Papers

Training neural networks directly in a low-rank parameterization is an appealing route to reducing memory, compute, and storage simultaneously during both training and inference. Dynamic low-rank training (DLRT), which confines weights to a rank-$r$ manifold via the Galerkin projection of the gradient flow, is particularly attractive because it identifies efficient subnetworks on the fly without specialized initialization or post-factorization. However, DLRT fails to find trainable networks under high compression. In this paper, we derive the gradient flow of the best rank-$r$ approximation and point out that the offset of DLRT comes from a curvature-coupling term which is large and thus non-negligible under aggressive compression. Guided by this analysis, we propose a stable dynamic low-rank training method, named SDLRT, which maintains a lightweight compensation buffer that reinjects the top neglected singular directions. Additionally, we introduce a negative feedback on the truncation tolerance to stabilize each layer's rank. Experimentally, SDLRT reliably finds trainable subnetworks where DLRT collapses and as a PEFT adapter on DeBERTa-v3, it achieves the best average score on SuperGLUE at only $2.8\%$ parameter overhead over LoRA.

In recent work, authors defined $\bar{b}^k_{r,s}(n)$ to be the number of overcolored partition $k$-tuples wherein both even and odd parts are colored with $r$ and $s$ colors, respectively. This function generalizes the overcubic partition $k$-tuples studied by Chacon and Sellers. The present work gives a uniform framework for studying congruences for $\bar{b}^k_{r,s}(n)$ modulo odd primes. For example, we prove that, for $n\ge 1$, \begin{align*} \bar{b}_{4,2}^4(5n)\equiv 0\pmod{5}. \end{align*}

Graph neural networks lose much of their advantage on heterophilic graphs, where connected nodes often carry different labels. Graph rewiring is a popular remedy, but rewiring methods are usually evaluated with a single classifier, which makes it hard to tell whether the gains come from the new topology or from that particular pairing. We propose an affinity-guided rewiring method that estimates the graph and the node representation together. It alternates, in the spirit of expectation maximisation, between training a lightweight graph neural network on the current graph and re-weighting candidate edges under a modularity objective with a pseudo-label homophily term. Candidate edges come from a compact pool scored by a contrastively learned node similarity and a neighbourhood-distribution affinity. The method returns two classifier-independent outputs: a rewired graph and a node embedding learned on it. Across six heterophilic benchmarks and five downstream classifiers, it improves accuracy over the original graph with normalised features in 23 of 30 classifier-dataset combinations, with a mean gain of 5.8 points, and reduces the accuracy spread between classifiers about fourfold. A controlled ablation shows that the two outputs are each useful and play complementary roles: the embedding contributes most of the accuracy gain, while the rewired graph makes different classifiers agree. A fully unsupervised variant, which uses no labels during rewiring, retains most of the improvement. The rewired graphs are also more homophilic and improve label propagation and community detection.

Finding reliable point correspondences is difficult when point clouds have low overlap or undergo non-rigid deformation. Iterative refinement can correct uncertain matches, but costly network evaluations limit the number of updates. We present LevyMatch, a Lévy-driven method that uses random jumps to refine a soft matching matrix. At each step, a network uses the current matching state and geometric information to predict a target matching matrix. A Brownian reference bridge gives an explicit formula for the update toward this target. A Gamma random clock sets the time step for each update. The updated matches provide new geometric feedback for the next target prediction. We further propose a fixed front-loaded Gamma policy that assigns more expected clock time to early updates and less to later ones, without retraining or extra network evaluations. Reordering the same sampled Gamma increments shows that placing larger increments early gives higher accuracy than placing them late. On 4DMatch and 4DLoMatch, our method improves both non-rigid feature matching recall (NFMR) and inlier ratio (IR) over the compared methods. The front-loaded policy achieves 93.09% NFMR and 92.11% IR on 4DMatch, and 82.79% NFMR and 79.07% IR on 4DLoMatch.

