Papers

Company name retrieval and final entity clustering can respond differently to encoder adaptation. We study this dependency through a controlled pipeline: train multilingual E5 encoders with matched positive examples and random or hard negatives, select checkpoints on development data, retrieve within equal country-specific edge budgets, and apply unchanged pair classifiers and guarded Union-Find clus- tering. Evaluation uses a subsequently collected GLEIF snapshot; a stratified, assisted human audit and a post-hoc temperature sweep examine label and parameter sensitivity. On 3,633 names with source-silver labels, adapted retrieval raises direct pair recall from 53.74% to 76.98%, whereas cluster recall moves from 32.54% to 33.33%. Most newly retrieved positives fail the existing classifier threshold. The study contributes a controlled comparison and pair-level diagnosis of this loss between retrieval and confirma-tion. It shows why evaluating a replacement retriever requires measuring the resulting entity partition, while leaving joint matcher retraining and independent gold-label evaluation for future work.

Predicting whether an LLM agent will fail has emerged as a promising direction for supporting intervention during execution. Recent approaches report strong predictive performance, often with AUROC values between 0.85 and 0.94. However, predictors are typically trained by pooling runs from many tasks. We hypothesize that part of this performance comes from recognizing that some tasks are harder than others, rather than detecting whether a particular run is heading toward failure. This distinction matters because task-level difficulty supports decisions about where to allocate computation, while run-level prediction is needed to decide whether to intervene in an ongoing trajectory. We study benchmarks with repeated attempts of the same task by the same agent and separate cross-unit comparisons from comparisons between successful and failed runs of the same model-task unit. Across the evaluated corpora, more than 99.93% of the positive-negative pairs underlying pooled AUROC are cross-unit. Accordingly, predictors that never observe the current run can achieve high pooled performance, including a difficulty oracle with AUROC up to 0.945, while remaining at chance within task. Early run-level discrimination is consistently weak across trajectory predictors, released monitors, and hidden-state probes, although it improves later in execution and is stronger for weaker agents. Under fixed token budgets, task-level allocation outperforms abort-only strategies, while early stopping becomes beneficial only when within-task AUROC reaches about 0.84-0.93, far above the 0.50-0.55 range observed for early monitors. These results show that failure prediction should be evaluated not only by outcome accuracy, but by whether the captured signal supports the intended deployment decision.

In safety-critical domains such as autonomous driving, systems must be evaluated across a large number of environment conditions, often represented as composite scenarios built from primitive scenarios. Existing statistical model checking (SMC) approaches analyze each composite scenario independently, requiring many expensive simulations and resulting in substantial redundant computation when scenarios share common structure. This work introduces a scenario-based compositional SMC framework for safety and co-safety specifications, enabling efficient analysis of composite scenarios. Our approach decomposes scenarios into primitives and specifications into sub-specifications, verifies each primitive independently, and composes the resulting statistical estimates using importance sampling and kernel density estimation. Our empirical evaluation shows that the proposed framework can accurately answer verification queries for previously unseen composite scenarios while reducing simulation cost through parallelization and trace reuse.

Existing thermodynamically consistent neural operators enforce GENERIC degeneracy by projecting the reversible operator, introducing state dependence without guaranteeing Jacobi. We instead use a compatible Lie–Poisson pencil $L=\alpha D+\lambda(uD+Du)$ for nonlinear transport and constant Poisson multipliers otherwise. Augmenting the observed field $u$ with latent entropy density $s$ makes $S=\int s$ a Casimir, so $L\,\delta S/\delta z=0$ without projection. Energy combines a fixed mechanical quadratic, learned gauge-free potential, and convex internal energy. The friction operator $M=AA^\top$ enforces $M\,\delta E/\delta z=0$ pointwise and supports diffusion and damping without an independent reversible transport generator. Skewness, positivity, and both degeneracies hold exactly; the continuum pencil satisfies Jacobi, verified numerically on the alias-free band. The parameterization represents the closed-form heat and damped-wave friction operators within its admissible range. Physical energy is bounded under coercivity assumptions, while a discrete-gradient integrator preserves both laws when solved to convergence. Across four PDEs in 1D and 2D and three backbones (FNO, Transolver, CNO), the model wins 61/72 seed-level comparisons against matched unconstrained baselines, recovers exact transport and wave symbols, matches heat and Burgers dissipation within 13%, and exhibits negligible advection dissipation. A constant-$L$ ablation exposes the cost of nonlinear transport, while a learned-energy ablation shows that conserving learned energy need not constrain physical energy.

