Papers

We count maximal cylinders on zero holonomy $\mathbb{Z}$-covers of genus $2$ square-tiled surfaces, up to $\mathbb{Z}$-action, obtaining quadratic asymptotics. We also show that the leading term of the asymptotic, called the Siegel-Veech constant, can be recovered via a large-genus approximation by intermediate finite covers. Our work applies to the infinite staircases introduced by P. Hubert and G. Weitze-Schmithüsen. For many members of this family, we explicitly compute the associated Siegel-Veech constants. In particular, we exhibit the first infinite family of examples of zero holonomy $\mathbb{Z}$-cover in which the number of cylinders grows sub-quadratically.

We show that first-order linear plants are globally asymptotically stable under antithetic feedback. This is shown by constructing an explicit smooth, convex Lyapunov function and by appealing to a Krasovskii-LaSalle invariance principle.

We present a discrete analogue of geometric quantization over finite fields which, when applied to certain classical error-correcting codes, yields quantum error-correcting codes. This provides a physical interpretation for a previously known quantum-classical correspondence in coding theory.

Estimating the logical error rate (LER) of a quantum error-correcting (QEC) code by Monte Carlo sampling takes $O(p^{-\lceil d/2 \rceil}/\varepsilon^2)$ samples at physical error rate $p$, code distance $d$ and relative error $\varepsilon$, which becomes intractable at large distances and low error rates, and especially for concatenated codes, whose distance grows as $d^{\ell}$ with the number of levels $\ell$. The fail fast method reduces this cost by sampling the failures of each weight separately, but it only works for unconcatenated codes, and does not model the soft information that the levels of a concatenated code pass to each other. We propose a predictor that takes the stabilizers, the minimum-weight logical operators and, for odd $d$, the logical operators of weight $d + 1$ of a code, and computes, without sampling, the leading monomial $c\,p^{o}$ of the LER when expressed as a polynomial in $p$, at every level of concatenation, in time polynomial in the code parameters and linear in $\ell$ for fixed budgets. We prove that our prediction is exact for any unconcatenated stabilizer code, for every logical observable and arbitrary per-qubit error rates, whenever no budget is exhausted. Furthermore, for concatenated codes, we construct a recursive approach that computes the leading monomial exactly in exponential time, and our predictor approximates this approach. Our predictions match exact enumeration at level 1 on every code we evaluate, and up to three levels for the iceberg code. Using our predictor, we evaluate and compare $37$ code configurations under four noise biases in $48$ core-hours, where Monte Carlo sampling would need more than $10^{12}$ shots at $p = 10^{-3}$ for $113$ of these $148$ cases.

Transformers asked to multiply multi-digit numbers in a single forward pass often fail, and interpretability studies of pretrained language models find arithmetic solved by input-range heuristics rather than by an explicit carry. We train small Llama-style transformers from scratch on 4x4 multiplication without chain of thought and find that the input format is decisive: inserting a space token between digits raises exact-match accuracy from 1% to 89%. Output positions are learned in carry-chain order, with the middle digits, which have the longest-range dependencies, learned last. Inside the model, the separator token that predicts each digit (its prediction slot) encodes the carry-in as an angle on a ring in the residual stream; examples with more distinct carry values fill more of the ring. Activation patching between examples matched on the column sum shows that this state is causally used before the last layer: patching the prediction slot alone transfers the source carry in up to 84% of cases after block 4 for one middle column of our best model, while for other columns the carry is first assembled at the neighboring answer slot before reaching its own. Remaining errors are almost always off by one, consistent with a small error on the carry or on the circular digit code.

