Papers

Longitudinal models forecast how a patient's imaging state evolves, but accuracy does not show whether the patient's observed trajectory drives the prediction. A population-average forecast may be useful but cannot establish a patient-specific world-model claim. We introduce Patient, Place, Prior (P$^3$), an audit asking whether a forecast benefits from the patient's longitudinal imaging history (Patient), benefits from patient-matched externally supplied spatial support (Place), and gains predictive value beyond a population-average prediction under matched support and context (Prior). We also propose Cancer JEPA, a one-step model that forecasts frozen representations of future breast dynamic contrast-enhanced MRI examinations during neoadjuvant therapy. It adds a lesion-constrained neural correction, trained with an occlusion-based latent objective, to a patient-conditioned low-complexity reduced-rank regression baseline. This factorization permits a post-hoc P$^3$ audit of the frozen model. In a validation cohort previously used in development, forecast error is lower when the neural correction receives the patient's history rather than another patient's and patient-matched lesion occupancy maps rather than substituted maps. However, the descriptive 95% interval comparing the correction computed from patient history with the population-average neural correction includes zero. P$^3$ thus separates input use from evidence of patient-specific predictive value beyond a population-level pattern.

MemoryAgentBench's Conflict Resolution split is read as measuring "selective forgetting". We execute the benchmark's own rule - the newest statement about a fact wins - as a zero-learning resolver frozen on one of the four fact lists. Under the official metric the rule answers 80.25% of the questions (74.5% on the three held-out lists). Of the rest, 67 items have a released gold that the last-write graph cannot reach but overwritten statements would ("The capital of India is New Delhi." superseded by "The capital of India is Grosseto."; gold New Delhi); such items are a third of the multi-hop questions at 262K. Two long-context models and our pre-registered approximate re-implementation of the benchmark's BM25 agent, one retained run per item and outcomes only, score 84.7%, 82.6% and 41.6% on the items the rule solves against 10.4%, 11.9% and 6.0% on those 67. The failures are a reachability split plus a small parser-scope residual; the per-item split, not the aggregate, is the unit at which a score here can be read.

Uncertainty quantification in thermoreflectance measurements of multilayer structures is challenging because thermophysical-property extraction involves nonlinear inverse problems with strongly coupled parameters. Covariance-based analytical propagation is efficient but assumes local linearity and approximately Gaussian fitted variables, whereas Monte Carlo (MC) propagation captures non-Gaussian behavior but is computationally expensive and can be unreliable when simultaneously fitting parameters spanning very different orders of magnitude. Here, we address these issues by combining normalized MC sampling, used to obtain reliable benchmark distributions, with physics-based variable transformations for analytical uncertainty propagation. From the multilayer heat-diffusion equation, we identify natural coordinates: the interfacial thermal resistance 1/G, the substrate combinations sqrt(k_z k_r) and sqrt(k_z C), and the thin-film combinations k_r/C, hC, and Ch^2/k_z. Across several representative multilayer systems and thermoreflectance modalities, these coordinates are approximately Gaussian even when the original physical parameters are skewed. Performing covariance-based propagation in the transformed space and mapping the results back to physical parameters yields asymmetric confidence intervals that closely match normalized MC benchmarks. The approach preserves the non-Gaussian uncertainty structure of the recovered parameters while avoiding repeated nonlinear refitting, providing a fast and physically interpretable methodology for thermoreflectance uncertainty quantification in multilayer systems governed by diffusive heat conduction.

Performing chess game position recognition solely from a single image of a three-dimensional board requires predicting the position and orientation of the board relative to the camera, the occupancy of squares and the piece type, which includes its colour. We propose an R-CNN-based framework with independent components for piece recognition and board geometry estimation, whose predictions are combined to reconstruct the position. For piece recognition, we adapt Faster R-CNN using a class-weighted objective and a deeper classification head. The detector operates directly on the input image, retaining alternative piece hypotheses that are subsequently refined using constraints on piece counts and square occupancy. For board detection, we introduce an octagonal arrangement of eight labelled boundary keypoints, predicted using the keypoint head of Mask R-CNN. These provide redundant correspondences for homography estimation and encode board orientation. The estimated homography maps representative points from the piece boxes to an 8x8 grid. On a synthetic dataset, the modifications to piece detection increase mean average precision from 61.59% to 90.14%. Of the predicted board keypoints, 97.11% are within 1% of the image diagonal of their labelled targets. Using ground-truth piece boxes with the predicted homographies gives correct square assignments for every test position. The complete framework recovers 76.61% of test positions exactly and 96.49% with at most one incorrect square.