The cryptocurrency market's volatility and complex price dynamics challenge portfolio diversification and risk management. This study examines price similarity across 347 cryptocurrencies from March 2020 to April 2024 using daily OHLCV data from the Binance API. Daily dynamics are summarized via a signed, capped intraday price-range metric, and pair similarity is assessed using the Pearson cross-correlation coefficient, capturing linear co-movement at a given lag, and Dynamic Time Warping (DTW) distance, capturing shape similarity independent of lag. Data are segmented into three market phases: an uptrend, a decline, and a subsequent uptrend. For each period, the 10 pairs with highest cross-correlation and lowest DTW distance are identified. BNB-CAKE, XLM-XRP, and MANA-SAND show the strongest cross correlations across the three periods, with coefficients of 0.78 or higher and maximum correlations at lag 0, indicating synchronized movements. Three to four of the ten lowest-DTW pairs coincide with the cross-correlation top 10 per period, showing the measures are related but not interchangeable. Two same-platform fan tokens rank among the most DTW-similar pairs despite weak cross-correlation, while a euro pegged asset and gold-backed token show the lowest DTW distance, driven by low volatility rather than shared dynamics. Results demonstrate substantial, measure dependent interconnectedness with implications for diversification strategies.

Large language models represent context with a key-value (KV) cache. Caches are model-specific: for the same text, models with different architectures or weights produce incompatible representations. This makes it costly to switch models over a shared context: although the context has already been processed by one model, the incoming model must process it again to build its own cache. We introduce KV-Lingo, a method for translating the KV cache of a source model into one that can be read by a target model. KV-Lingo consists of a collection of linear maps, typically one per layer of the target model, that are applied independently on all tokens' key and value representations. We train these maps using distillation, minimising the divergence between the target model's predictions from its native cache and those from the translated cache. We consider several model pairs spanning multiple sizes and architectures, training one translator per pair on a generic text corpus. The resulting translators preserve strong downstream performance in both small-to-large and large-to-small transfers. Since a switch then costs a linear map and a single decoding step instead of a prefill, replacing re-prefill with cache translation reduces the time to first token after a model switch by 9.6x already on a 64-token prompt for Qwen models on an Apple M3 Ultra, and by up to 29x at 32k context length on an H100. These gains make KV-Lingo particularly useful for dynamic model routing: a context can be processed by one model and handed off to another only when needed, without re-prefilling the shared prefix. We finally show that KV-Lingo can be used for seamless model switching, staying close to re-prefill across repeated switches in our multi-turn evaluations.

Pinching-antenna systems (PASS) enable flexible wireless transmission by activating pinching antennas (PAs) along dielectric waveguides. However, existing PASS analyses commonly rely on tractable analytical or statistical channel abstractions that do not jointly capture in-waveguide field evolution, sequential PA power extraction, and site-specific indoor multipath propagation. This paper develops a physics-driven deterministic framework for end-to-end modeling of indoor PASS. Specifically, the parabolic wave equation (PWE) resolves the position-dependent electromagnetic field inside the dielectric waveguide, and coupled-mode theory (CMT) maps the local guided field to the radiation power and phase of each PA. Ray tracing (RT) subsequently models the site-specific indoor electromagnetic propagation from each PA to the users, including LoS, reflected, and diffracted components. To enable efficient repeated evaluations, we combine a reusable PWE-CMT field representation with a physics-assisted neural-network-based RT surrogate that preserves propagation geometry, visibility, and phase information. The proposed framework achieves a complex-channel NMSE of -19.14 dB while reducing the end-to-end single-link evaluation time from approximately 2.5 s to 77 ms. Its application to single- and multi-user deployment demonstrates that the physical model can be efficiently reused for PA-position and power-allocation optimization while preserving the underlying position-dependent propagation physics.