We introduce Factoriax, a GPU-accelerated factory-building simulator written in JAX. In Factoriax, an agent must collect resources, build machines using those resources, and then automate the collection and crafting process by arranging machines on the map to build production pipelines. This paper discusses the structure of the Factoriax simulator and an initial benchmark called Easy Rocket in which an agent is tasked with building a resource-intensive machine called the Rocket in a limited number of game ticks to escape the planet. We also publish results from a number of PPO-based training runs on Easy Rocket. Factoriax is built to be fast. A 1-billion-step PPO training run, equivalent to 500,000 episodes, runs on Easy Rocket in about 8 minutes on a single NVIDIA A100. A standard laptop GPU can complete the same run in about 84 minutes. Our trained PPO agent learns to gather resources, craft machines from those resources, and place them on the map through a curriculum reward directly tied to a manually designed set of achievements. After training, the agent does not place machines in a functional spatial configuration, failing to fully complete the benchmark, and leaving the challenge open for future attempts.

For an arbitrary prime $p$ and arbitrary positive integers $r$ and $d_{1}, \ldots, d_{r}$ with $d_{r} > \cdots > d_{1}$, we show that $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}} + x^{d_{1}} + p$ removed of all of its monic irreducible reciprocal factors is irreducible. As a consequence, we establish a number of results related to a conjecture of Charles Nicol that, over the rationals, the sum of two cyclotomic polynomials $\Phi_{n}(x) + \Phi_{m}(x)$ is a product of cyclotomic polynomials times either $2$ or an irreducible polynomial, where $n$ and $m$ are integers exceeding $1$. We also establish similar results for $\Phi_{n}(x)\Phi_{m}(x)+1$.

Let $R$ be a $\phi$-ring and put $N=Nil(R)$. We determine the $\phi$-weak global dimension of every $\phi$-Prüfer ring. Its only possible values are $0$, $1$, and $\infty$: the value is $0$ when $R/N$ is a field, it is $1$ when $R$ is strong and $R/N$ is a nonfield Prüfer domain, and it is infinite when $R$ is not strong. No nilpotence assumption on $N$ is needed. The proof is based on the canonical kernel $K=ker(R\to\phi(R))$. In the local non-strong case, $K$ is a nonzero torsion divisible module over the valuation domain $R/N$, and its self-Tor groups satisfy \[ Tor^R_{2n}(K,K)=0\quad(n\geq 1), \qquad Tor^R_{2n+1}(K,K)\neq 0\quad(n\geq 0). \] It follows that $fd_RK=\infty$, and a filtered-colimit argument transfers this obstruction to cyclic quotients by nonnil principal ideals. We also prove the parallel trichotomy for the $\phi$-global dimension of $\phi$-Dedekind rings. For strong $\phi$-rings we obtain a change-of-rings theorem without assuming that the quotient map $R\to R/N$ splits. If $D=R/N$, $Q=Frac(D)$ and $T=T(R)$ is the total quotient ring, then \[ R\cong T\times_Q D. \] Using Ferrand's flat patching theorem and Milnor's projective patching theorem, we prove that every torsion $D$-module $M$, regarded as an $R$-module through $R\to D$, satisfies \[ fd_R(M)=fd_D(M), \qquad pd_R(M)=pd_D(M). \] Consequently, for every strong $\phi$-ring, \[\phi-wgd(R)=wgld(R/N), \qquad \phi-gld(R)=gld(R/N). \]

Human health is a continuous, dynamic trajectory shaped by the cumulative interplay of biological processes, clinical events, behaviors and environmental exposures across the life course. Unifying the full breadth of lifelong health information, including longitudinal records, genetic variation, molecular profiles and environmental histories, is essential for whole-person modeling and remains a major challenge. We introduce LifeLong Digital Twin, a unified, event-driven modeling paradigm that organizes Life Events into daily Health States and accumulates them into Lifelong Health Context. An accompanying Agent Harness incorporates multimodal evidence beyond the language model's textual context. We evaluate four language models across 25 disease endpoints on three tasks: Disease Trajectory Forecasting, Disease Risk Ranking and Multi-horizon Disease Prediction. The approach yields marked gains over the reference condition: model-averaged F1 increases by 22.0% for disease identification in trajectory forecasting and 18.3% for five-year disease outcomes; thyroid-disease F1 reaches 0.669. The framework provides a foundation for whole-person digital twins and research on personalized lifelong disease prevention.