Information causality (IC) was introduced as a physical principle that imposes constraints on the non-local correlations between two parties (Alice and Bob) in a Bell scenario. Specifically, it states that the information that Bob can gain about an $n$-bit database held by Alice is bounded by the information she communicates to him. To date, the question whether IC for any $n \in \mathbb{N}$ singles out the set of quantum correlations remains open, meaning that it is unknown whether for any number of inputs $m$ and outputs $d$ of the two parties the set of correlations that satisfy IC exactly coincides with the quantum correlations. In this work, we answer this question in the negative. Firstly, we show that for any finite database length $n \geq 2$, there is a bipartite set of correlations that satisfies IC for all compatible protocols and that exhibits post-quantum correlations in the Bell scenario with $n+1$ inputs and $2$ outcomes per party. This result relies on constructing an entropic proof of IC for GPTs that may be of independent interest. We further show that in the Bell scenario with $n+1$ inputs and $2$ outcomes per party, our constructed sets of correlations lead to neither a superset nor a subset of the quantum correlations. Secondly, we construct a set of correlations in the Bell scenario with $3$ inputs and $2$ outputs per party that satisfies IC (for all database sizes $n \in \mathbb{N}$) and that includes post-quantum points. Consequently, all known formulations of information causality fail to fully characterize the bipartite set of quantum correlations, already in the $3$-input, $2$-outcome Bell scenario.

Text from multiple sources can become interleaved into a single sequence when attribution metadata is lost, such as overlapping speech transcripts, document reading flows, or concurrent agent streams. We formalize this challenge as Word-Level Text Unmixing: given an interleaved lexical stream and source count K, recover the original source sequences while preserving every word occurrence and its within-source order exactly. Directly generating separated texts with LLMs can omit, duplicate, or hallucinate words, violating this exact-reconstruction objective. We therefore propose Evidence-Preserving Ownership Routing (EPOR), which decouples source-ownership prediction from reconstruction. EPOR adapts a causal LLM to predict canonical ownership routes conditioned on the mixed stream and prior routing decisions. At inference, completion-safe constrained decoding is combined with deterministic indexed reconstruction, yielding structurally valid K-source partitions that preserve every observed occurrence exactly once. We also introduce UNMIXBENCH, covering controlled synthetic mixtures, timestamp-derived speech from AMI and ICSI, layout-derived document streams from ReadingBank, and simulated concurrent digital outputs. Across five evaluation tracks, a 4B EPOR model achieves the lowest mean minimum-permutation word error rate among finetuned baselines, reducing the five-track mean by 22.3% relative to compact source-array generation and remaining competitive with zero-shot frontier LLMs. These results show that when lexical evidence is fully observed, separating ownership inference from lexical regeneration provides a reliable alternative to direct generation.

Early osteoarthritis detection through quantitative MRI (qMRI) requires accurate cartilage and meniscus segmentation, traditionally necessitating time-consuming, costly 3D high-resolution Double Echo Steady-State (DESS) MRI scans. This study developed a multi-task conditional generative adversarial network (MT-cGAN) to simultaneously synthesize DESS-like images and segment tissues directly from qMRI echo images. This retrospective study evaluated 508 knee MRI volumes from 361 subjects (mean age: $40.4 \pm 12.2$ years; 179 female) across three cohorts. Ground truth segmentation masks were generated from DESS images using a pretrained model with manual correction, and $T_{1\rho}$ and $T_2$ maps were computed from magnetization-prepared angle-modulated partitioned $k$-space spoiled gradient echo snapshots (MAPSS) echo images. MT-cGAN was trained to jointly synthesize DESS-like images and segment cartilage and meniscus directly from echo images. Model performance was evaluated using Dice score for segmentation accuracy and coefficient of variation (CV) for $T_{1\rho}$ and $T_2$ quantification. MT-cGAN achieved the highest segmentation performance, mean Dice score 0.84 (range: 0.80–0.86) across all cartilage and meniscus compartments and significantly outperformed the state-of-the-art conditional GAN model with transfer learning (mean Dice, 0.82; $p < 0.001$, Wilcoxon signed-rank test). For relaxometry quantification, MT-cGAN demonstrated the highest consistency with the reference DESS protocol, yielding the lowest CV ($T_{1\rho}$: 1.84%, $T_2$: 1.81%). The proposed MT-cGAN accurately segmented cartilage and menisci while providing reliable $T_{1\rho}$ and $T_2$ quantification directly from echo images. By eliminating the need for separate morphological DESS scans, this workflow reduces required scan times to facilitate the clinical translation of qMRI.