The problem of thermal equilibrium in general relativity is discussed and the unique role played by the fluid associated with the cosmological constant is emphasized. In addition to being the only fluid that is always in thermal equilibrium, it is shown here that its energy can also be seen as a universal quantity given by $E_\Lambda=\rho_\Lambda V$, where $V$ is a spatial volume. Furthermore, if the cosmological constant turns out to be a universal constant, then the conclusion that any spatial volume $V$ has an intrinsic energy follows naturally from the approach considered here. A possible application to quantum theories of gravity that postulate the existence of a minimal length scale is discussed. In studying the energies, the so-called teleparallel equivalent of general relativity is used, and the difficulty with the zero-point energy is discussed in light of the gravitational energy problem. The quasi-local energies of the Reissner-Nordström-de Sitter black hole and of a regular black hole are calculated. The results obtained here with the teleparallel theory are consistent with our expectations.

Spoken conversational systems must recover information from prior interactions (i.e., memory), yet relevant information in speech extends beyond what was said to who said it, how it was spoken, and what was audible, information that exists only in the audio signal and cannot be recovered from a transcript. Beyond what to remember, memory also demands diverse operations: retrieving a single fact, integrating evidence across turns, tracking an evolving state. Real interactions further unfold across sessions, meaning information accumulates across distinct episodes rather than a single continuous recording. Existing benchmarks fall short on all three dimensions: they focus primarily on lexical content, adopt limited and ad hoc memory operations, and treat memory as a single-session problem. We argue that principled memory evaluation requires jointly characterizing the acoustic evidence to be retained and the operations applied to it, and introduce a taxonomy along these two axes. Building on this taxonomy, we present VoxMem: 3,196 evaluation instances over 34,743 spoken sessions (177 hours) crossing four acoustic evidence types (speech semantics, speaker identity, paralinguistic cues, environmental sound) with four memory operations (information extraction, multi-session reasoning, temporal tracking, and answer refusal), grounded in multi-session histories and stratified across context budgets from 8K to 64K tokens. Evaluating 15 LALMs, no model exceeds 40% at 32K. Models retain what was said far better than who said it, how, or what was audible, a gap that widens for complex operations, grows with history length, and manifests as qualitatively distinct failure modes across evidence types. VoxMem aims to provide a foundation to measure and drive progress on the full scope of spoken conversational memory.

We study the problem of approximating the John ellipsoid (JE) of a given (centrally symmetric) polytope of $n$ constraints in a Euclidean space under differential privacy (DP). We give the first differentially private algorithm for this problem under the standard model, where neighboring datasets may differ arbitrarily in one a single constraint. Our work also extends to the complimentary problem of Minimum Enclosing Ellipsoid of $n$ points in the Euclidean space. Our approach is based on the recent non-private multiplicative-weights algorithm of~\cite{pmlr-v99-cohen19a}. First we introduce a non-private generalization of the Cohen et al algorithm, yielding a $(1+\gamma)$-approximation of the JE problem while violating at most $\kappa n$ constraints in $O(\log(1/\kappa)/\gamma)$ iterations. This variant works by projecting the intermediate weights assigned to the constraints onto the set of $\kappa$-dense distributions, similarly to~\cite{bun2020efficientnoisetolerantprivatelearning}. We then design a $\rho$-zCDP variant of this algorithm by adding Gaussian noise to the weighted covariance matrix aggregated in each step of the algorithm. Under a mild goodness assumption on the data we can assert that the resulting noisy matrix is close to the true matrix, thereby achieving essentially the same guarantee as the non-private algorithm provided sufficiently many input points. Thus our method achieves an efficient DP poly-time algorithm under concrete sample complexity bounds.

Networks of interacting Hebbian networks have recently been shown to perform a task beyond associative memory, namely pattern disentanglement: when fed with a spurious mixture of stored patterns, the different modules spontaneously specialize on, and retrieve, the different constituents of the mixture. So far, this capability has only been established for pairwise interactions, which limits the number of patterns that can be handled. Here we introduce a dense extension of these modular networks, in which both the auto-associative couplings within each module and the hetero-associative couplings among modules are promoted to higher-order Hebbian interactions. We show that, with a suitable choice of the interaction orders, the network disentangles mixtures while storing a number of patterns that scales linearly with the module size, a regime where its pairwise counterpart fails. Through a statistical-mechanical analysis based on Guerra's interpolation, we derive the self-consistency equations for the order parameters and draw the phase diagrams identifying the region where disentanglement is achieved; these predictions are confirmed by Monte Carlo simulations. Finally, we show that disentanglement provides a natural decoding primitive, and we illustrate it with two applications: the explicit reconstruction of all the hidden patterns from the Hebbian tensors and a stream of unlabeled mixtures, and a proof-of-concept communication protocol in which each message token is transmitted as a masked mixture of hidden patterns and decoded by the network dynamics. Owing to its attractor-based decoding, the protocol degrades gracefully under strong channel corruption, where conventional secure-transmission pipelines fail abruptly.