Plasma edge simulations with codes like EMC3-EIRENE are widely used to study fusion magnetic confinement devices. However, numerical errors can significantly impact the simulation solution and are often insufficiently characterized. These errors consist of the statistical error, bias, and time integration error, resulting from the finite sampling and tracking of Monte Carlo particles, and the discretization error, resulting from a finite grid resolution. This work presents the first comprehensive numerical error analysis of EMC3-EIRENE simulations in stellarator geometries, focusing on edge plasmas in the Helically Symmetric eXperiment (HSX). Fundamental plasma and neutral quantities are analyzed, and error reduction rates are compared against theoretical expectations. The statistical error, bias, and time integration error are fully characterized; however, quantification of the discretization error remains challenging because of the complex grid geometries used in EMC3-EIRENE. The commonly used volume averaged relative change metric is shown to systematically underestimate the statistical error, highlighting a critical flaw in EMC3-EIRENE analysis, where convergence is claimed despite significant noise remaining in the simulation solution. Dominant contributions of the time integration error are shown to differ in stellarator simulations compared to tokamak simulations, related to the relative importance of cross-field transport between the two devices. Based on these results and existing literature, we establish best practices towards improved accuracy and efficiency in general stellarator modeling with EMC3-EIRENE.

We propose SwinDS-BWE, a decision-science-inspired bandwidth extension (BWE) model with two coupled contributions: (1) Swin Transformers with lattice-style cross-stream interaction yield locality-aware modeling with linear-in-sequence per-window attention cost and reduce the prior AP-BWE generator size 0.5x from 33M to 17M. (2) Three novel lightweight decision-science-inspired discriminators augment AP-BWE's performance: a CVaR discriminator tail-pools activations to emphasize worst high-frequency (HF) segments, a Chance-Constraint HF discriminator penalizes excessive HF energy via a differentiable barrier, and a Multi-Criteria Utility discriminator learns convex style weights over spectral criteria. SwinDS-BWE surpasses prior AP-BWE with a 30x smaller discriminator (42.3M vs. 1.36M) and higher fidelity on English and French datasets. This work shows that decision-science-inspired critics can supervise BWE to reduce discriminator size.

Probability-only models, which TypeSafe calls System One models, return calibrated probabilities for fixed choices in milliseconds and generate no text. We study one such model, Jev, through two tasks that require decisions under tight constraints. In bullet chess, a bot that places Jev's judgment inside Stockfish search alongside an opening book and endgame tablebases climbs above a 2200 Lichess bullet rating against other bots. Live model calls are too slow for search, so we distill pairwise judgments into a compact evaluator that runs at every position. We then ask how best to spend a fixed labeling budget when an LLM, Qwen3-32B, is available as a second teacher. In chess, averaging both judges' labels beats spending the whole budget on Qwen alone by 9.6 Elo (95% interval 4.3 to 14.9), and the gain replicates on fresh openings; a second answer from the same judge is no substitute, and Jev is the strongest partner for Qwen among the models tested. In passage reranking, Jev's labels alone train a reranker that scores as high as Qwen's, from 21 minutes of API calls instead of 5.1 GPU-hours, and adding Qwen gains at most a few thousandths in ranking quality. Search supplies the lookahead, distillation makes the judgment cheap enough to use at every position, and an LLM partner pays off in chess.

