern machine learning, yet their theoretical properties in the Bayesian framework remain largely unexplored. In this paper, we study Bayesian mixture-of-experts models, focusing on the ubiquitous softmax-based gating mechanism. Specifically, we investigate the asymptotic behavior of the posterior distribution for three fundamental statistical tasks: density estimation, parameter estimation, and model selection. First, we establish posterior contraction rates for density estimation, both in the regimes with a fixed, known number of experts and with a random learnable number of experts. We then analyze parameter estimation and derive convergence guarantees based on tailored Voronoi-type losses, which account for the complex identifiability structure of mixture-of-experts models. Finally, we propose and analyze two complementary strategies for selecting the number of experts. Taken together, these results provide one of the first systematic theoretical analyses of Bayesian mixture-of-experts models with softmax gating, and yield several theory-grounded insights for practical model design.

Simulation-based testing of autonomous driving systems (ADS) must uncover realistic and diverse failures in dense, heterogeneous traffic. However, existing search-based seeding methods (e.g., genetic algorithms) struggle in high-dimensional spaces, often collapsing to limited modes and missing many failure scenarios. We present PtoP, a framework that combines adaptive random seed generation with Stein Variational Gradient Descent (SVGD) to produce diverse, failure-inducing initial conditions. SVGD balances attraction toward high-risk regions and repulsion among particles, yielding risk-seeking yet well-distributed seeds across multiple failure modes. PtoP is plug-and-play and enhances existing online testing methods (e.g., reinforcement learning--based testers) by providing principled seeds. Evaluation in CARLA on two industry-grade ADS (Apollo, Autoware) and a native end-to-end system shows that PtoP improves safety violation rate (up to 27.68%), scenario diversity (9.6%), and map coverage (16.78%) over baselines.

Predictions from machine learning algorithms can vary across random seeds, inducing instability in downstream debiased machine learning estimators. We formalize random seed stability via a concentration condition and prove that subbagging guarantees stability for any bounded-outcome regression algorithm. We introduce a new cross-fitting procedure, adaptive cross-bagging, which simultaneously eliminates seed dependence from both nuisance estimation and sample splitting in debiased machine learning. Numerical experiments confirm that the method achieves the targeted level of stability whereas alternatives do not. Our method incurs a small computational penalty relative to standard practice whereas alternative methods incur large penalties.

Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a lottery over options that clears all stakeholders' acceptability bars? We study a query model where the algorithm proposes lotteries and receives only binary accept/reject feedback. We give deterministic and randomized algorithms that either find a unanimously acceptable lottery or certify infeasibility; adaptivity can avoid eliciting many stakeholders' constraints, and randomization further reduces the expected elicitation cost relative to full elicitation. We complement these upper bounds with worst-case lower bounds (in particular, linear dependence on the number of stakeholders and logarithmic dependence on precision are unavoidable). Finally, we develop learning-augmented algorithms that exploit natural forms of advice (e.g., likely binding stakeholders or a promising lottery), improving query complexity when predictions are accurate while preserving worst-case guarantees.

GUI grounding models report over 85% accuracy on standard benchmarks, yet drop 27-56 percentage points when instructions require spatial reasoning rather than direct element naming. Current benchmarks miss this because they evaluate each screenshot once with a single fixed instruction. We introduce GUI-Perturbed, a controlled perturbation framework that independently varies visual scenes and instructions to measure grounding robustness. Evaluating three 7B models from the same architecture lineage, we find that relational instructions cause systematic accuracy collapse across all models, a 70% browser zoom produces statistically significant degradation, and rank-8 LoRA fine-tuning with augmented data degrades performance rather than improving it. By perturbing along independent axes, GUI-Perturbed isolates which specific capability axes are affected-spatial reasoning, visual robustness, reasoning calibration-providing diagnostic signal that aggregate benchmarks cannot. We release the dataset, augmentation pipeline, and a fine-tuned model.

Creative ideas often arise by associating remote concepts. Can random associations reliably increase originality, and do they help humans and large language models (LLMs) in the same way? We asked human participants and seven LLMs to design products by drawing inspiration from a random source or addressing an unmet user need. Humans reliably benefited from cross-domain mappings, while LLMs generated more original ideas than humans but showed no overall benefit from the intervention, though this changed with semantic distance. More distant source-target pairings produced more original ideas in both humans and LLMs. Humans benefited at nearly any distance, while only the highest-rated LLMs benefited when the source was sufficiently remote. Humans and LLMs also used sources differently: humans tended to transfer surface features, while LLMs transferred structural and functional properties. These findings reveal the generative role of remote associations and systematic differences in how humans and AI respond to the same creativity intervention.