As AI increasingly assumes operational control, human-computer interaction is shifting from operating systems through explicit interfaces to inhabiting intelligent environments. This raises a fundamental question: when users no longer directly manipulate a system, what mediates their relationship with intelligent technologies? We introduce environmental interfaces: designed environmental conditions that shape human-AI relationships through ambient, holistic, and evaluative pathways rather than explicit functional interaction. Using autonomous vehicle cabins as a revealing context, we conducted a within-subject experiment with 24 participants (216 observations), manipulating lighting and scent in a simulated autonomous driving environment. Three findings emerged. First, perceived atmosphere accounted for 66.5% of the variance in overall journey experience, showing that environmental conditions can function as an interface rather than merely a supporting design element. Second, multisensory processing followed a hierarchical architecture: individual sensory appraisals were initially independent, while cross-modal integration emerged during higher-order environmental evaluation. Third, olfactory stimuli influenced affective responses and experience evaluation more strongly than visual stimuli, challenging the visual dominance of automotive interaction design. Environmental quality and sensory congruency also predicted trust in the autonomous system, suggesting that passengers may use environmental cues as proxy signals when direct assessment of AI competence is difficult. These findings establish environmental interfaces as a distinct interaction modality and point to a broader transition from designing interfaces for operating intelligent systems to designing environments for inhabiting them.

Quantum information enables many cryptographic primitives that are impossible in the classical world. A line of works has developed cryptographic protocol under the assumption that quantum adversaries are restricted to noisy intermediate-scale quantum (NISQ) computing power, enabling strong one-time functionalities. But the advent of early fault-tolerant quantum computers eras will allow deeper logical quantum circuits, calling into questions the applicability of these NISQ-based assumptions. In this work, we adapt the classically accessible random oracle model (CAROM) as in [BDF+11] and [AK22], in which adversaries are only allowed to classically query the random oracle. The restriction is well motivated for NISQ quantum adversaries and may remain plausible in the presence of early fault-tolerant quantum computers. Then, we show that an efficient simulation-secure one-time memory (OTM) is possible under CAROM. Our protocol uses only BB84 states and has quadratic communication: for a $\lambda$-bit message and integer-valued parameters $n=n(\lambda)$ and $\ell=\ell(\lambda)$, the construction uses $n\ell$ qubits and $(n+2)\lambda$ classical bits, and for any quantum adversary with at most $2^{\ell/2-1}-1$ classical queries to the random oracle, its simulation advantage is at most $(n+3)\left(\frac{3}{4}\right)^n.$ Hence exponentially small simulation advantage in $n$.

Adversarial attacks optimized on a single open-weight LLM can transfer to and jailbreak architecturally different models, allowing an attacker with white-box access to one model to compromise independently deployed systems. This creates a shared vulnerability across models, yet existing defenses are not designed for this cross-model threat. We find that cross-model transfer aligns with shared internal representation geometry, making it a natural defense target. AnchorRep targets this geometry directly with a lightweight LoRA adapter that pushes the defended model's internal representations of harmful prompts away from those of a frozen anchor model on the same prompts. Training uses a small set of harmful prompts and no adversarial examples. Across five models and four architectural families, AnchorRep reduces cross-model attack success rate to <=1.1% on 2,000 transferred attacks (0% on two), including the largest drop on Mistral (36% -> 1.1%). Existing defenses can reduce transfer, but only at high cost either inducing up to 77% degenerate benign output or increasing over-refusal by up to 18%. Because such degenerate benign outputs are not captured by standard refusal-based metrics, we introduce the Benign Garble Rate to quantify them. Our results suggest that cross-model robustness can be achieved by shaping representation geometry, without requiring attack-specific training