Multi-robot task allocators in dynamic missions commonly admit newly released tasks immediately, potentially invoking allocation for each new arrival. We evaluate task-admission coalescing as a mechanism for controlling allocator processor work while accounting for target-service latency, using CBAA, ACBBA, PI, and HIPC as a representative MRTA suite. The study comprises a 3,000-mission AGX Orin campaign with measured computation delay, 3,000 paired zero-compute missions, and a 96-mission Pololu 3pi+ RP2040 allocator hardware-in-the-loop campaign. Immediate (Eager) admission is compared with thresholds of two, four, and eight tasks and a four-task policy with a 10-s waiting bound across three arrival rates. Across the AGX experiments, coalescing reduces both allocator calls and processor work in 31 of 48 evaluated conditions, although the magnitude of the saving varies by allocator. The principal cost appears under sparse arrivals, where four-task batching increases online-target mean latency by 20.08-23.57 s, predominantly through admission waiting. Bounded admission reduces mean work in ten of twelve allocator-load conditions, including a 19.35% reduction with a 1.40-s mean latency increase for high-arrival HIPC. RP2040 experiments show that this tradeoff can become more favorable as processor constraints tighten. Across four matched medium-arrival HIPC scenarios, Count b=4 reduces mean RP2040 work by 59.85% and service latency by 39.47%, while the corresponding AGX cases increase latency by 27.69%. These results show that the usefulness of task-admission coalescing depends on arrival intensity, allocator-specific behavior, and the relative cost of computation on the execution platform.

We argue that pattern recognition and step-by-step reasoning are two ends of a spectrum. A large language model (LLM) learns to reason step-by-step when data is structured such that the next token depends on a small amount of preceding context. Inference in LLMs resembles pattern recognition when the next token depends on a large amount of preceding context. If the next token depends on only the $c$ most recent tokens, reasoning traces are paths on a De Bruijn graph whose nodes are $c$-length contexts and edges are next-token transitions between contexts. The set of reasoning traces of a task forms a directed acyclic subgraph of the De Bruijn graph. An LLM that has learned all edges of this subgraph can compose them to solve longer, unseen tasks, i.e., it reasons step-by-step. We prove that the number of edges is vanishingly small compared to the number of reasoning traces. Empirically, the number of training samples a transformer needs is a power law in the number of edges, so learning to reason step-by-step is sample efficient. We can induce De Bruijn structure in any task by maintaining a “state” that makes future reasoning independent of the past. The frequency of states in the reasoning trace determines $c$. We show, by fine-tuning Qwen2.5-1.5B-Instruct to solve equations and answer questions about stories, that frequent states (small $c$) result in higher accuracy but greater fragility to perturbations at test time. LLMs trained with a large $c$ are only as good as models that perform pattern recognition without reasoning. A moderate density of states balances accuracy and robustness. We show that real-world data has De Bruijn structure: Qwen3-14B and Qwen3-32B retain over 75% of their accuracy on GSM8K, MATH-500 and GPQA-Diamond when attention is restricted to a sliding window less than 15% as long as the full reasoning trace.

Cine cardiovascular magnetic resonance (CMR) captures the cardiac cycle as a four-dimensional (4D) sequence, but standard acquisition requires electrocardiogram (ECG) gating and repeated breath holds. Visual realism alone does not establish accurate patient-specific ejection fraction (EF) or ventricular volumes. We present PhaseFlow3D, a generative framework that synthesizes a complete 4D cine sequence from a single end-diastolic (ED) three-dimensional (3D) volume without ECG. To capture asymmetric systolic and diastolic dynamics, it represents the cardiac cycle as a piecewise linear phase anchored at ED and end-systolic (ES) time points. At inference, a population-level canonical template supplies this phase without patient-specific temporal information. A phase-conditioned rectified flow model generates a cardiac motion trajectory in latent space. Radial Contraction Decomposition converts each latent state into a 3D displacement field, combining a physics-informed radial component for centripetal myocardial contraction with an image-conditioned residual for rotation and out-of-plane motion. Each frame is generated by directly warping the ED volume, bypassing variational autoencoder decoding. On the combined ACDC and M&Ms benchmark, PhaseFlow3D achieves the lowest EF mean absolute error, the only positive left-ventricular volume-curve $R^2$, and the best distributional quality among compared methods. Ablations confirm each component's contribution. Downstream evaluations demonstrate the utility of the synthesized sequences and displacement fields for segmentation, pathology classification, label propagation, and myocardial strain analysis.

