arXiv:2602.03001v2 Announce Type: replace Abstract: To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune. Existing adaptive strategies based on gradient noise scale (GNS) offer a principled alternative. However, their assumption of SGD's Euclidean geometry creates a fundamental mismatch with popular optimizers based on generalized norms, such as signSGD / Signum ($\ell_\infty$) and stochastic spectral descent (specSGD) / Muon ($\mathcal{S}_\infty$). In this work, we derive gradient noise scales for signSGD and specSGD that naturally emerge from the geometry of their respective dual norms. To practically estimate these non-Euclidean metrics, we propose an efficient variance estimation procedure that leverages the local mini-batch gradients on different ranks in distributed data-parallel systems. Our experiments demonstrate that adaptive batch size strategies using non-Euclidean GNS enable us to match the validation loss of constant-batch baselines while reducing training steps by up to 66\% for Signum and Muon on a 160 million parameter Llama model.
Science Journals
arXiv:2602.05800v2 Announce Type: replace Abstract: For quasi-linear elliptic interface problems with discontinuous diffusion coefficients, randomized neural network approximations may exhibit stagnation because the associated objective functional is generally nonconvex. This paper proposes a Local Randomized Neural Network (LRaNN) perturbation-correction method, denoted by LRaNN-PC, to alleviate this stagnation. The method represents the solution using an LRaNN on each subdomain, coupled through the interface conditions in a domain-decomposed framework. It consists of a primary stage and a perturbation-correction (PC) stage. The primary stage computes the primary approximation by minimizing the original nonconvex objective functional. The PC stage constructs a residual-driven correction by performing a local expansion of the residual around the primary approximation and representing the correction in an independently generated randomized trial space. The correction coefficients are obtained by solving a least-squares residual-correction subproblem in this trial space. For the solution-dependent quasi-linear elliptic model under the stated sufficient assumptions, we derive a residual-controlled upper bound for the broken $H^1$ seminorm error. The bound involves the discrete residual, the quadrature error, the residual of the perturbation-correction subproblem, and the truncation remainder of the perturbation expansion. Numerical experiments further test irregular interfaces and high-contrast coefficients within this setting, and also examine gradient-dependent diffusivities and moving-interface extensions. In the tested benchmarks, LRaNN-PC reduces the relative $L^2$ error by up to $4$--$7$ orders of magnitude compared with the primary LRaNN stage.
arXiv:2602.05999v4 Announce Type: replace Abstract: How does the amount of compute available to a reinforcement learning (RL) policy affect its learning? Can policies using a fixed amount of parameters, still benefit from additional compute? The standard RL framework does not provide a language to answer these questions formally. Empirically, deep RL policies are often parameterized as neural networks with static architectures, conflating the amount of compute and the number of parameters. In this paper, we formalize compute bounded policies and prove that policies which use more compute can solve problems and generalize to longer-horizon tasks that are outside the scope of policies with less compute. Building on prior work in algorithmic learning and model-free planning, we propose a minimal architecture that can use a variable amount of compute. Our experiments complement our theory. On a set 31 different tasks spanning online and offline RL, we show that $(1)$ this architecture achieves stronger performance simply by using more compute, and $(2)$ stronger generalization on longer-horizon test tasks compared to standard feedforward networks or deep residual network using up to 5 times more parameters.
arXiv:2602.07267v2 Announce Type: replace Abstract: Evaluating the real-world capabilities of AI systems requires grounding benchmark performance in human-interpretable measures of task difficulty. Existing approaches that rely on direct human task completion time annotations are costly, noisy, and difficult to scale across benchmarks. In this work, we propose BRIDGE, a unified psychometric framework that learns a latent difficulty scale from model responses and anchors it to human task completion time. Using a two-parameter logistic Item Response Theory model, we jointly estimate latent task difficulty and model capability from model performance data across multiple benchmarks. We demonstrate that latent task difficulty varies linearly with the logarithm of human completion time, allowing human task completion time to be inferred for new benchmarks from model performance alone. Leveraging this alignment, we forecast frontier model capabilities in terms of human task length and independently reproduce METR's exponential scaling results, with the 50% solvable task horizon doubling approximately every 6 months.