Industrial refrigeration consumes substantial electricity, and compressors are the dominant energy consumers in these systems, making their operation central to improving energy efficiency. Compressors are most efficient when operated at full capacity, but the cooling they provide at full capacity can exceed the facility's immediate needs. This motivates pre-cooling, where compressors operate at full capacity and the excess cooling is stored as thermal inventory for future heat loads. However, stored cooling is inherently lossy: colder spaces attract additional heat from their surroundings, creating a tradeoff between maximizing compressor efficiency and avoiding cooling that dissipates before it can be used. We study this tradeoff through a retention factor, defined as the fraction of thermal inventory that survives after one minute, with the goals of understanding how retention affects the value of pre-cooling and designing effective control policies that account for this lossiness. We formulate compressor control as a stochastic inventory problem, solve for an optimal policy via dynamic programming alongside two simpler alternatives, and evaluate the performance of these policies using models fit from real industrial refrigeration facility data. Our results show that (i) pre-cooling can provide substantial energy savings when thermal inventory is sufficiently persistent, but that failing to account for retention can make aggressive pre-cooling increasingly costly as losses grow, and (ii) structurally simple policies that account for lossiness can still achieve near-optimal performance in lossy systems.

Automatically extracted narrative networks – graphs with entities as nodes and their relations as edges – have proven useful for revealing central narrative structures through salient entities and their connections (Tangherlini et al. 2020; Labatut and Bost 2019). But a narrative is more than those central structures that everything else revolves around. This work is concerned with the everything else: brief sub-plots, small clusters of descriptions, or associations between minor characters that go under the radar at the macro-level. We present an approach to unearth such peripheral structures. They involve rare entities with limited textual presence, overshadowed by dominant entities and lost among each other in the long tail of many but rare entities (Baayen 2001). We leverage the known tendency of pointwise mutual information (PMI, Church and Hanks 1990) to inflate for rare events, turning its weakness into a strength by weighting edges with PMI to foreground peripheral entity configurations. Communities extracted from the resulting network are structural traces of underlying narrative elements. We demonstrate the approach on The Lord of the Rings. From measures of how concentrated or dispersed a community's activations are across the text, a typology emerges that reveals that peripheral structures form more than a single class: episodic passages, echoing long-distance connections, and recurring threads each surface as distinct configurations. The approach is conceptually simple and surfaces fine-grained narrative details that are lost in abundance, though its deliberate amplification of weak signals comes with inherent sensitivity – best understood as a lens for exploration rather than a robust extraction pipeline.

We demonstrate on a network testbed a Digital Twin-aided multi-agent LLM for autonomous class-aware optical network management. The system detects soft failures and autonomously adapts modulation format per service class requirements, ensuring continuous, marginless channel quality with minimal human intervention. {\copyright}2026 The

Action-conditioned robot world models must respond precisely to robot trajectories while preserving realistic visual dynamics, yet learning both from heterogeneous robot videos remains challenging. Simulation offers structured motion supervision, but appearance differences hinder direct transfer, and inaccurate simulation predictions can misguide real-video generation. We present SimForcing, a simulation-guided framework that uses simulation both as a source of transferable motion knowledge and as a controllable reference for prediction. First, we transfer motion knowledge from a simulation teacher through latent-motion distillation, aligning temporal changes in latent space to internalize motion priors while mitigating the influence of appearance differences. Second, we introduce multi-block simulation conditioning with condition dropout to exploit predicted simulation trajectories without relying excessively on their accuracy. Our simulation-conditioning classifier-free guidance scheme unifies these two ideas by balancing predictions based on internalized motion knowledge with those additionally guided by simulation latents. The jointly trained student generates both simulation conditions and real-domain videos, requiring no additional world model at inference. On Bridge, SimForcing achieves the best PSNR, SSIM, LPIPS, and FVD among the compared methods without external embodied pretraining. Evaluation on InternData-A1 further supports its applicability across robot datasets. Moreover, using our trained world model to initialize a vision-language-action model improves LIBERO success, suggesting its utility for downstream policy learning. \url{https://github.com/Wang-Xiaodong1899/SimForcing}