Vulnerability-detection benchmarks score the verdict an agent reaches, not the evidence it gathered. A model that recalls a CVE from pretraining therefore scores the same as one that traced the data flow. We study a task where this difference matters, deciding whether a commit introduces a vulnerability. Instead of scoring the verdict, we score whether the agent retrieved the code its conclusion depends on. We present VulContextBench, a benchmark of 111 vulnerability-introducing commits (VICs) across 83 repositories, 63 CWEs, and five languages. Existing datasets label such commits by tracing a fix back through the version history, which often points to the wrong commit. We therefore audit every case by hand against an explicit four-criterion definition of a VIC, so the benchmark does not inherit that label noise. Each case is annotated with gold context, 464 code blocks in total, each tagged by its role in the evidence for the vulnerability. We evaluate seven frontier models with precision, recall and F1 at three granularities (file, block, and line), scored separately on the context an agent viewed while exploring and on the context it finally declared as evidence. The gap between the two is the main finding. Every model opens most of the gold context while exploring, but reports only part of it as evidence. At the level of code blocks, the share of the gold context a model reports is 37 to 73 percentage points below the share it viewed. Qwen3-Coder-Next views 86.3% of the lines in annotated code blocks but cites only 12.9% in its final report. GPT-5.5, which cites the most, views 73% and reports 36%. These results highlight a gap between finding relevant code and selecting it for the final report, which verdict-level benchmarks cannot reveal.

Software development requires more than editing code: developers repeatedly run software, interact with its interfaces, visually inspect its behavior, and use these observations to decide what to change next and whether a change works. Existing coding agents and computer-use agents are largely studied in isolation, leaving this integrated development process underexplored. Diagnosing a runtime interaction failure requires agents to connect visual observations with the responsible code, then use the application again to verify the repair. We introduce CUA-SWE, a benchmark, environment, and evaluation pipeline for software engineering with computer use. Beyond studying how GUI feedback supports diagnosis and repair, we ask whether agents can complete software engineering tasks when required specification or operational information is available only through the running application's visual interface. CUA-SWE spans four software engineering domains and requires agents to modify code and configuration, execute commands, interact with running software, and inspect visual feedback within the same task. Each task includes deterministic, task-specific tests that verify whether the resulting software satisfies the requirements and preserves specified behavior. Our evaluation characterizes how frontier agents combine source-level execution with application screenshots and graphical interaction to produce verified software changes. We examine performance across domains and task information requirements, alongside the development behaviors associated with successful repairs. CUA-SWE provides a unified testbed for studying how agents use visual feedback and interaction to guide software engineering, with executable correctness criteria for the resulting software.

Let $X$ be a quasi-projective scheme of dimension $d$ over an infinite field $k$, such that $X$ is reduced after removing all components of dimension $<d$, and let $X^*\subset X$ be a closed subset of dimension $<d$ such that $X\setminus X^*$ is regular of dimension $d$. Using a modification $\text{CH}^d(X, X^*)$ of the Chow group of 0-cycles on a singular variety defined by C. Weibel and the author in 1985, we construct a Chern class map $c_d:K_0(X)\to \text{CH}^d(X, X^*)$, a cycle class map from $\text{CH}^d(X, X^*)$ onto a subgroup $F^dK_0(X)$ of $K_0(X)$, and prove a Riemann-Roch theorem computing the two compositions of these two maps.

In this paper, we provide a rigorous study of the direct scattering problem proposed by Kodama, Ablowitz and Satsuma for the complete integrability theory of the Intermediate Long Wave (ILW) equation. We derive the Lax operators for ILW, and study their spectral theory. We show finiteness and simplicity of the discrete spectrum, existence and uniqueness of the Jost solutions, and construct the scattering data for the Lax operator. We also show that the Jost solutions satisfy a nonlocal Riemann-Hilbert problem whose singularity data are given by the scattering data, and that the scattering potential can be reconstructed from the Jost solutions. This work paves the way for a solution to ILW via the inverse scattering transform.