arXiv:2607.01573v1 Announce Type: new Abstract: We initiate the study of *unate distributions* over $\{\pm1\}^n$ -- a natural analogue of unate Boolean functions -- by considering two basic testing problems that parallel well-studied questions for monotone distributions: - Uniformity Testing of Unate Distributions: We show that $\widetilde{\Theta}(n^{3/2})$ samples are sufficient and necessary, in contrast to the $\widetilde{\Theta}(n)$ sample complexity of the analogous problem for monotone distributions (Rubinfeld and Servedio, STOC 2005; Adamaszek, Czumaj, and Sohler, SODA 2010). - Unateness Testing of Arbitrary Distributions: We give a tester that uses $\widetilde{O}(n^{3/2})$ conditional samples in the subcube conditional model. On the other hand, every tester that draws conditional samples in a similar fashion, namely from $O(1)$-dimensional subcubes, must have an $\widetilde{\Omega}(n^{2/3})$ complexity. In the same model, the complexity of monotonicity testing was recently shown to be $\widetilde{\Theta}(n)$ (Chakrabarty et al., STOC 2025). Our algorithms for both problems significantly outperform the naive approach of reducing to the monotone case, which would incur $\Omega(n^2)$ sample complexity. Our uniformity tester relies on a subroutine that "weakly" learns the hidden orientations of a unate distribution, together with a new correlation bound for these estimates. Both tools may be of independent interest in studying monotonicity and unateness over $\{\pm1\}^n$.
arXiv:2607.01617v1 Announce Type: new Abstract: Large language model (LLM) serving increasingly combines prefill-decode (PD) disaggregation with tensor parallelism (TP) to support large models and long contexts. In conventional 2D/2.5D chiplet architectures, layer-wise prefill-to-decode KV-cache transfer decode-side TP collectives share the same lateral die-to-die (D2D) interconnect, creating mixed-traffic contention on the decode critical path. This contention increases communication latency, prolongs token generation intervals, and degrades end-to-end serving performance. We propose 3DLS, a logic-on-logic 3D-stacked chiplet architecture that separates traffic classes by routing KV-cache transfers through vertical interconnects while preserving decode-side TP collectives on the lateral D2D fabric. 3DLS achieves up to 1.49$\times$ throughput and 60.2\% lower end-to-end (E2E) latency over the shared-fabric planar baseline, and still achieves up to 1.17$\times$ throughput and 31.4\% lower E2E latency over a workload-aware priority-managed planar baseline. These results highlight that physical isolation is an important design principle for future chiplet-based PD-disaggregated LLM serving systems.
arXiv:2607.01602v1 Announce Type: new Abstract: SRAM-based FPGAs provide an attractive platform for energy- and latency-constrained CNN inference at the network edge, yet transient faults can lead to silent errors that compromise reliability. Always-on redundancy (e.g., full TMR) improves correctness but incurs substantial performance and energy overhead, while reactive recovery may introduce unacceptable latency on the critical path. We propose \textbf{ProWAFT}, a proactive workload-aware fault-tolerance framework for FPGA-based CNN accelerators that uses partial reconfiguration to selectively apply TMR across reconfigurable partitions. ProWAFT quantifies workload criticality, models fault propagation and reconfiguration overhead, and selects configurations that minimize a composite objective over latency, energy, and reliability risk. Implemented on a Xilinx Zynq UltraScale+ ZCU104 platform with six reconfigurable regions and evaluated on a 500-task trace derived from ResNet-18, MobileNetV2, and EfficientNet-Lite under time-varying SEU injection, ProWAFT achieves lower composite cost than static TMR and reactive reconfiguration while maintaining high task success rate and near-baseline throughput with low online decision overhead.