Fault and error detection is crucial for ensuring the correctness of safety-critical systems. Safety verification often addresses reachability of bad system states, where exhaustive state inspection may be intractable due to the large state spaces of complex systems. We propose a reachability relaxation for hybrid trace nets, a useful mathematical model for analyzing concurrent event systems, to efficiently verify system safety. We further use our relaxation to effectively identify invariants, expressions that hold in all reachable states, allowing state-space reduction for efficient verification. Empirically, our approach proves unsafe states unreachable in 1.5x more instances, generates 2.5x more invariants with up to 2 orders of magnitude faster generation times than the baselines in the tested problems.

Quantization-aware training (QAT) leverages lower-precision arithmetic to reduce the cost of LLM deployment, but aggressive quantization degrades final model performance. A common remedy is mixed-precision training, in which high precision is assigned to some of the layers to maintain performance while keeping the cost constrained. This approach then requires precision assignments for model layers during training. We provide a new approach, called Q-PACE, consisting of a second-order sensitivity model that predicts the loss increase as a sum of quantization noise MSE weighted by per-layer curvature coefficients. During training, we periodically re-compute these coefficients using perturbations across layers, and re-assign precision. Pretraining and supervised fine-tuning experiments on LLMs of up to 4B parameters show that Q-PACE consistently improves over existing mixed-precision training recipes, and achieves comparable loss at substantially lower total memory budgets. We further find that quantization sensitivity is highly predictable by depth and layer type, and its stability during training allows for infrequent, cheap recalibration.

The optical theorem dictates that the wave scattering of an object in the forward direction is proportional to the total power extinguished from the excitation. For passive objects, this relationship is a by-product of the intuitive notion that scattering and absorption necessarily create shadows, and that zero forward scattering, i.e., no shadow, can only be obtained if the object is fully transparent, i.e., it neither scatters nor absorbs. Materials with gain can be in principle leveraged to suppress forward scattering while preserving a large scattering signature in other directions. However, sufficient optical gain is challenging to realize, and it inherently leads to instabilities and nonlinearities. Here, we experimentally demonstrate shadow-free \ scattering from a passive high-index dielectric sphere by exciting it with a complex frequency signal tailored to mimic the presence of material gain. We achieve as much as 26dB suppression of the forward scattering when compared with optimal monochromatic excitations, while preserving strong scattering in other directions. More broadly, our results demonstrate how complex frequencies offer a natural pathway to enhance control over the scattering signature of passive objects, with implications for a range of photonic applications.

Atmospheric warming raises evaporative demand, but actual evapotranspiration (ETa) may track demand or decouple under water limitation. Here, we quantified demand-tracking ability from regression slopes relating deseasonalized ETa and reference evapotranspiration (ETo) anomalies across California during 2008-2024. Forests and croplands retained similar positive tracking under severe drought, whereas grasslands and shrublands showed weak or negative responses. Despite similar demand tracking, forest responses were consistent with subsurface-storage access, whereas cropland responses reflected managed water access and crop-system adjustment. Positive ETa-ETo coupling on active fields coexisted with a higher statewide crop-attributed fallow share of managed cropland than under no drought, showing that active-field estimates alone did not capture whole-crop-system adjustment. Late-period demand-tracking ability was lower at 54.9% of grid cells, with larger regional declines accompanying greater groundwater-storage losses. Our results indicate that similar ETa responses mask contrasting modes of water access, requiring joint consideration of hydrology and management when interpreting drought responses.

The rapid growth of low-cost and open-source spectrophotometers has created a need for systematic methodologies to evaluate and compare alternative instrument architectures. This study presents a comparative assessment of three representative open-source spectrophotometric platforms, encompassing discrete multispectral sensing and continuous-spectrum imaging approaches. Their performance was evaluated against a commercial Thermo Scientific Genesys 30 spectrophotometer in terms of spectral agreement, portability, implementation complexity, and cost. The results demonstrate that no single architecture is universally optimal; instead, each presents distinct trade-offs that determine its suitability for specific applications. Multispectral sensor-based systems offer compact, low-power solutions for field deployment, whereas imaging-based platforms provide spectral performance closer to laboratory-grade instrumentation. All hardware designs, firmware, and software developed in this work are released as open-source resources to support reproducibility and further development. The study highlights the importance of matching instrument architecture to application requirements and proposes a practical framework for the evaluation and selection of low-cost spectrophotometers, facilitating the adoption of open-source analytical tools for water quality monitoring and related applications.