We study triples of distinct nonconstant polynomials $a,b,c$ over $\mathbb{R}$, $\mathbb{Q}$ or $\mathbb{Z}$ for which $$ ab+1,\qquad ac+1,\qquad bc+1,\qquad abc+1 $$ are all polynomial squares. We show that, up to permutation and a common invertible affine change of variable, there is exactly one such triple of quadratic polynomials in $\mathbb{R}[X]$, the one arising from a recent construction of Jurasić, and that none exists in $\mathbb{Q}[X]$ or $\mathbb{Z}[X]$. Moreover, for arbitrary nonconstant entries over $\mathbb{R}$ or $\mathbb{Q}$, we prove that the degree pattern $(2n,2m,2l)$ with $1\le n\le m\le l$ satisfies either $l=m$ or $l>n+m$. For the case $l=m$, we derive factorization systems and reducibility restrictions. In the equal-degree case over $\mathbb{Q}$, we further show that every entry has at least two distinct irreducible factors. As an application, we show that in a natural regular parametrized family of polynomial Diophantine triples in $\mathbb{Q}[X]$ the fourth expression $abc+1$ is never a square when the parameter is constant or the first entry is a square.

Text embedding models trained with contrastive learning learn to follow task instructions from instruction-paired data, while instruction-tuned LLMs already know how to follow them. We show that this instruction-following ability can carry over from an LLM to a Transformer-based embedder without any training. We propose Attention Relay, which passes the attention weights an LLM produces to the embedder's own attention. Across six instruction-tuned LLMs from the Qwen3, Llama 3.1 and OLMo 3 families and ten widely used embedding models that differ in tokenizer, size and pooling type, Attention Relay makes nearly every combination instruction-aware. Experiments that break the method down into its parts show that the LLM's attention weights track the instruction in its later layers and come largely from instruction tuning. They also show that relaying these weights selects which content in the text matters: it makes the aspect of the text that the instruction asks about dominant in the embedding, or restores that aspect where averaging had diluted it.

Small language model (SLM) agents need safety controls that track consequences across tool calls with little monitoring overhead. A private read, for example, becomes a leak when a later action sends that data outside the system. We introduce CARB (Conformal Agent Risk Budget), which calibrates when to stop an agent using a ledger of harm incurred before stopping. Under exchangeable episodes, standard conformal risk control bounds this declared loss in expectation over calibration and a future episode. G-CARB selects scorer evidence along observable dependencies from private sources to outgoing actions. The ledger still covers the entire executed history, and computing the gate score requires no additional language-model inference. On AgentDojo replay with two 14B backbones, G-CARB roughly halves scorer-input records at intermediate risk budgets while improving autonomous task completion relative to full-prefix scoring; random context of the same size achieves similar gains. Controlled examples show how retaining the relevant dependency can further avoid stopping benign work.

Let $X$ be a nonsingular projective curve of genus $g\ge2$ over an algebraically closed field of odd characteristic $p$. Giulietti and Korchmáros established a quadratic genus bound with constant $900$ forcing zero $p$-rank for curves of even genus. We extend this bound to odd genus: for every $g\ge2$, positive $p$-rank implies $|\Aut(X)|<900g^2$. Starting from Montanucci's two-short-orbit reduction, we combine ramification estimates and a minimum-genus argument to reduce a counterexample to an almost-simple group acting on a cover of the projective line with two branch points. The main ingredients are an intrinsic description of the second ramification group via Hasse–Arf and genus bounds for intermediate quotients associated with parabolic subgroups. These, together with order and local-structure estimates, exclude every possible simple socle. The proof uses the classification of finite simple groups.