arXiv:2607.01605v1 Announce Type: new Abstract: CityGML, the OGC standard for modeling, storage, and exchange of semantic 3D city models, describes urban objects with detailed semantics, geometry, and topology. Yet this richness is difficult to query directly: CityGML's XML encoding is designed for exchange rather than analysis, and relational mappings expose it through schemas requiring expert knowledge. We present pykci (Python Knowledge Graph for Cities), an open-source system that transforms CityGML 2.0 datasets into a compact urban knowledge graph in Neo4j and makes it queryable in natural language. The graph schema covers all thematic feature modules of CityGML 2.0 across all levels of detail and is spatially indexed with an R-tree for efficient geometric retrieval. A complete end-to-end Python pipeline ingests CityGML datasets into the knowledge graph, exports them to OGC 3D Tiles for interactive visualization, and supports lossless round-trip export of all content back to CityGML. For querying, the graph is paired with a large language model through a model-agnostic text-to-Cypher mechanism: the graph schema is supplied as context, and the model translates natural-language questions into Cypher queries executed against the graph. We evaluate both a locally running open-weight model, which keeps sensitive city data on-premise, and a state-of-the-art commercial model for the most demanding spatial and semantic queries. Answers are grounded in exact city data rather than the model's parametric memory, reducing hallucination and providing auditable provenance for every response. We demonstrate the system on open-government CityGML LoD2 datasets from Hamburg, Germany, including complex semantic and spatial queries such as identifying roof surfaces suitable for greening. pykci enables urban planners, GIS practitioners, and citizens to interact with semantic 3D city models without expertise in query languages and database schemas.
arXiv:2511.20274v2 Announce Type: replace Abstract: In the paradigm of computer vision-based precise real-world scene understanding, joint reasoning in terms of contextual understanding about the objects present in a scene, their inter-object relations, and the action being performed is an essential prerequisite. However, prior works have not addressed all three jointly, and no large-scale dataset provides grounded annotations at all three levels across diverse visual scenarios. Hence, this work introduces the SCLARO (Scene-Contextual Localisation of Actions, Relations & Objects) dataset, consisting of 615,805 images spanning indoor, outdoor, and driving scenarios, annotated with global action captions, object bounding boxes, and relation triplets that supply structured scene context beyond a free-text caption. To benchmark the dataset, we propose ScenarioCLIP, a tri-level reference model that jointly encodes global scene context, objects, and inter-object relations using disentangled encoders and EMA-based knowledge distillation. We benchmark across a comprehensive suite of tasks on the SCLARO Dataset, namely zero-shot retrieval, linear probe, object detection, predicate classification, scene-graph classification, and out-of-domain generalisation. ScenarioCLIP's disentangled encoders improve over the previous works, such as PyramidCLIP's shared encoder, most notably at the object and relation levels and on out-of-domain generalisation. Code for the data generation pipeline and ScenarioCLIP is available at https://github.com/scenario-clip/SCLARO-ScenarioCLIP
arXiv:2511.22459v2 Announce Type: replace Abstract: We propose a method to reconstruct dynamic fire in 3D from a limited set of camera views with a Gaussian-based spatiotemporal representation. Capturing and reconstructing fire and its dynamics is highly challenging due to its volatile nature, transparent quality, and multitude of high-frequency features. Despite these challenges, we aim to reconstruct fire from only three views, which consequently requires solving for under-constrained geometry. We solve this by separating the static background from the dynamic fire region by combining dense multi-view stereo images with monocular depth priors. The fire is initialized as a 3D flow field, obtained by fusing per-view dense optical flow projections. To capture the high frequency features of fire, each 3D Gaussian encodes a lifetime and linear velocity to match the dense optical flow. To ensure sub-frame temporal alignment across cameras we employ a custom hardware synchronization pattern -- allowing us to reconstruct fire with affordable commodity hardware. Our quantitative and qualitative validations across numerous reconstruction experiments demonstrate robust performance for diverse and challenging real fire scenarios.
arXiv:2607.01642v1 Announce Type: new Abstract: Hardware-agnostic strategies for accelerating text-to-image diffusion, such as timestep distillation and feature caching, can reduce inference time without custom kernels or system-level optimization. Among them, multi-resolution generation strategies have recently received broad attention, attaining more than 5x speedup without any training. However, the design of performing upsampling in the latent space, together with the selective modification of partial regions, causes these methods to exhibit noticeable blurring or artifacts. To this end, we propose MrFlow, a training-free multi-resolution acceleration strategy for pretrained flow-matching models built upon a staged low-to-high-resolution pipeline. MrFlow first rapidly generates the main structure at low resolution, then performs super-resolution in the pixel space using a lightweight pretrained GAN-based model, subsequently injects low-strength noise to enable high-frequency resampling, and finally refines the details at high resolution. Quantitative and qualitative results on FLUX.1-dev and Qwen-Image show that MrFlow exploits the quadratic token reduction and reduced step requirement of low-resolution sampling to achieve 10x end-to-end acceleration while keeping OneIG within a 1% gap relative to that before acceleration, significantly surpassing other training-free acceleration strategies, and requiring no training or runtime dynamic identification whatsoever. MrFlow can further be directly combined orthogonally with pre-trained timestep distillation strategies, achieving even higher generation acceleration of up to 25x.