Symbolic regression (SR) aims to discover compact and meaningful mathematical equations from data, but searching the vast combinatorial space of symbolic structures remains challenging. Existing methods typically guide this process using expression-level objectives, such as fitting error, which assess a candidate equation as a whole but provide little information about whether an individual term contributes genuinely new structure or is largely redundant with the rest of the expression. We introduce Sobolev Novelty, a term-level measure of structural independence for symbolic equations. For each term, we construct an empirical Sobolev signature from its function values and exact derivatives over the observed inputs, and quantify how much of this behavior cannot be reconstructed by the remaining terms. We further derive a theory-calibrated threshold, yielding a principled and tuning-free criterion for identifying structurally novel terms. Using this threshold, 92.6% of terms in benchmark ground-truth equations exhibit sufficient structural novelty, compared with only 38.3% on average for expressions produced by 15 SR methods, revealing a substantial gap between scientific equations and current SR solutions. As a lightweight plug-in, Sobolev Novelty can be incorporated into diverse SR paradigms to support term pruning, search guidance, LLM feedback, and data selection, yielding consistent performance gains and demonstrating broad applicability.

Feed-forward models regress dense 3D point trajectories directly from monocular video, yet the residual after global alignment is substantial and lacks a structural explanation. Measured on dynamic query points across models and datasets, the error concentrates along the view direction, while the scale correction each motion group requires differs. The predicted displacement direction nevertheless supports reliable grouping, with a median angle far below the 90{\deg} random baseline. The systematic part of the residual is therefore a family of radial degrees of freedom per motion group, along directions 2D observations cannot constrain. We call it group-wise view inconsistency. We present GAUGE (Group-wise Adaptive Unsupervised Gauge Estimation), a training-free and model-agnostic post-hoc module. It recovers motion groups from direction consistency and spatial connectivity, then estimates a per-frame radial scale and group-level translation from 1% to 5% metric anchors, four degrees of freedom per group and frame. On dynamic query points of eight trackers, including D4RT, 4RC and SM4RT, our correction lowers endpoint error by 15.1% to 62.6% over the uncorrected predictions, while spending the same anchors on gradient fine-tuning improves the same models by only -1.1% to 15.2%. Code is publicly available at https://github.com/HCPLab-SYSU/GAUGE.

Safe and robust robot navigation across diverse environments requires a high-level understanding of complex scenes and the ability to carry it into stable motion. Recent works tackle this with learning-based models trained at scale and with approaches built on vision-language models (VLMs). However, learning-based models break down outside their training distribution, while VLM-based approaches bring that understanding but rarely ground it in the scene or align the action with it. To address these limitations, we present RECAST, a robot navigation framework that combines the reasoning of a VLM with the spatial grounding of vision foundation models to build an Actionable Cost map. Given the robot's front view and the user's instruction, we first decompose the scene with the VLM, judging which surfaces are traversable, which objects pose a risk, which heading to prefer, and which gaps are passable. Vision foundation models then ground these surfaces and objects in the image, and all four judgments are spatially recast into one compact cost map. This map both conditions the trajectory decoders and scores their proposals to select the one to execute. As the VLM's answers trail the live scene, both steps draw on cost maps from two points in time: the pivot frame the VLM judged, which carries all four judgments, and the current frame, whose terrain and collision costs are rebuilt from the current image. RECAST improves success over the strongest prior method by 13.3 points in simulation and 31.4 points on a real quadruped, and reduces the collision rate relative to it by 9.6 and 14.3 points, reaching the lowest collision rate among all methods. The project page is available at https://recast-nav.github.io/