As data propagates through a Transformer, the norm of its hidden states grows by orders of magnitude with depth, a phenomenon framed as 'curse of depth' and nearly universally treated as a pathology to be suppressed. We take the opposite view. Across 16 pre-trained LLMs from 9 families, spanning dense, mixture-of-experts and hybrid architectures and Pre-, Peri- and Post-Norm designs, we find that this growth reflects an emergent depth-positional encoding, carried by the only learned per-layer gain on the residual stream, the normalization weight $\gamma$: with depth, $\gamma$ grows in magnitude and rotates in direction, jointly encoding the layer index. We make this depth-conditioned encoding explicit with LayerRoPE, an implicit analog of RoPE along the depth axis, which replaces all layerwise $\gamma$ vectors with a single shared vector and depth-conditioned scalars, at a net reduction in parameters and $<0.02\%$ change in FLOPs. Across a model ladder scaled up to $100$B+ tokens, LayerRoPE consistently outperforms Pre-, Post- and Peri-Norm and Layer-Norm Scaling, reaching Pre-Norm's 1.3B loss with $3.4\times$ less compute; LayerRoPE is the only approach that shows strong convergence and improves near monotonically as depth scales to 512 layers. It improves learning-rate sensitivity by $3$-$10\times$, and transfers naively to and consistently improves looped latent models and Vision Transformers. Inspecting its learned schedule inverts the prevailing premise: LayerRoPE does not shrink the residual stream but widens it, damping what each block reads while amplifying what it writes. Depth stability, our results suggest, calls not for suppressing the residual stream, but for depth-conditioned regulation of the computational blocks it feeds.

Action tokenization converts continuous robot actions into discrete symbols that can be modeled autoregressively. However, existing tokenizer-based policies typically ignore the tokenizer's learned latent code structure: after tokenization, the policy treats tokens as unrelated class indices and learns a new classifier from scratch. We show that this discarded structure is valuable. We introduce Codebook-Aligned Prediction (CAP), a method that directly reuses the tokenizer's code vectors as policy class prototypes while leaving the tokenizer and policy backbone otherwise unchanged. Across four quantizer families, three simulation benchmarks, and two real-robot tasks, CAP consistently improves task success over standard token classification heads while holding the tokenizer (and therefore its reconstruction quality) fixed. Our analysis further shows that these gains are not explained by higher token accuracy or changes in the policy head alone. Instead, reusing the tokenizer codebook provides the policy with valuable information about the tokenizer's learned latent structure across tokens, making token prediction errors more benign in action space and improving the representations learned by the policy backbone. These results suggest that action tokenizers learn useful action-aware latent structure beyond discrete targets that should be preserved when training downstream policies.

Visual document retrievers are trained contrastively: each query is matched to one page labelled relevant - the positive - and pushed away from negatives, pages presumed irrelevant. Recent methods distil a vision-language model (VLM) teacher into the retriever by enriching that positive, transferring the teacher's attention over it or a description of it. We ask whether the teacher is better spent on the other side, judging the candidates the retriever mines as negatives, which the label says nothing about. With student, data, optimizer and evaluation fixed, teacher-judged hard negatives and score distillation raise ViDoRe v2 nDCG@5 from 55.2 to 62.6 and 63.0; description alignment, as adapted here, gains 2.6 points and attention grounding nothing measurable. Against teacher-free rules that select four candidates from the same mined pool at identical training compute, the best of which is the positive-aware threshold current systems use, the teacher's judgement adds 4.1 points on v2 and 1.7 on v3. This is consistent with how incomplete the labels are. Annotators judge about two of a query's four top-ranked mined candidates relevant, none of them labelled, so training pushes the retriever away from relevant pages treated as negatives. What reaches the student is coarse: under a greedily decoded 0-100 rating prompt, 82% of the teacher's ratings come back at one end of the scale or the other, and a relevant/irrelevant partition keeps most of the distillation gain. A ten-annotator audit places the teacher within the range of variation among human annotators, and finds it reliable where a query has a single determinate answer. We release the code, the teacher's 3.3M judgements and page descriptions, the mined pools, the human audit and the trained adapters at https://github.com/elastic/vdr-teacher-signals.