LLM agents increasingly execute complex workflows involving multi-turn reasoning, tool use, and parallel agents. Efficient serving requires decisions that span two layers with complementary information: the agent harness understands workflow dependencies, context lifecycles, and execution objectives, whereas the inference engine observes request queues, KV-cache state, resource pressure, and execution capabilities. Existing interfaces do not systematically connect these views, limiting workflow-aware execution. HEAR, a bidirectional Harness–Engine Pairing protocol for agentic LLM serving. HEAR standardizes how the harness communicates workflow intent and execution requirements and how the engine returns runtime state, capabilities, and outcomes. By separating protocol semantics from optimization policies, HEAR supports diverse coordination strategies without changing workflow or model semantics. We instantiate HEAR for online cache-aware runtime coordination and workload-aware execution-mode selection for agent roles. Across four conversational and research-agent benchmarks under memory-constrained, concurrent serving, HEAR achieves a $1.61\times$ batch speedup and reduces median time-to-first-token by $2.23\times$ on SCBench. Mooncake shows that workflow intent and live engine state provide complementary benefits across load regimes. On BrowseComp-Plus and DeepResearchBench, workload-specific configurations yield $1.23\times$ and $2.45\times$ end-to-end speedups, respectively, without observed task-quality degradation. These results establish HEAR as a reusable coordination substrate for efficient agentic LLM serving.

Short-wave infrared (SWIR) imaging has emerged as a promising modality for autonomous driving, yet its practical benefits over RGB remain poorly characterized across diverse conditions. This paper presents a systematic comparative study of paired RGB and SWIR object detection on the RASMD dataset, covering four weather conditions and two real-time detection architectures, with various fine-tunings evaluated against a unified ground truth. Overall, RGB demonstrates comparable or superior performance in most scenarios, while RF-DETR exhibits greater robustness across varying conditions. Beyond aggregate metrics, we propose a sensor-dominance mining framework that combines multi-model agreement with targeted manual inspection to identify scenarios where one sensing modality provides more reliable detections using largely unannotated paired data. This analysis reveals that SWIR offers clear advantages in four safety-critical situations, including windshield glare, water droplets on the windshield, low-contrast object visibility, and long-range vehicle detection. The findings suggest that SWIR should be viewed as a complementary modality that enhances perception in rare but challenging conditions. The datasets will be available upon request, and all code and trained model weights are publicly released at https://github.com/comsee-research/swir-adverse-env-analysis.

A classic result of Poly and Raby \cite{Poly-Raby:1984} states that, in finite-dimensional Euclidean spaces, $\mathcal{C}^k$-smoothness (with $k\geq2$) of the squared distance function near a point of a closed set characterizes smoothness of the set as a submanifold, with the same order of differentiability. In this work, we show that this characterization splits in infinite-dimensional Hilbert spaces: $\mathcal{C}^k$-smoothness of the squared distance function characterizes weakly $\mathcal{C}^k$-submanifolds, while $\mathcal{C}^k$-submanifolds are characterized by this smoothness together with an additional pointwise equicontinuity condition on the highest-order derivative of the squared distance. The diffeomorphism of Poly and Raby, its associated graph representation, and the description of its inverse remain the common geometric basis of both characterizations. The development of this work was assisted by GPT-6 Astra.