We consider the privacy amplification properties of a sampling scheme in which a user's data isused in $k$ steps chosen randomly and uniformly from a sequence (or set) of $t$ steps. This sampling scheme has been recently applied in the context of differentially private optimization (Chua et al., 2024a; Choquette-Choo et al., 2025) and communication-efficient high-dimensional private aggregation (Asi et al., 2026), where it was shown to have utility advantages over the standard Poisson sampling. Theoretical analyses of this sampling scheme (Feldman & Shenfeld, 2025; Dong et al., 2025) lead to bounds that are close to those of Poisson sampling, yet still have two significant shortcomings. First, in many practical settings, the resulting privacy parameters are not tight due to the approximation steps in the analysis. Second, the computed parameters are either the hockey stick or Renyi divergence, both of which introduce overheads when used in privacy loss accounting. In this work, we demonstrate that the privacy loss distribution (PLD) of random allocation applied to any differentially private algorithm can be computed efficiently. When applied to the Gaussian mechanism, our results demonstrate that the privacy-utility trade-off for random allocation is at least as good as that of Poisson subsampling. In particular, random allocation is better suited for training via DP-SGD. To support these computations, our work develops new tools for general privacy loss accounting based on a notion of PLD realization. This notion allows us to extend accurate privacy loss accounting to subsampling which previously required manual noise-mechanism-specific analysis.

Learned gates can approximate sparse attention patterns on frozen transformers, yet provide limited benefit over random gates when trained jointly with the model. We investigate this difference in a controlled 31M-parameter transformer and attribute it to routing absorption: model representations co-adapt to the imposed mask, reducing the incremental benefit of learned routing. Four experiments characterize the phenomenon. Differentiable soft gating yields perplexities of 48.73 plus or minus 0.60 with learned gates and 49.83 plus or minus 0.04 with frozen random gates over three seeds. Hard top-k masking provides no gradient path to the gate scores in the tested implementation. Gates distilled onto co-adapted and dense-trained Q/K/V both achieve high F1 against oracle masks, but hard-mask deployment yields perplexities of 601.6 and 48.6, respectively. Stochastic mask training also leaves a substantial deployment penalty: dense evaluation yields 78.2 perplexity, compared with 37.3 for the dense baseline. Experiments on Qwen3-1.7B show that increasing the number of trainable attention layers reduces the gap between learned and random gates. We relate these results to co-adaptation in Mixture-of-Experts and propose parameter asymmetry between the gate and the model as a contributing mechanism. For the tested per-query, token-level gates, freezing the model provides stable routing targets and enables effective post-hoc sparsification. The results motivate random-routing controls and separate evaluation of routing quality and model adaptation in sparse attention methods.

We present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to accommodate image editing at inference time. Approaches that expose conventional autoregressive (AR) models in visual generation to arbitrary sequence orders via random permutation suffer from degraded sampling performance or compromise the flexibility in sequence order choice at inference time. Instead, STAR utilizes traversal orders of uniform spanning trees in a lattice defined by the positions of image patches. Traversal orders are obtained via breadth-first search, allowing us to efficiently construct a spanning tree via rejection sampling whose traversal order ensures that the connected partial observation of the image appears as a prefix for native image inpainting support. Through the tailored yet structured sequence order randomization strategy, STAR preserves the capability of postfix completion while maintaining sampling performance, without any significant changes to the model architecture widely adopted in language AR modeling.

Robotic fabric manipulation remains challenging due to fabric deformability and occlusions from wrinkles and the manipulator. This paper defines Random-to-Target Fabric Flattening (RTFF) as the task of bringing a randomly wrinkled fabric to an arbitrary user-specified wrinkle-free target pose. RTFF requires simultaneous flattening and pose alignment, where the two objectives are inherently coupled since flattening the fabric displaces its pose, while realigning it tends to introduce wrinkles. To solve this task, this paper anchors both the current and target fabric states to the same template mesh, enabling direct vertex-level wrinkle and pose assessment without registration. Building on this representation, a hybrid Imitation Learning--Visual Servoing (IL--VS) RTFF policy is proposed. A novel Mesh Action Chunking Transformer (MACT) leverages structured mesh observations to achieve goal-conditioned coarse alignment from a compact demonstration set, after which VS ensures precise convergence to the target. The policy is validated on a real dual-arm teleoperation system, demonstrating precise alignment to unseen target poses, fabric types, and scales. Code and videos: https://kaitang98.github.io/RTFF_Policy/