arXiv:2607.01654v1 Announce Type: new Abstract: We investigate volumetric reconstruction for compressive sensing light-sheet microscopy (CS-LSM), where fast volumetric imaging is achieved by encoding multiple axial planes into each camera exposure. To recover the underlying volume from highly multiplexed measurements, we propose a plug-and-play (PnP) framework that flexibly incorporates any user-specified denoiser into the reconstruction process. Building on a slice-based formulation, we further introduce an axial-coupled model that exploits correlations between adjacent slices to improve volumetric continuity. For efficient computation, we derive a Woodbury-based update for the data-consistency step in both the slice-based and axial-coupled formulations, and employ a Gauss-Seidel sweep for the denoising step in the axial-coupled model. Under a weakly convex regularization assumption, we establish subsequential convergence of the proposed algorithm. Experiments on synthetic and real zebrafish-heart data demonstrate that the proposed framework successfully recovers cellular structures from compressed measurements, and provide practical insights into the comparative performance of commonly used denoisers within the PnP framework under the CS-LSM setup.
arXiv:2607.01657v1 Announce Type: new Abstract: Visual recognition models often fail when deployed in new environments. Domain Generalization (DG) addresses this by learning representations that remain invariant to environment-specific variations. Recent approaches increasingly rely on large vision-language models, assuming that preserving their expressive visual representations improves robustness. However, we show that such visual expressiveness can instead propagate spurious cues that tie representations to the training environments, hindering invariant learning. We therefore discard visual guidance and instead treat the language embedding space as the primary source of domain invariance, naturally acting as an information bottleneck that preserves core semantics while suppressing domain-specific variations. Extensive experiments across diverse backbones exhibit state-of-the-art performance and further analyze what makes guidance effective for robust generalization. These findings shift the focus of DG from improving representations to designing supervision that enforces invariance.
arXiv:2607.01664v1 Announce Type: new Abstract: Substrate-agnostic perspectives are currently attracting increased attention. For example, it has become customary to refer to agnostic biosignatures to reflect the range of alternative extraterrestrial biospheres and to account for the deeper philosophical dependence of candidate biosignatures on the underlying theory of life. Analogously, one can formulate a concept of agnostic technosignatures, reflecting that the more we expand the search for technosignatures, the more we invite theories of technology that undo the terrestrial bias. For this reason, this paper argues that there exists a strong theoretical justification for an integrated study of technosignatures and biosignatures, articulated in a unified perspective on substrate-agnostic ecologies. The paper introduces the concept of substrate-agnostic ecology as an abstraction unconstrained by terrestrial circumstances, anchored instead in a functional understanding of agent-ecology coupling provided by niche construction theory.
arXiv:2607.02365v1 Announce Type: new Abstract: We compute the weight distribution of the third-order Reed--Muller code RM(3,11) of length 2048. The weight enumerator is assembled from the coset weight enumerators of f+RM(2,10), evaluated for representatives of all 3691560 nonzero GL(10,2)-orbits of Boolean cubic forms in ten variables. The computation rests on a structural theorem: a nondegenerate Boolean cubic form admits a nondegenerate hyperplane restriction, except for a single orbit in each odd dimension. The same pass determines the second-order nonlinearity of every cubic form: the relative covering radius of RM(2,10) in RM(3,10) is 408, attained on 179 orbits. This raises the best known lower bound on the covering radius of RM(2,10) from 400 to 408. A complementary heuristic search shows that the relative covering radius of RM(6,10) in RM(7,10) is at most 32, improving the previous bound of 50.