Feed-forward visual geometry transformers such as VGGT reconstruct dense 3D structure from images in a single forward pass, simplifying multi-view 3D reconstruction. However, their quadratic attention complexity makes them difficult to scale to long sequences with thousands of frames. Chunk-and-align frameworks address this by splitting a long sequence into overlapping chunks and stitching their local reconstructions into a pose graph. Yet existing methods connect only sequentially adjacent chunks, so small per-frame errors accumulate along the chain into large-scale drift. To move beyond sequential edges, we propose VGGT-Bridge, which adds long-range skip edges that directly constrain non-adjacent chunks without retraining. By running VGGT on sparsely sampled coarse chunks, each coarse chunk bridges distant fine chunks into a single direct constraint. We further turn VGGT's first-frame scale bias into a drift correction by feeding selected coarse chunks in reverse, and a loop-aware policy keeps this reversal compatible with existing loop closures. VGGT-Bridge reduces ATE by 28.3% on KITTI Odometry, 18.8% on Virtual KITTI, and 10.0% on Waymo Open over the SwiftVGGT baseline, achieving the best performance among all chunk-and-align methods. Our code is available at https://github.com/BeCow5X5/VGGT-Bridge.

We study a notion of backward stochastic differential equation on the Wasserstein space, called a W-BSDE. This work extends to the common noise setting recent results of the first author. The equation is formulated in Markovian form along admissible flows of conditional laws generated by McKean-Vlasov dynamics with common noise. A solution is a pair of fields $(Y,Z)$, where $Y$ is a functional on the space of probability measures and $Z$ is the corresponding intrinsic Wasserstein gradient. Our main result shows that the well-posedness of the W-BSDE can be reduced to a characteristic equation for a field $p$. Whenever this equation admits a suitable solution, we construct a W-BSDE solution and identify $Z$ with both the characteristic field $p$ and the intrinsic gradient of $Y$. This gives an existence result for the W-BSDE and, at the same time, a probabilistic construction of a functional on the Wasserstein space together with its intrinsic gradient. We then develop several consequences of the theory. We obtain verification principles for McKean-Vlasov control problems and for mean field games with common noise, without relying on convexity or separability assumptions. We also show that the characteristic field admits a dynamic representation through a McKean-Vlasov forward-backward SDE. The first component $Y$ solves the associated semilinear PDE on the space of probability measures in the viscosity sense, including the second-order term induced by common noise. Under additional smoothness, $Y$ is a classical solution. Finally, we prove that W-BSDEs arise as intrinsic mean-field limits of classical finite-dimensional BSDEs written on empirical measures, with convergence of both the value component and the rescaled martingale integrands.

The differences between the energy spectra reported by the Pierre Auger Observatory and the Telescope Array Collaboration are well-known. In an effort to understand these differences, we have studied the residuals of the fluxes measured in early work at AGASA, Volcano Ranch and Haverah Park with reference to the spectrum reported by the Auger Collaboration. After an empirical adjustment to the energies in the region before the ankle, where fluxes from the two hemispheres are expected to be the same, it is found that historic data are in good agreement with measurements made at the Pierre Auger Observatory above 30 EeV. Thus, the tensions between the spectra measured by the Telescope Array and the Auger Observatory remain.