Multi-attribute user records are inherently heterogeneous, often combining continuous, categorical, and binary attributes, and they frequently exhibit strong cross-attribute dependencies. Designing high-utility metric differential privacy (mDP) mechanisms for such records is challenging. Simple predefined mechanisms, such as distance-based noise, may be poorly aligned with task-specific utility loss, whereas fully optimization-based mechanisms can be computationally prohibitive for multi-attribute records. We propose Dependency-aware Heterogeneous Data Perturbation (DepHDP)}, a framework for multi-attribute mDP that combines dependency-aware attribute grouping with heterogeneous perturbation design. Rather than applying a one-size-fits-all mechanism, DepHDP selects an appropriate perturbation strategy for each attribute or attribute group, choosing between efficient predefined mechanisms, such as Laplace or Exponential mechanisms, and optimization-based designs. This selection is guided by both domain size and a predefined-noise adequacy criterion, which quantifies whether task-induced utility loss can be well explained by perturbation magnitude. To support scalable end-to-end optimization, DepHDP estimates group-level utility loss through sampling and lightweight surrogate modeling, and jointly optimizes privacy-budget allocation and group-wise mechanism design under a global $\ell_p$-metric mDP constraint. Across three case studies, DepHDP improves privacy–utility trade-offs over uniform baselines at lower computational cost than full-record OPT on evaluated domains.

We continue the study of the convex hull $D\subset\mathbb{R}^{d+n}$ of a disjunction of $n+1$ polytopes in $\mathbb{R}^d$, managed by $n$ binary indicator variables. Previously, $D$ had been characterized for arbitrary polytopes when $d\in\{1,2\}$, for polytopes sharing a common constraint matrix (under a technical condition, including hyper-rectangles), and for two generalized cross polytopes ($n=1$). Here we give a complete description of $D$ for arbitrary $n$ and $d$ when all $n+1$ polytopes are generalized cross polytopes. Every vertical facet is described by a normalized support inequality, and such an inequality is facet describing if and only if its equality graph, a bipartite graph on the polytopes and the coordinates, is connected; all vertical facets are generated explicitly from feasible spanning trees. We characterize when such a facet is one of the previously known pairwise inequalities, and we show that pairwise inequalities suffice when $d\leq3$, but not in general. We establish a bijection between the vertical facets and the maximal cells of a regular subdivision of $\Delta_n\times\Delta_{d-1}$\,, which yields the sharp bound $n+1+2^d\binom{n+d-1}{n}$ on the number of facets of $D$, attained for generic data. We also give a polynomial-time separation algorithm that returns a violated facet, which is maximally violated among the normalized support inequalities. Computational experiments show that the facets that are not pairwise inequalities close a large part of the gap left by the pairwise inequalities.

Industrial sequential recommender systems operate over massive item catalogs (e.g., 10^5–10^7 items). Multi-label recommendation models are trained with Binary Cross-Entropy (BCE) loss over the full vocabulary, but standard BCE materializes a dense [B, N, V] logits tensor in High Bandwidth Memory (HBM), incurring prohibitive $O(BNV)$ memory and fatal Out-Of-Memory (OOM) errors. While chunked loss optimizations exist for Softmax Cross-Entropy in LLMs, large-scale multi-label BCE optimization remains unexplored across deep learning ecosystems. We propose CutBCE, an exact, hardware-accelerated BCE loss and gradient operator implemented in JAX and Pallas for large-vocabulary workloads. CutBCE introduces (1) an exact fused reformulation evaluating dense background loss and sparse target corrections; (2) a custom Vector-Jacobian Product (VJP) with a dedicated Pallas TPU backward kernel computing logit tiles on-chip in both passes so logits and their gradients never reside in HBM; (3) dynamic VMEM budgeting and sharding-aware collective hoisting for distributed meshes; and (4) count-based zero-overhead training metrics. On single-chip TPU v5e/v6e mini-benchmarks, CutBCE eliminates OOM errors with up to 91.9% speedup. On 8-chip TPU slice training for multi-label SASRec with 876k items (Yambda-50M), CutBCE reduces peak HBM by 65.7% (>14 GiB saved per chip) and increases training speed by 225.9% with comparable accuracy. CutBCE is open-sourced at https://github.com/AI-Hypercomputer/RecML/blob/main/recml/core/ops/binary_cross_entropy_ops.py.