Multi-agent flow policies learn cooperative behavior from fixed offline datasets, but often struggle to complete tasks in situations not covered by the offline data. In these situations, agents must both adapt to changes in the environment and coordinate with one another, yet action patterns learned offline are often insufficient for effective adaptation and coordination. To address this problem, we propose Multi-Agent Flow-Pretrained Policy Optimization (MA-FPPO), which uses online fine-tuning to improve the cooperative behavior of models pretrained with flow matching through new interactions with the environment. Building on the behavior learned during pretraining, we construct policies with explicit action likelihoods for discrete and continuous action spaces. We then update the pretrained model using shared team advantages to further improve coordination based on team performance. Our method achieves, on average, relative gains of 52.8% over the strongest listed offline baselines across 30 settings and 29.8% over purely online learning across 38 comparisons with matched online budgets and evaluation protocols.

Current machine learning algorithms primarily rely on instantaneous signals such as loss, margin, and prediction confidence to characterize model behavior. These signals indicate how difficult a prediction is at the current optimization step, but they do not capture how long the model has remained incorrect. We study this temporal dimension of learning and introduce Age of Learning (AoL), a learning-state variable that measures the persistence of prediction errors over time. AoL increases while an error remains unresolved and resets when a correct prediction is achieved, thereby distinguishing persistent under-learning from transient mistakes. We develop AoL-based training strategies for both offline and streaming settings. In offline learning, sample-level AoL is accumulated over training and aggregated into class-level states that guide adaptive reweighting and resampling. In streaming learning, where full historical access is unavailable, we maintain lightweight class-level AoL states using current and buffered observations. Across long-tailed classification settings, AoL improves or matches standard training baselines, with larger benefits when learning difficulty persists over time. Multi-seed streaming experiments further show reproducible gains under temporally stable imbalance. Analysis of class frequency, loss, and margin shows that AoL is related to conventional difficulty measures but captures additional information about error duration. These results suggest that temporal persistence provides a useful complementary signal for characterizing and controlling learning dynamics in imbalanced and non-stationary environments.

Fixed-capacity streaming video memory requires repeated eviction decisions whose effects accumulate over time. Yet existing policies are evaluated primarily in terms of retained information or downstream accuracy, leaving how repeated updates alter the futures supported by memory largely unexamined. We define a memory's predictive state as the future representations supported by its retained history and formulate eviction as counterfactual control over transitions in this space. We introduce SPACE (Sparse Predictive Attractor via Counterfactual Eviction), which uses a frozen multi-horizon JEPA to predict the future representations induced by alternative eviction actions. Counterfactual utility identifies future-useful alternatives, while slow predictive-basin geometry determines when to correct avoidable drift and when to adapt to sustained predictive change, without online parameter updates. We further introduce MABS-Bench, which evaluates future-task sufficiency, within-regime predictive stability, transition responsiveness, and perturbation recovery under matched causal streams and memory budgets. Across multiple video datasets, SPACE yields consistent improvements in dataset-native task performance while reducing predictive-state drift.

Data-driven model predictive control (MPC) combines learned world models with online trajectory optimization, achieving strong performance in continuous control. However, the per-step cost of sampling and evaluating hundreds of candidate trajectories restricts deployment to control frequencies well below what real-time robotics demands. Motivated by the dual-process theory of human cognition, which distinguishes between fast, intuitive processing (System 1) and slower, deliberative reasoning (System 2), we ask whether every decision requires the same degree of computational deliberation. We propose Fast-TD-MPC, a lightweight framework that adaptively routes between fast policy execution and test-time planning, reserving costly deliberation for states where it is most needed. Fast-TD-MPC delivers competitive task performance across 103 continuous control tasks while achieving up to ~4x faster inference. Under external disturbances, Fast-TD-MPC selectively falls back to planning, maintaining robustness comparable to the original planner.