How much of a conference accept/reject decision would change if the same paper were reviewed by a different set of reviewers? Running a second independent program committee is the gold standard for answering this, but it is prohibitively expensive: done only twice (NeurIPS 2014 and 2021). We build an observational estimator of this quantity from public review data alone, calibrate it twice, and apply it to nine years of ICLR (2017-2025; 36,113 papers, 134,912 reviews). The estimator decomposes scores with a Bayesian ordered-probit model into paper quality and reviewer noise, maps scores to decisions with a logistic model, and simulates two independent committees (posterior draws B=1,000; committee sizes k=2,3,4). Estimated disagreement rates are 23-30% at k=2 and 18-24% at k=4; 30-50% of accepted papers would be rejected. External calibration: at the NeurIPS 2021 reviewer-count caliber (k=3), the simulated 2021 disagreement rate is 23.3% [21.7%, 25.0%] vs. reported 23.0% (bias +0.3pp); accept precision and committee correlation agree within 5pp and 0.04. Internal calibration: on 18,740 papers with 4+ reviews, random model-free 2+2 reviewer splits agree with the k=2 simulation within 1pp in 2018 and 2021-2025. Longitudinally, we find no robust time trend in reviewer noise over 2017-2025. The high accepted-paper flip rates of 2020 and 2021 have distinct mechanisms: the 2020 four-point scale compressed scores (23.7% of papers had zero within-paper variance), and a counterfactual shows coarsening the scale raises disagreement by about 7pp; 2021 instead combined the lowest signal-to-noise ratio in the sample with the most threshold-crowded acceptances. For the LLM era, a 2023 breakpoint test on within-paper score variance finds no break, but the design has almost no power, and no post-2022 review text or confidence data exist, so no LLM attribution is attempted.

Recommender systems leveraging generative models often generate item identifiers directly, rather than ranking catalog items by a recommendation score. Recent work extends beyond pure sequential interaction signals by incorporating item content and structured relationships among items, with two distinct directions emerging. Semantic IDs (SIDs) enrich item representations by replacing opaque, randomly initialized embeddings with hierarchically quantized discrete codes derived from item content. Knowledge-graph (KG) path reasoning instead generates entity-relation paths that ground recommendations in structured relationships between items, attributes, and external entities, thereby enriching the relational context. These two lines have complementary limitations: SID-based models lack relational grounding, while KG-based generative recommenders still represent items as arbitrary, opaque tokens tied to large embedding tables, limiting parameter sharing and generalization. We propose SPRIG, a generative recommender that integrates content-derived SIDs into KG path reasoning. SPRIG is trained on information-rich KG paths that terminate in items represented as discrete, content-derived tokens, combining the advantages of both approaches. We evaluate SPRIG on movie and music recommendation datasets against baselines spanning sequential language models, KG-augmented methods, and SID-based approaches. Our results show that SPRIG achieves competitive performance over prior generative models while using fewer parameters and a lower compute cost. Code: https://github.com/justinhangoebl/semantic-id-knowledge-graph-recommender

Motivated by the Merino–Welsh conjecture, we consider the smallest $c\ge0$, denoted by $c_*$, for which the inequality $T_M(c,0)T_M(0,c)\ge T_M(1,1)^2$ holds for every loopless and coloopless finite matroid $M$. The counterexamples constructed by Beke, Csáji, Csikvári, and Pituk [Adv. Math. 446 (2024), 109674] give the lower bound $x_0$, where $x_0\approx2.22668$ is the largest real root of the polynomial $x^3-9(x-1)$. Later, Csikvári [European J. Combin. 137 (2026), 104402] improved the known upper bound for this constant to $2.35$ and then conjectured that the above inequality holds at $c=x_0$. This conjecture was recently proved by Liu (2026). We give an alternative direct inductive proof that $c_*=x_0$, without computer-assisted finite verification.

Long-horizon camera-controlled video generation relies on persistent memory to maintain scene consistency. Existing systems follow two strategies to achieve this consistency. Full-history approaches retain all generated observations, causing unbounded storage and retrieval costs. Selective-construction approaches reduce redundancy, but make one-time retention decisions that are never revisited, even as an observation's value changes with the evolving memory bank. Both strategies leave a shared question unresolved: as the generated history evolves, which stored observations should still remain in memory? Our key insight is that the value of a stored observation is not fixed, but relational: it depends on the alternatives currently available in the memory bank. A view supported by many geometrically and visually similar substitutes can be relinquished with little loss of coverage, whereas an observation with few viable alternatives should remain regardless of age. We introduce Keepsake, an online, training-free controller for fixed-capacity spatial memory. At each update, Keepsake constructs a pose-appearance graph over retained and newly generated observations, combining camera-pose proximity with visual similarity. A retention priority jointly captures the number of strong substitutes and the similarity of the closest alternative, allowing Keepsake to continually reassess memory value, preserve observations with little alternative support, and evict highly replaceable ones under a fixed budget. The controller modifies only the persistent-memory update; the host generator, denoising schedule, and retrieval rule remain unchanged. Across MemCam and WorldMem, Keepsake improves FVD and LPIPS under a fixed memory budget. On 180-second MemCam trajectories, it retains only 32 of 5,397 frames while reducing FVD by 35.1%.