The Dobrushin coefficient of each attention-rollout factor satisfies $\kappa(\frac12(I+A))\le\frac12(1+\kappa(A))$, and multiplying these inequalities over layers bounds the coefficient of the whole rollout. We characterise exactly when the layerwise bound is tight: equality holds if and only if some token pair attaining $\kappa(A)$ is mutually self-dominant - each of the two attends to itself at least as strongly as the other attends to it. The condition is far from automatic: uniformly random stochastic matrices satisfy it only 24-30% of the time. When tested on the head-averaged attention of each individual input and restricted to content tokens - image patches, words or tabular features, excluding cls, register and separator tokens - the condition holds for essentially every input at every layer of DINOv2 (three model sizes), RoBERTa and DistilBERT. In the supervised models DeiT-B and ViT-B/16 it holds for 91% and 64% of input-layer pairs respectively, with all failures occurring late in depth. In FT-Transformer trained on two standard tabular benchmarks it holds for only 11-44% of input-layer pairs. The special tokens account for almost all failures in DINOv2 and the language models: when they are included, the condition holds for only 82-97% of input-layer pairs.

Sompolinsky and Zippelius obtained Parisi's solution of the Sherrington-Kirkpatrick (SK) model from the relaxational dynamics of soft spins in continuous time, by assuming a hierarchy of widely separated time scales. Here we carry out the same programme for a discrete-time dynamics in which all Ising spins are updated at once. This dynamics, synchronous Monte Carlo (SyncMC), introduces Gaussian auxiliary fields so that the spins become conditionally independent, and it samples the Boltzmann distribution exactly for any system with symmetric pairwise couplings. We show that, for any such system, the correlation and response functions of SyncMC obey an exact fluctuation-dissipation relation in discrete time in equilibrium. The dynamical mean-field equations of SyncMC for the SK model contain two terms absent in continuous-time dynamics, a self-coupling of each spin and a noise correlated through the couplings; both affect only the fast relaxation. As a result, under the same assumptions as in the Sompolinsky-Zippelius construction (widely separated time scales, and on each slow scale the same relation with a reduced ratio x, as expected in relaxation from random initial conditions), the long-time structure of SyncMC reproduces the Parisi equations, including the Parisi partial differential equation and the equation for the distribution of local fields. Equilibrium simulations with replica exchange for up to N=2048 spins exclude the replica-symmetric distribution of the actual local fields and are consistent with the Parisi solution. The function x(q) estimated from the overlap distribution, and from the response in relaxation from random configurations for up to N=4096 spins, is also consistent with Parisi's.

Multiple epidemic waves are often taken as evidence that simple compartmental models are structurally inadequate. Yet the key question is not whether a simple model can reproduce multiple peaks, but how much time-varying structure is minimally required to preserve observed epidemic-wave patterns and what can legitimately be inferred from such a representation. Using the susceptible-infectious-removed (SIR) model, we develop a framework for peak-preserving dynamic parsimony linking dynamical systems, inverse problems, statistical inference, and infectious-disease modeling. We establish exact multi-wave representability under time-varying transmission, characterize conditions for epidemic peaks and resurgence, and show the incidence-only non-identifiability of time-varying transmission and removal rates. Our main methodological contribution is minimal peak-preserving complexity (MPPC): the smallest dimension of a positive time-varying transmission function whose posterior-predictive trajectories preserve salient features, including peak count, timing, height, trough depth, and whole-curve agreement. We estimate MPPC using peak-aware approximate Bayesian computation and evaluate it through six reproducible stress tests, a Philippine COVID-19 reported-case proof of concept, and short-term future-knot projection. Across diverse data-generating mechanisms, low-dimensional time-varying SIR models can preserve aggregate epidemic-wave topology with modest dynamic complexity. However, accurate trajectory compression does not imply recovery of the underlying mechanism or reliable long-term counterfactual prediction. The framework therefore separates four often-conflated questions: representability, minimal dynamic complexity, mechanistic identifiability, and projection validity, providing a basis for parsimonious modeling of complex epidemic trajectories.

Feedback can improve the reliability of communication over additive white Gaussian noise (AWGN) channels. Classical feedback codes are interpretable, or easy to understand, but often rely on linear estimation, while deep-learned feedback codes can achieve strong performance but require many learned parameters and are often black boxes that are difficult to interpret. In this work, we propose a new posterior-mean feedback coding framework for AWGN channels with feedback. The proposed scheme uses posterior-mean refinement to construct nonlinear feedback codes under both noiseless passive feedback and noisy active feedback, with maximum a posteriori (MAP) decoding at the receiver. This scheme is analytically described, but a few learned parameters related to power allocation, and hence we consider this an “interpretable,” or human-understandable code. We further develop a projection-based design to improve robustness under noisy feedback and support larger message sizes. Numerical results show that the proposed schemes achieve strong finite-blocklength performance and outperform several analytical and learned feedback coding baselines, while using only a small number of learned design parameters.