A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process. In building this connection, we use a performance of a learning task as a probe of compression, over series of compression cycles within a cascade. The Gibbs entropy at each cycle measures the degree of randomness. Consequently a lossy compression process can be seen as an equivalent to {\it directed randomness} that preserves information content under certain bounds of Gibbs entropy and the performance of the learning task. The term directed means we guide the compression process with set of mathematical rules on how to reduce the model size. We formulate this connection with a theorem using a $δ$ and $ε$ bounds, and demonstrated a logical proof via comonotonic relationship within a very small decrease in compression ratio and the performance. We have showcase the validity of this proposition with a canonical vision task in deep learning with three different model compression processes as {\it a baseline model}. We use the following, simpler to more complex model compression approaches: (1) random pruning, (2) magnitude pruning, and (3) a more complex compression by using dual tomographic compression, which utilizes compressed sensing in dual fashion. We use remaining weights of deep learning network as a measurement vector where we measure the Gibbs entropy. The proposition is supported with the experimental evidence, resulting in very high correlation between learning performance and the Gibbs entropy over compression ratios for all different compression processes. We show case the idea that there is an inherent computable connection between compression probed by performance degradation and randomness from an entropy measure on the learned model.

This paper explores the performance of a random Gaussian smoothing zeroth-order (ZO) scheme for minimising quasar-convex (QC) and strongly quasar-convex (SQC) functions in both unconstrained and constrained settings. For the unconstrained problem, we establish the ZO algorithm's convergence to a global minimum along with its complexity when applied to both QC and SQC functions. For the constrained problem, we introduce the new notion of proximal-quasar-convexity and prove analogous results to the unconstrained case. Specifically, we derive complexity bounds and prove convergence of the algorithm to a neighbourhood of a global minimum whose size can be controlled under a variance reduction scheme. Beyond the theoretical guarantees, we demonstrate the practical implications of our results on several machine learning problems where quasar-convexity naturally arises, including linear dynamical system identification and generalised linear models.

Control barrier functions (CBFs) provide a principled framework for safety-critical control, but their construction typically requires an explicit and differentiable description of the safe or unsafe region. It becomes challenging for data-defined unsafe regions that may evolve over time. This paper proposes SafeLink, a data-driven CBF construction and adaptation method based on a cost-sensitive random vector functional link (RVFL) network. SafeLink introduces asymmetric misclassification costs to promote conservative unsafe-region representation while preserving a closed-form solution. We establish the Lipschitz continuity of the learned CBF and its derivatives, and derive sufficient conditions for conservative unsafe-region coverage and the corresponding interval-wise safety guarantees. Analytical updates are further developed for adjusting the misclassification cost and for incrementally adding or decrementally removing samples, avoiding full retraining when the unsafe region changes. Experiments on a two-link manipulator demonstrate that SafeLink rapidly adapts to evolving unsafe regions, enables collision-free target reaching, and achieves substantially lower update runtimes than baselines.

Fetal brain tissue segmentation from magnetic resonance imaging (MRI) is crucial for studying neurodevelopment, but remains challenging due to data heterogeneity and limited annotations. Domain randomization (DR) has recently emerged as a promising strategy for single-source domain generalization by synthesizing training images with randomized artifacts, contrast, and resolution. In this work, we investigate how to maximize the out-of-domain (OOD) generalization of DR-based methods. We evaluate several synthetic data generation strategies for DR, with a particular focus on our recently proposed framework, FetalSynthSeg. We show that simple Gaussian mixture-based intensity modeling outperforms more complex physics-based simulations, and that intensity clustering (subdividing tissue classes based on intensity) improves OOD robustness. Evaluated on 348 fetal subjects from four sites spanning 0.55-3T and both T1w and T2w contrasts, FetalSynthSeg reaches state-of-the-art performance on several FeTA 2024 testing datasets (80-85 Dice score) and, for the first time, offers robust segmentation on modalities other than T2w for fetal brain segmentation (80 Dice on dHCP-T1w dataset). Compared with state-of-the-art methods such as BOUNTI, nnU-Net ensemble, and the FeTA 2024 winner, FetalSynthSeg delivers comparable or superior accuracy while maintaining strong robustness across domain shifts. Our code, model weights, and Docker image ready for easy inference are available at https://hub.docker.com/r/vzalevskyi/fetalsynthseg.