We construct a two-parameter family of polynomial vector fields in $\mathbb{R}^3$ and prove that, on a nonempty open set of parameter values, every member of the family is Hurwitz and possesses two non-constant periodic orbits, one of saddle type and one attracting. This answers Problem 19 in Gasull's list of open problems on low-dimensional dynamical systems concerning the existence of non-constant periodic orbits in Hurwitz smooth vector fields on $\mathbb{R}^3$. This also provides counterexamples to the expected non-existence of non-constant periodic orbits for Hurwitz polynomial vector fields; a question that arose from the first counterexamples to the Markus-Yamabe conjecture in the late 1990s and that was stated by Meisters in his featured MathSciNet review of the Bernat-Llibre counterexample.

The quickest path reliability problem is to compute the probability that a given flow is transmitted along a single source-destination path within a given time limit. When a budget is imposed, path feasibility is jointly dependent on lead time, transmission cost, and capacity. Existing exact methods may require enumeration of all minimal paths a priori or examination of many partial paths that cannot be completed feasibly. In this paper, we propose an exact algorithm that generates the corresponding lower boundary state vectors without first enumerating minimal paths. Shortest-lead-time, least-cost, and widest-capacity information yield admissible destination-based bounds. Stronger capacity-aware bounds are derived from capacity-filtered subnetworks. These bounds allow early pruning of infeasible branches while keeping all solutions. The algorithm generates the exact complete set of lower bounds without any duplicates, and its correctness and computational complexity are proven.

Reliable and interpretable trajectory prediction is critical for cooperative and autonomous driving in complex and uncertain environments. This paper introduces a Context-Aware Attention-based Gaussian Mixture Model (CAA-GMM) for multimodal, uncertainty-aware motion forecasting. The proposed approach models future motion as a probabilistic mixture conditioned on both scene context and agent dynamics, capturing diverse behavioral modes with interpretable Gaussian components. A lightweight attention mechanism adaptively encodes inter-agent interactions and contextual salience, enabling efficient fusion of rasterized environment cues and motion history in dense traffic scenes. Comprehensive evaluations on the nuScenes and Argoverse 2 datasets demonstrate that CAA-GMM achieves competitive or superior accuracy compared with state-of-the-art raster-based baselines, while maintaining low computational complexity. Ablation analyses confirm the importance of the attention module for robust contextual reasoning and predictive precision. Furthermore, evaluations under imperfect communication and perception conditions highlight the framework's resilience to uncertainty, establishing CAA-GMM as an efficient and scalable solution for cooperative trajectory prediction in intelligent transportation systems.

3D foundation models enable efficient novel view synthesis by carrying a Gaussian head on the representation they already use for reconstruction. However, the views they render fall short of the geometry they recover, because that geometry is estimated under a metric objective and never scored on how it renders. Recent methods alleviate this by updating the backbone weights, but they thereby discard the metric predictions the model was built for and must be repeated for every new backbone. To this end, we propose RDGSplat, a framework that decodes a second geometry dedicated to rendering from a frozen 3D foundation model, leaving its metric predictions intact. In particular, we devise Render-Dedicated Geometry Decoding, which duplicates the pretrained decoders and optimizes the duplicates under photometric supervision alone. Then, a Target-Pose Conditioned Adapter is introduced to reformulate the representation those decoders read, conditioned on the target camera pose rather than the target image. Extensive experiments show that RDGSplat improves novel view synthesis across three feed-forward backbones on four benchmarks, with every pretrained weight frozen. On RE10K, it raises WM2.0 from 20.918 to 24.266\,dB while training 205.5\,M added parameters against a frozen 1.4\,B backbone, and the depth and pose the same model predicts are unchanged.