Solid State Drives (SSDs) are becoming the dominant medium for performance-critical storage. Zoned Namespace (ZNS) SSDs are getting more and more attractive because sequential writes and explicit zone resets reduce address-mapping, over-provisioning, and internal garbage-collection costs. However, reclaiming space requires resetting an entire zone, so deleting one file does not free its space while other files there must be kept. This erase-before-write constraint becomes a bottleneck for write-intensive workloads, particularly AI checkpointing during model training, where frequent saves of model and optimizer state compete for space with long-retained checkpoints. We observe that retention policies inherently encode when data can be retired, avoiding the need for a learned lifetime predictor. We present RetainZ, a storage backend that translates these policies into explicit reclaim epochs. Its allocator isolates long-retained data and groups objects with nearby reclaim epochs, balancing delayed space reclamation against unused space at zone ends. Evaluated on FEMU with multi-tenant streams and checkpoint manifests up to Pythia-1B, RetainZ reduces space occupied by deleted data and unused zone tails by 41.7% and mean per-input checkpoint p99 latency by 47.5% at 84% target load compared with the allocator of ZenFS, an established lifetime-aware ZNS backend, and lowers host write amplification from 1.165 to 1.003.

The Nine-Hole Peg Test (9-HPT) is a widely used clinical measure of manual dexterity in multiple sclerosis (MS), but its primary outcome, task completion time, provides limited information about the visuomotor mechanisms contributing to impaired performance. Instrumented approaches can provide richer kinematic information but often require modifications to the task or physical instrumentation that may alter natural hand-object interaction. We developed a multimodal computer-vision pipeline that enables synchronized analysis of gaze, hand kinematics, and object state during an unmodified 9-HPT. Gaze was recorded using Pupil Labs Invisible glasses, three-dimensional hand landmarks were reconstructed using WiLoR, and a custom YOLO26x-seg model detected and tracked the pegboard, holes, pegs, and collection bin. Eye-tracking, hand, and object data were temporally synchronized at the video-frame level and spatially registered to a common pegboard-centered coordinate system using frame-specific projective transformations. The pipeline further integrated hole-state transitions, hand-zone classification, and fingertip kinematics to identify PICK and PLACE events and segment hand transport and stationary phases, while fixation and saccade labels were derived from the eye-tracking system. Automated detections were visually reviewed and corrected when necessary. The resulting framework provides synchronized, event-resolved measures of gaze behavior, hand movement, object interaction, and eye-hand coordination while preserving standardized 9-HPT administration. This approach extends the 9-HPT beyond completion time and provides a reproducible platform for investigating the visuomotor mechanisms underlying dexterity impairment in MS and other neurological disorders.

Three-dimensional gait analysis guides rehabilitation after spinal cord injury but depends on marker-based motion capture and force plates, which few clinics have. Monocular markerless pipelines have been established in fewer healthy adult cohorts but not in neurological cohorts. We present the SCAI SCI Gait dataset, comprising 239 adult individuals with spinal cord injury with synchronized video, motion capture, and force-plate measurements, we fitted a parametric body mesh to a single sagittal-view video, driving an anthropometrically scaled OpenSim model via virtual markers. Markerless lower-body kinematics showed state-of-the-art agreement with motion-capture measurements (r = 0.68-0.90, p < 0.001, and RMSE = 4.18-6.49 degrees), and accurate kinematics-based predicted ground-reaction forces closely matched those measured by force plates (r = 0.85-0.87, p < 0.001, and RMSE = 2.13-2.19 Newton per kg). Furthermore, conditional-dependence graph analysis with Markov blankets revealed that waveform components were conditionally associated with functional independence, and speed-stratified clustering revealed distinct mechanical strategies among individuals walking at similar speeds. These findings establish the use of monocular video as a scalable approach for clinically meaningful biomechanical assessment and data-driven phenotyping in patients with spinal cord injury. Github: https://github.com/SCAI-Lab/SCAI-SCI-Gait-Dataset