arXiv:2602.08337v2 Announce Type: replace Abstract: In this paper, we focus on motion discrete tokenization, which converts raw motion into compact discrete tokens--a process proven crucial for efficient motion generation. In this paradigm, increasing the number of tokens is a common approach to improving motion reconstruction quality, but more tokens make it more difficult for generative models to learn. To maintain high reconstruction quality while reducing generation complexity, we propose leveraging language to achieve efficient motion tokenization, which we term Language-Guided Tokenization (LG-Tok). LG-Tok aligns natural language with motion at the tokenization stage, yielding compact, high-level semantic representations. This approach not only strengthens both tokenization and detokenization but also simplifies the learning of generative models. Furthermore, existing tokenizers predominantly adopt convolutional architectures, whose local receptive fields struggle to support global language guidance. To this end, we propose a Transformer-based Tokenizer that leverages attention mechanisms to enable effective alignment between language and motion. Additionally, we design a language-drop scheme, in which language conditions are randomly removed during training, enabling the detokenizer to support language-free guidance during generation. On the HumanML3D and Motion-X generation benchmarks, LG-Tok achieves Top-1 scores of 0.542 and 0.582, outperforming state-of-the-art methods (MARDM: 0.500 and 0.528), and with FID scores of 0.057 and 0.088, respectively, versus 0.114 and 0.147. LG-Tok-mini uses only half the tokens while maintaining competitive performance (Top-1: 0.521/0.588, FID: 0.085/0.071), validating the efficiency of our semantic representations. Code and checkpoints are available at https://eanson023.github.io/LG-Tok/
arXiv:2602.08542v3 Announce Type: replace Abstract: Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center. In the dynamic setting, the graph is subject to adversarial edge updates, and the goal is to maintain explicitly an exact $(k, z)$-clustering solution in the induced shortest-path metric. While efficient dynamic $k$-center approximation algorithms on graphs exist [Cruciani et al. SODA 2024], to the best of our knowledge, no prior work provides similar results for the dynamic $(k,z)$-clustering problem. As the main result of this paper, we develop a randomized incremental $(k, z)$-clustering algorithm that maintains with high probability a constant-factor approximation in a graph undergoing edge insertions with a total update time of $\tilde O(k m^{1+o(1)}+ k^{1+\frac{1}{\lambda}} m)$, where $\lambda \geq 1$ is an arbitrary fixed constant. Our incremental algorithm consists of two stages. In the first stage, we maintain a constant-factor bicriteria approximate solution of size $\tilde{O}(k)$ with a total update time of $m^{1+o(1)}$ over all adversarial edge insertions. This first stage is an intricate adaptation of the bicriteria approximation algorithm by Mettu and Plaxton [Machine Learning 2004] to incremental graphs. One of our key technical results is that the radii in their algorithm can be assumed to be non-decreasing while the approximation ratio remains constant, a property that may be of independent interest. In the second stage, we maintain a constant-factor approximate $(k,z)$-clustering solution on a dynamic weighted instance induced by the bicriteria approximate solution. For this subproblem, we employ a dynamic spanner algorithm together with a static $(k,z)$-clustering algorithm.
arXiv:2602.08711v3 Announce Type: replace Abstract: This paper proposes Omni Dense Captioning, a novel task designed to generate continuous, fine-grained, and structured audio-visual narratives with explicit timestamps. To ensure dense semantic coverage, we introduce a six-dimensional structural schema to create "script-like" captions, enabling readers to vividly imagine the video content scene by scene, akin to a cinematographic screenplay. To facilitate research, we construct OmniDCBench, a high-quality, human-annotated benchmark, and propose SodaM, a unified metric that evaluates time-aware detailed descriptions while mitigating scene boundary ambiguity. Furthermore, we construct a training dataset, TimeChatCap-42K, and present TimeChat-Captioner-7B, a strong baseline trained via SFT and GRPO with task-specific rewards. Extensive experiments demonstrate that TimeChat-Captioner-7B achieves state-of-the-art performance, surpassing Gemini-2.5-Pro, while its generated dense descriptions significantly boost downstream capabilities in audio-visual reasoning (DailyOmni and WorldSense) and temporal grounding (Charades-STA). All datasets, models, and code are available at https://github.com/yaolinli/TimeChat-Captioner.