The problem of fast Doppler counter-aliasing for short-dwell weather-radar measurements is addressed. The proposed approach realizes a log-periodic slow-time design by changing only the waiting time between otherwise unchanged frequency-modulated continuous-wave (FMCW) chirps. The fast-time waveform, bandwidth, and range-processing chain are preserved while the acquisition changes the Doppler ambiguity structure. We formulate a novel moment-space ambiguity function for distributed weather spectra. It measures statistical ambiguity jointly in mean Doppler velocity and spectral width and expresses the competing sidelobes through their expected relative likelihood. A complex Gaussian process (CGP) maximum-likelihood estimator reconstructs the spectrum from the measured aperiodic samples. A deterministic basin-selection and optimization strategy accelerates the same CGP likelihood without defining a different statistical estimator. Real precipitation measurements establish central-branch stability over an extended search domain. Using 64 slow-time sweeps, we compare three acquisitions and their associated estimators. Periodic data are processed by the discrete Fourier transform (DFT) and parametric spectral estimation (PSE), log-periodic data by the nonuniform discrete Fourier transform (NUDFT) and CGP, and staggered data by velocity-difference and CGP estimators. The differences become more pronounced when the dwell is reduced to 32 sweeps. The results show that aperiodic time sampling enables extended-domain branch identification without degrading spectral-width estimation.

We study the conjectural characteristic class analogue of the Hodge index theorem for singular complex algebraic varieties, formulated by Brasselet-Schürmann-Yokura which expresses the Goresky-MacPherson homology $L$-classes in terms of suitable Hodge-theoretic $L$-classes, for quotient spaces $X/G$, where $G$ is a finite group and $X$ is a pure-dimensional complex projective variety. Assuming that an equivariant $K$-theoretical version of the conjecture holds for $X$, we show that the characteristic class conjecture holds for $X/G$. Without assuming the equivariant $K$-theoretical version, we show that the characteristic class conjecture holds for $X/G$, provided that it holds for all fixed point sets $X^g$ and that a suitable normally nonsingular inclusion assumption is satisfied. Our approach is to work in equivariant analytic $K$-homology and equivariant algebraic $G$-theory and to identify the corresponding localized classes. On the analytic side, we identify the Banagl-Zagier equivariant $L$-classes with localized Chern character of the equivariant $K$-homology class of the signature operator defined by Banagl-Leichtnam-Piazza. On the algebraic side, we compute the localization of the equivariant motivic Hodge-Chern class transformation of the intersection Hodge module.

Autoregressive action-token policies such as vision-language-action models require action tokenizers to translate discrete token sequences into precise control actions in continuous space. Many action tokenizers learn the mapping between tokens and actions via a reconstruction objective. However, as we show through extensive analysis, sufficiently accurate action reconstruction is only one part of what makes a downstream robot policy successful. It is also critical that the policy is able to predict the right tokens for new observations, and that unseen policy token predictions still decode into reasonable actions. These properties are downstream of tokenizer training and are not directly incentivized by a reconstruction objective alone. In this work, we introduce Predictable and Robust Action Tokenization (ProAct), a tokenizer training method that strategically augments reconstruction with the goal of improving downstream predictability and robustness. ProAct is policy-agnostic and uses only action datasets for training. Across the Robomimic, LIBERO, and RoboTwin benchmarks and a diverse set of tokenizer architectures, ProAct improves rollout success by an average of 11.3 percentage points. These improvements also translate to vision-language-action policies and real-world robotic manipulation, yielding average gains of 21.8 and 36.7 percentage points, respectively. These results suggest that effective action tokenization should be designed as a policy interface that balances fidelity, predictability, and robustness, rather than as a reconstruction problem alone.

A conference signal is a complex-valued function on a finite abelian group that vanishes at 0 in both the time and frequency domains, and is otherwise flat in both domains. For example, the Legendre symbol is a conference signal on $\mathbb{Z}_p$ since it vanishes at $0$, takes values $\pm 1$ away from zero, and is a scalar multiple of its Fourier transform. More generally, any nontrivial multiplicative character on a finite field is a conference signal on its additive group. Until now, conference signals have mainly been studied by number theorists, who wanted to know if multiplicative characters were the only conference signals on finite fields. The state of the art uses fancy tools from symplectic geometry to prove that non-character conference signals exist on non-small fields. The same tools show conference signals exist on every abelian group of odd order, without saying what they are. In this (human-friendly!) paper, we explain how conference signals produce other objects of interest in algebraic combinatorics and applied harmonic analysis, and then we present some new, explicit constructions of conference signals on $\mathbb{Z}_n$. In particular, we give the first explicit conference signals for composite $n$ and the first explicit non-character examples for prime $n$.