We study the free-energy gradient flow associated with the depth-$N$ deep linear network on the space of invertible real $d\times d$ matrices. The loss observes only the diagonal, \[ E_d(W)=\frac12\sum_{i=1}^d(W_{ii}-1)^2, \] and the regularizer is the Boltzmann entropy of the balanced factorization fiber computed by Menon and Yu. This is a natural higher-dimensional version of a matrix-completion problem posed by Menon as a test of whether entropy selects among a noncompact family of minimizers. For diagonal completion, every width $d\geq2$, depth $N>2$, and inverse temperature $\beta>0$, we prove that the free energy is unbounded below and has exactly $2^d$ full-rank critical points, one in each diagonal sign chamber. Every critical point is diagonal and hyperbolic. Its unstable dimension is $\binom d2$ and its stable dimension is $d(d+1)/2$. We also prove that a full-rank trajectory cannot converge to a finite rank-deficient matrix. Consequently, almost every full-rank initial condition has an unbounded forward orbit. Thus finite-temperature fiber entropy does not provide an equilibrium selection principle for diagonal completion.

The component that dominates a latent world model's prediction error need not be the one whose repair most improves action selection. We show this by comparing action sequences from identical physical starts and separating endpoint error into a candidate-pool center and action-relative responses. Across four model families and four tasks, a confirmation pool of 256 new starts per task and 300 shared candidates per start shows that center error dominates MSE in 14/16 model-task cells. Yet in six of these cells, an oracle that corrects only the action-relative responses yields better physical rank correlation and top-30 elite quality than one that corrects only the center, while leaving more latent MSE (family-wise corrected intervals). The preference differs across the evaluated settings: a separate LeWorldModel (LeWM) study that executes oracle-selected actions favors center repair on PushT and on Reacher with a render-matched goal. Matched-candidate tests localize ordering loss: for LeWM, encoding realized endpoints raises physical Spearman from 0.464 to 0.975 on that Reacher setting and from 0.193 to 0.631 on PushT (64 starts per task), while Cube's encoded-goal cost remains uninformative. A 72-run objective study improves selected response diagnostics, while incremental closed-loop planning gains remain unconfirmed. These results separate error magnitude from the decision effects of oracle correction and motivate evaluating representation, prediction, and planning as separate stages.

We formulate joint estimation of common-slope decay rates and amplitudes from room impulse responses (RIRs) as parameterized nonnegative matrix factorization with the Itakura–Saito divergence as the loss function (IS-NMF). Estimation at each short-time Fourier transform frequency bin produces detailed reverberation time (RT) curves directly from RIR powers with no backward integration needed. Standard space-alternating generalized expectation-maximization (SAGE) algorithm yields closed-form amplitude updates and a convex subproblem for each decay rate update. To accelerate estimation, we introduce contribution-weighted SAGE, which emphasizes observations where each component contributes strongly to the modeled power. Experiments with synthetic data show accurate recovery of well-separated decays and faster loss reduction than standard SAGE. Application to measured coupled-room RIRs yields frequency-dependent RT curves and reveals complementary space-time contributions of the shared decay components.

This paper derives analytical expressions for the asymptotic variance of the Hermite-Domain Predictor-Based Subspace Identification (HD-PBSID) method. Unlike continuous-time subspace approaches that rely on intermediate-domain transformations, HD-PBSID identifies continuous-time state-space matrices directly. The derivation first establishes the uncertainty of the estimated state-space matrices and then exploits these results to obtain asymptotic variance expressions. These expressions provide analytical uncertainty bounds for system eigenvalues, which are invariant under similarity transformations and therefore uniquely characterize the identified dynamics. The proposed formulas are first validated in an ideal Hermite-domain setting, where the conditions underlying the derivation are satisfied, and then assessed on noisy time-domain data through Monte Carlo simulations. The predicted bounds show very good agreement with the eigenvalue distributions in the ideal setting and acceptable agreement in the time-domain case when the innovation sequence is enforced to be white.