arXiv:2602.10431v4 Announce Type: replace Abstract: Large language models (LLMs) demand substantial computational and memory resources, posing challenges for efficient deployment. Two complementary approaches have emerged to address these issues: token-adaptive layer execution, which reduces floating-point operations (FLOPs) by selectively bypassing layers, and quantization, which lowers memory footprint by reducing weight precision. However, naively integrating these techniques leads to additional accuracy degradation due to reduced redundancy in token-adaptive models. We propose QTALE (Quantization-Robust Token-Adaptive Layer Execution for LLMs), a novel framework that enables seamless integration of token-adaptive execution with quantization while preserving accuracy. Conventional token-adaptive methods reduce redundancy in two ways: (1) by limiting the diversity of training paths explored during fine-tuning, and (2) by lowering the number of parameters actively involved in inference. To overcome these limitations, QTALE introduces two key components: (1) a training strategy that ensures diverse execution paths are actively explored during fine-tuning, and (2) a post-training mechanism that allows flexible adjustment of the execution ratio at inference to reintroduce redundancy when needed. Experimental results show that QTALE enables seamless integration of token-adaptive layer execution with quantization, while keeping the accuracy gap to quantization-only models below 0.5% on CommonsenseQA benchmarks. By combining tokenadaptive execution for FLOPs reduction and quantization for memory savings, QTALE provides an effective solution for efficient LLM deployment.
arXiv:2602.14110v2 Announce Type: replace Abstract: As industrial recommender systems enter a scaling-driven regime, Transformer architectures have become increasingly attractive for scaling models towards larger capacity and longer sequence. However, existing Transformer-based recommendation models remain structurally fragmented, where sequence modeling and feature interaction are implemented as separate modules with independent parameterization. Such designs introduce a fundamental co-scaling challenge, as model capacity must be suboptimally allocated between dense feature interaction and sequence modeling under a limited computational budget. In this work, we propose MixFormer, a unified Transformer-style architecture tailored for recommender systems, which jointly models sequential behaviors and feature interactions within a single backbone. Through a unified parameterization, MixFormer enables effective co-scaling across both dense capacity and sequence length, mitigating the trade-off observed in decoupled designs. Moreover, the integrated architecture facilitates deep interaction between sequential and non-sequential representations, allowing high-order feature semantics to directly inform sequence aggregation and enhancing overall expressiveness. To ensure industrial practicality, we further introduce a user-item decoupling strategy for efficiency optimizations that significantly reduce redundant computation and inference latency. Extensive experiments on large-scale industrial datasets demonstrate that MixFormer consistently exhibits superior accuracy and efficiency. Furthermore, large-scale online A/B tests on two production recommender systems, Douyin and Douyin Lite, show consistent improvements in user engagement metrics, including active days and in-app usage duration.
arXiv:2602.16662v2 Announce Type: replace Abstract: LLM-powered AI assistants acting on behalf of users can produce poor collective outcomes at scale. We introduce a framework for evaluating their emergent behaviour in social dilemmas, applied to three iterated games (Public Goods, Collective Risk, Common Pool Resource). We prompt each model to produce a natural-language strategy, then have the same model translate it into code. This aims to isolate strategic reasoning from input-parsing, enables pre-deployment inspection, and scales to populations of hundreds of agents. We propose three analyses: behavioural fingerprinting via exhaustive evaluation over opponent histories; self-play robustness across mixtures of a model's strategies with either a Selfish or Collective disposition; and cultural evolution under payoff-biased imitation. Applied to three state-of-the-art LLMs, we find substantial cross-model differences in self-play welfare, and that cultural evolution converges to low-welfare, Selfish-dominant equilibria in larger groups.