AI voice assistants often use Automatic Speech Recognition (ASR) with LLM-based reasoning, yet existing systems struggle with regional British accents, including Scottish, Irish, and Welsh accents, since most ASR models are trained predominantly on American English voice data. Consequently, errors can carry through to the LLM stage, corrupting tool-call arguments and producing wrong or missing responses, which is especially costly in finance. Deployable ASR must also meet tight latency and memory budgets, making an accent-robust model choice even harder. We introduce CavaBench, the first internally collected benchmark of spoken financial queries, and use it to evaluate a range of ASR models and their end-to-end ASR-LLM pipeline behaviour across self-reported British accents. We find that WER strongly predicts downstream tool-calling accuracy ($r = -0.93$) but can fail to reflect task-level performance, with accent-related failures varying substantially across models and acoustic conditions. These findings guide the design of more inclusive, reliable voice-based financial assistants.

This survey studies C*-algebraic crossed products arising from topological dynamical systems with an eye toward their classifiability in the sense of the Elliott program. We introduce the crossed product construction for actions by discrete groups in full generality, and then focus on commutative systems to establish some of the fundamental structural results: nuclearity of the crossed product is equivalent to amenability of the action, and in this setting simplicity is equivalent to the combination of minimality and topological freeness. With these properties in place, the only condition left to translate into dynamical terms is tensorial absorption of the Jiang-Su algebra $\mathcal{Z}$. We present the main dynamical tools known to obtain $\mathcal{Z}$-stability, both in the settings of amenable and nonamenable groups, and highlight the two conjectures that are believed to capture the full picture. The aim of the survey is to provide both an accessible entry point and a comprehensive reference on the classification of crossed products, describing the state of the art and a number of central open problems in the field.

On the set $\mathbb{YF}_n$ of words in $1$ and $2$ with digit sum $n$, we consider the probability distribution $\mu_P$, corresponding to the Plancherel measure on paths in the Young–Fibonacci graph. We study the asymptotics as $n$ grows of the entropy of the distribution $\mu_P$ and of the minimum number of words on which $\mu_P$ is almost entirely concentrated.

The release decision for frontier AI systems increasingly relies on cyber capability benchmarks, yet public vulnerability benchmarks can expose agents to previously published advisories, exploits, and fixes, making it difficult to distinguish prior exposure from capability on unseen vulnerabilities. We evaluate open-weight and proprietary AI models on exploit generation, vulnerability repair and subsequent attacks in five nonpublic software environments, including vulnerabilities we privately disclosed while they remained unpatched. Researcher-developed and reviewed deterministic graders, not LLM judges, determine task scores. Comparisons with 209 disclosed vulnerabilities and cryptographic challenges reveal substantial variation across systems and vulnerability types. Repair scores exceed attack scores in two nonpublic environments and fall below them in three. Passing an initial security test is also insufficient: another exploit succeeds in 92 of 524 non-independent defender test intervals after the initial exploit is stopped. These results motivate vulnerability-specific attack-repair comparisons and subsequent resistance tests.