Digital libraries, repositories, and AI-mediated knowledge services increasingly rely on generative systems to produce summaries, descriptions, and other multi-claim knowledge objects. Yet generation can scale far more easily than verification capacity: a reviewer may need to decide whether an object is suitable for publication or downstream use after checking only a small fraction of its claims. This creates a fundamental gap between claim-level verification and confidence in the object as a whole. The central question is therefore what a successful partial check implies about the reliability of the complete artifact when its size grows but the verification budget does not. This paper contributes a Bayesian model of bounded verification centered on the Predictive Value of Pass (PVP). The model predicts that evidentiary value decreases as artifacts grow under fixed verification capacity, improves with larger verification budgets, and is especially fragile when errors are sparse. Controlled experiments on FEVEROUS and FEVER support these predictions and show that adding supported claims around a fixed number of false or unsupported claims can make passing more likely while making a pass less informative. The model further yields the minimum verification budget required to maintain a target PVP, providing a practical component for AI-assisted quality-assurance workflows in which generated knowledge objects must be checked before publication or downstream use.

LiDAR-inertial odometry (LIO) is widely used for state estimation in ground-based autonomous mobile robots. However, the geometric constraints provided by the local ground surface remain largely underexploited in existing LIO systems. This paper proposes a filter-based local ground-aware LIO framework that explicitly incorporates local ground plane geometry into the state estimation process to improve both localization accuracy and computational efficiency. Specifically, a local ground plane is parameterized by the robot orientation and the body-to-ground (B-G) height and continuously propagated within the state estimation process. Based on the proposed B-G geometry model, a propagated local ground plane enables efficient and reliable ground segmentation. The segmented ground points are then incorporated into the filter update through point-to-plane geometric constraints, improving both state estimation accuracy and efficiency. Furthermore, a planar motion update is introduced to exploit the propagated local ground plane as an additional geometric constraint, effectively suppressing vertical drift and improving estimation robustness. To address the initially unknown B-G height, an efficient initialization strategy is developed, followed by an online calibration procedure for continuous refinement. The proposed system is evaluated on several public benchmark datasets and self-collected real-world datasets covering diverse operating scenarios. Experimental results demonstrate that the proposed method consistently outperforms representative LIO methods in terms of both localization accuracy and computational efficiency.

Active IP geolocation techniques rely on the responsiveness of Internet hosts, while passive techniques depend on data sources that are unevenly adopted and prone to staleness and error. In this work, we invert the active IP geolocation problem by listening at a geographically distributed set of vantage points for unsolicited Internet scans. By reactively completing connections with these scanners, we obtain round-trip time (RTT) measurements from hosts that may otherwise be unresponsive and use those measurements for geolocation. Over the course of 20 days in August 2026, we recorded 46.8 million scans from 289,746 distinct scanners, with a reactive RTT for each scan. We show that reactive RTTs align with those obtained by sending active probes, with more than three-quarters of 990,204 measurement pairs differing by at most 10 ms. Over half of the scanners that yielded a reactive RTT did not answer our active probes, highlighting the value of our approach. We demonstrate the feasibility of multilateration using purely reactive RTTs for 56,112 distinct IP addresses. Finally, using speed-of-light constraints, we refute commercial geolocation claims for 6,852 addresses.

Real-world deployment of active learning typically forces practitioners to choose an acquisition strategy before any data is labeled. This is a daunting task: strategy performance varies widely across settings (e.g. datasets, surrogate models) and cannot be assessed without deployment. Existing strategy selection methods explore one strategy from a portfolio at each round and identify the optimal one using bandit feedback or model retraining. Many acquisition rounds are therefore spent exploring strategies rather than collecting the most informative data. Such overhead is a major barrier to AL-driven design of high-throughput experiments, such as genetic perturbation screens and directed evolution, where AL runs consist of only a few rounds with large batch sizes. This regime permits a natural alternative: acquiring data using multiple AL strategies within a single batch. We refer to this as soft strategy selection and introduce FractAL, a method specifically designed for this task. FractAL infers a per-strategy reward using influence-function-based data attribution, which requires no additional retraining, and then computes budget shares for each strategy in the portfolio using online mirror descent. We benchmark FractAL across 7 setups spanning classification, regression, and genetic perturbation effect prediction. The results highlight that strategy selection is a hard problem: every existing method performs worse than random sampling on at least one setup. FractAL, however, matches or outperforms every baseline, including random sampling, on all 7 setups. Its allocations concentrate budget on the strongest strategies in the portfolio while pruning the weakest. FractAL is therefore a reliable choice for real-world deployments, where the optimal strategy is unknown in advance, an important step towards making AL practical for high-throughput experiments and modern scientific discovery.