arXiv:2602.17514v4 Announce Type: replace Abstract: Through two-dimensional, three-velocity-component particle-in-cell simulations of freely decaying subion turbulence, intermittent localized regions with $\mathbf{E} \cdot \mathbf{B} \neq 0$ are found, in the early electron-scale interaction phase, to be statistically associated with decreases in $|H_{V_s}|$, the fixed-gauge structure-integrated magnetic-helicity diagnostic. This structure-level behavior coincides with a decline of the Saffman helicity-variance plateau value $I_H$. Motivated by these observations, we propose a source-compensated, history-dependent helicity density that satisfies an exact local balance identity by construction, enabling Saffman-type two-point correlation integrals, which, under standard flux-decorrelation assumptions, can exhibit intermediate-scale plateaus that are roughly time independent. In the simulations, such plateaus are observed to remain approximately invariant over the measured kinetic interval even as $I_H$ evolves during the early kinetic stage. Under approximate single-scale self-similarity, the plateau behavior of the magnetic integral is consistent with the two-dimensional decay constraint $BL \sim \text{const}$. For initially net-helical configurations, we observe rapid development of mixed-signed magnetic-helicity patches and a decrease of the global fractional helicity, such that the decay over the kinetic interval is again most consistent with the cancellation-dominated scaling constraint.
arXiv:2607.01746v1 Announce Type: new Abstract: Recurrent representations are trajectories, but representation geometry is often measured from static snapshots. We develop finite-lag operator geometry for recurrent hidden states from observed source-successor pairs $(X_t,X_{t+\Delta})$. The primitive is the conditional transport law $Q_\Delta(dy\mid x)$, estimated by a dense Gaussian source-smoothing operator. From this directed finite-lag law we derive a source-centered transport tensor $G_\Delta$, which decomposes exactly into conditional spread and coherent displacement, and an antisymmetric coordinate circulation $W_\Delta^\rho$, which summarizes directed lagged flow. We prove affine covariance with explicit metric dependence of scalar summaries, dense estimator stability on bounded trajectory clouds, and a finite-lag separation result showing that source-centered transport detects deterministic recurrent motion not recorded by infinitesimal carre-du-champ geometry. A linear-Gaussian closed form calibrates the quantities in terms of the update $A_\Delta$, source covariance, and innovation covariance. Controlled experiments validate the decomposition, circulation, covariance, and stability predictions. In performance matched repeat-copy networks, the framework reveals architecture dependent differences in total transport scale and coherent displacement trace, while coherent displacement fraction is metric and resolution dependent.
arXiv:2602.18803v2 Announce Type: replace Abstract: We present LoTIS, a model for visual navigation that provides robot-agnostic image-space guidance by localizing a reference RGB trajectory in the robot's current view, without requiring camera calibration, poses, or robot-specific training. Instead of predicting actions tied to specific robots, we predict the image-space coordinates of the reference trajectory as they would appear in the robot's current view. This creates robot-agnostic visual guidance that easily integrates with local planning. Consequently, our model's predictions provide guidance zero-shot across diverse embodiments. By decoupling perception from action and learning to localize trajectory points rather than imitate behavioral priors, we enable a cross-trajectory training strategy for robustness to viewpoint and camera changes. We outperform state-of-the-art methods by 20-50 percentage points in success rate on conventional forward navigation, achieving 94-98% success rate across diverse sim and real environments. Furthermore, we achieve over 5x improvements on challenging tasks where baselines fail, such as backward traversal. The system is straightforward to use: we show how even a video from a phone camera directly enables different robots to navigate to any point on the trajectory. Videos, demo, and code are available at https://finnbusch.com/lotis.
arXiv:2602.20358v2 Announce Type: replace Abstract: The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly interactions such as interviews. We show how to reach interim-stable matchings, under which all matched pairs must have interviewed and agents use expected utilities whenever true values remain unknown, while minimizing both the expected number of interviews and the expected number of interview rounds. We introduce two adaptive algorithms that produce interim-stable matchings: one operates sequentially, and another is a hybrid algorithm that begins by scheduling some interviews in parallel and continues sequentially. Focusing on cases where agents are ex-ante indifferent between agents on the other side, we show that the sequential algorithm performs 2 interviews per agent in expectation. We complement this by showing that any algorithm that performs less than 2 interviews per agent, does not always guarantee interim-stability. We also demonstrate that the hybrid algorithm requires only polylogarithmic expected number of rounds, while still performing only about 2 interviews per agent in expectation. Additionally, the interviews scheduled by our algorithms guarantee an interim-stable matching when Deferred-Acceptance is run after all interviews are completed.