Fast transforms such as the Discrete Cosine Transform can be expressed as the real part of a product of complex-valued structured sparse matrices known as Kronecker-sparse factors. More generally, products of such structured sparse matrices appear in square dyadic butterfly and monarch matrices, which are known to represent many fast transforms efficiently. Yet, it has remained unclear whether taking the real or the imaginary part of such products preserves this structure. In this letter, we give a condition on the factors to ensure that the structure is preserved. This condition is satisfied in the case of the Discrete Cosine Transform, the Discrete Sine Transform and the Discrete Hartley Transform, allowing us to provide a new representation of these transforms as products of real-valued Kronecker-sparse factors, which opens new avenues for efficient GPU implementations using low-precision numerical format.

World-model controllers rely on action-conditioned dynamics for prediction and planning, yet real control systems often execute commands asynchronously due to communication delay, packet loss, reordering, and actuator buffering. We study how asynchronous execution changes the action semantics assumed within world-model controllers, rather than treating it only as an external control disturbance. Through controlled interventions, we identify two architecture-dependent failure modes: planning-based controllers such as TD-MPC2 suffer from a future-action timeline mismatch between imagined and executed action sequences, while recurrent world models such as DreamerV3 can attribute observed transitions to commands that were not actually applied. Our analysis shows that TD-MPC2 requires the correct future action sequence during latent dynamics rollout, whereas DreamerV3 requires timely attribution of each transition to the action that generated it. Based on these findings, we introduce two lightweight execution-consistent interfaces, Future-Sequence for TD-MPC2 and Applied-Action Feedback for DreamerV3, that correct these mismatches without modifying the pretrained world models. Experiments across delays, packet loss, reordering, multiple control domains, measured network traces, and a process-separated asynchronous stack consistently support both diagnoses and the corresponding architecture-specific corrections.

Increasing capacity can induce a machine learning model to generalize worse until it perfectly interpolates the training data, and better once it moves beyond interpolation. This inversion, known as double descent, is well understood for independent features. For correlated features, its shape is governed by the spectrum of the feature covariance, but existing analyses typically yield only implicit equations. We first close this gap for classical linear regression, analytically characterizing the entire risk curve through two quantities, namely the condition number of the feature population covariance and a spectral measure of correlation strength. Then, we apply this theory on quantum models, focusing on quantum extreme learning machines (QELMs). We show that three tunable design knobs, i.e., encoding strength, input reuploads, and measurement shots, each regularize the QELM output covariance, and derive conditions under which the interpolation threshold remains stable. Finite measurement shot noise can be leveraged to guarantee this stability. Numerical experiments confirm each prediction, yielding concrete design principles for QELMs that generalize well beyond interpolation.

Spike-and-slab regression is a standard Bayesian formulation of variable selection: it returns a posterior distribution over which candidate effects are active rather than a single selected subset, so that every candidate effect carries an inclusion probability. Its cost grows exponentially with the number of candidate effects, so the posterior can be enumerated exactly only when the number of predictors is small. Beyond that reach, the posterior has to be approximated, typically by Markov chain Monte Carlo over the model space, which requires a fresh run for every dataset and, within a fixed budget of steps, may fail to converge. We present LinearPFN, a prior-data fitted transformer network that amortizes spike-and-slab inference for linear models with main effects and pairwise interactions. The network is pretrained once on synthetic datasets, drawn from an explicitly specified prior, and a single forward pass over a new dataset returns posterior inclusion probabilities, posterior-mean coefficients and posterior predictive distributions with no per-dataset fitting. The prior is conjugate by design, so that the posterior for each fixed set of active effects has a closed form, and wherever the exact posterior is still computable by enumeration we verify the network's outputs against it. On real predictor matrices from published social-science datasets, with outcomes drawn from the prior so that the true active set is known, LinearPFN attains a higher per-dataset selection AUC and a higher F1 under the median probability model rule than five classical baselines. The lead holds when the coefficients, the interactions or the noise depart from the prior. Code: https://github.com/schiekiera/LinearPFN. Trained model: https://huggingface.co/schiekiera/LinearPFN.