Central limit theorems in survey sampling are typically established under specific sampling designs rather than from generic characteristics of a design. Motivated by the search for more general conditions, we investigate whether low-order inclusion probabilities can provide such a basis. First- and second-order inclusion probabilities determine the first two moments of sampling estimators such as the Horvitz–Thompson estimator, but we show that even exact agreement of these probabilities with those of simple random sampling without replacement (SRSWOR) does not preserve asymptotic normality. We construct a sequence of fixed-size sampling designs having exactly the same first- and second-order inclusion probabilities as SRSWOR, together with a sequence of finite populations for which the sample total converges to $N(0,1)$ under SRSWOR but to a centered standard exponential distribution under the alternative designs. Thus, the two sample totals have exactly the same mean and variance at every stage of the sequence, yet have different limiting distributions. The alternative designs are obtained from balanced incomplete block designs arising from finite projective planes. Their cyclic structure allows us to prescribe the distribution of the sample total under block sampling, while a probabilistic permutation argument, combined with an exponential inequality for sampling without replacement, yields finite populations satisfying the SRSWOR central limit theorem. The result shows that low-order inclusion probabilities do not control the global dependence structure relevant to asymptotic normality and therefore cannot, by themselves, provide general conditions for central limit theorems under complex sampling designs.

Jailbreak defenses for large language models are usually calibrated on a fixed set of known attack methods. However, new attack methods keep appearing after deployment, and existing detectors are observed to degrade under the new attacks (Piet et al., 2025). This paper studies how to detect, from a stream of attack prompts, that the prompts come from an attack source outside the known ones. We formulate it as a sequential test whose null hypothesis is that the stream comes from one of the known sources. Methodology-wise, we compute a conformal p-value against each known source, and reject the null only when the evidence against every known source is large. Using these source-wise p-values, we build Persist-3 and analyze its stationary false-alarm probability and detection power. The technical contribution of Persist-3 lies in a detection guarantee that uses only a finite window of recent observations. Our theoretical analysis reveals that its detection probability approaches one exponentially fast as the window grows, and thus a short window suffices to detect unseen sources that are well separated from all known sources. Empirically, we validate Persist-3 on top of two recent jailbreak defenses, MTK (Zhang et al., 2026) and Prompt Guard 2 (Chennabasappa et al., 2025), and observe a significant defense enhancement.

Standard diffusion samplers generate samples through repeated evaluations of a learned score function. Parallel sampling methods seek to accelerate generation by trading additional evaluations for fewer sequential rounds. This raises the question of how much sequential dependence is unavoidable, even when many score queries can be made simultaneously. We establish the first polynomial parallel-round lower bounds for diffusion sampling with approximate scores. Specifically, we prove (1) a $\widetilde{\Omega}(d^{1/3})$-round lower bound for sampling smooth, near-isotropic Gaussian mixtures in $R^d$, and (2) an $\Omega(d)$-round lower bound for uniform sampling from anisotropic axis-aligned boxes contained in the unit ball. Both bounds hold for arbitrary randomized algorithms making polynomially many queries per round at arbitrary locations and noise levels, with inverse-polynomial score error and constant total variation accuracy. The linear bound is tight for our box family. Our constructions use fixed approximate score oracles that enforce sequential access to hidden information while satisfying the accuracy guarantee at every noise level.

Planning motions that respect the intrinsic geometry of a robot's configuration space, including its curvature and a configuration-dependent notion of cost, yields shorter, lower-energy, and more natural trajectories than planning under the ambient flat metric. Existing libraries for optimization on manifolds provide rich geometric primitives but do not plan around obstacles. While general-purpose motion planning libraries support many state spaces and custom distance functions, they do not yet treat a configuration-dependent Riemannian metric as the geometry that drives distance, interpolation, and geodesics. We present geodex, an open-source C++20 library with Python bindings. The library exposes the manifold, its Riemannian metric, the retraction, and the sampler as independent, interchangeable components through a single sampling-based motion planning interface. The same planner runs unchanged on canonical spaces $\mathbb{R}^n$, $\mathbb{T}^n$, $\mathbb{S}^n$, matrix Lie groups such as $SO(2)$, $SE(2)$, $SO(3)$, and $SE(3)$, products of these spaces, and articulated-robot configuration spaces, each equipped with a user-defined Riemannian metric. We make geodex publicly available with documentation, tests, and a reproducible benchmark suite.