Work on memory for multimodal agents optimizes what is written, updated and retrieved. Between retrieval and the answer, however, is a stage that multimodal memory evaluations do not isolate: what of the retrieved memory reaches the model, and in what form. We call it delivery, and a controlled decomposition on MemLens locates the remaining room there. With the retrieved evidence set exactly fixed, delivering the original pixels instead of withholding them raises accuracy by 13.87 points on an 8B backbone, whereas making retrieval perfect on those same messages improves it by 2.31. Delivery is the larger term on all three MemLens backbones and grows with backbone strength; retrieval grows too, without closing the gap. We propose DeliverMem, an instantiation of delivery as three decisions: keep the original modality, give each item a readable identity, and state when it was seen, with a retrieval-side adapter for the one property delivery cannot supply. Each is measured against a delivery-matched control that alters only its own variable. DeliverMem leads the strongest published memory agent on MemLens at all four context lengths, and beats DMV-Bench's own strongest method at every setting on both backbones. On MemLens it does this on a tenth to a seventieth of the input. Each decision helps only where the question lacks what it supplies, and is null elsewhere. A single fixed configuration nonetheless leads both benchmarks, without training any component or modifying the stored records. Project page: https://avalon-s.github.io/DeliverMem/

The least regular norm of a factorization of antipodal differences through sign differences on \((\mathbb Z/m\mathbb Z)^n\) is \(m/2\) when \(4\mid m\). On these tori, when \(2\sqrt n\le m\le4\sqrt n\), normalized divergence equations admit selections with pointwise norm bound \(3/2\), while the least linear lifting norm and global Lipschitz selection constant equal \(\sqrt n/2\). Higher-moment lifting bounds follow from a quoted sharp \(L_1\) inequality.

We study the fractional perimeter per period of planar sets with prescribed horizontal period and area per period. We prove that sufficiently wide strips are the unique minimizers among all measurable competitors, up to vertical translation and null sets. For period one, a half-width of at least $14$ suffices for every fractional exponent $s\in(0,1)$. The proof first replaces each vertical section by a centered interval of the same length. We then establish a quantitative lower bound for the perimeter excess in terms of the deviation of the resulting half-width profile from its mean. The main difficulty is that the perimeter of a strip is a concave function of its width. We show that, at large mean width, the interaction cost of unequal sections dominates the corresponding concavity deficit and leaves a positive remainder for every nonconstant profile. Estimates at small and large horizontal separations make the sufficient width bound independent of $s$. The argument applies to arbitrary nonnegative integrable profiles, including unbounded profiles and profiles that vanish on sets of positive measure.

We prove that any block of a profinite group with a topologically finitely generated defect group $D$ is isomorphic to a block of a virtually pro-$p$ group, and if $D$ is finitely presented then so is the basic algebra of the block over $k$. Using these general results we then prove that any block with defect group $D=\mathbb Z_p^n$ is Morita equivalent to $\mathcal O_\alpha[[\mathbb Z_p^n\rtimes E]]$ for a finite $p'$-group $E$ acting faithfully and a $2$-cocycle $\alpha\in H^2(E,k^\times)$. In particular, Donovan's conjecture holds for such blocks of profinite groups.

We investigate the internal structure of the newly observed charm-strange meson $D_{s1}(2933)^{+}$, which was reported by the LHCb Collaboration in $B^{0}\to D^{+}D^{-}K^{+}\pi^{-}$, in the quark model by treating it as the $2P_{1}$ state of the $c\bar{s}$ system. The coupled-channel corrections to the ${}^{1}P_1$–${}^{3}P_1$ mass matrix are evaluated through the two-point self-energy loops involving the $DK^{*}$, $D^{*}K$, $D^{*}K^{*}$, $D_{s}\phi$, $D_{s}^{*}\phi$ and $D_{s}^{*}\eta$ intermediate channels. Requiring the corrected eigenvalue to reproduce the measured mass yields a cutoff scale of about $0.82~\mathrm{GeV}$, a $2P_{1}^{\prime}$ partner state at $3012~\mathrm{MeV}$, and a mixing angle of $-12.9^{\circ}$ that deviates significantly from the heavy-quark ideal-mixing angle. Moreover, the predicted three-body branching ratio fraction $R_{\text{th}}=1.98$ for $D_{s1}(2933)\to D^{+}K^{+}\pi^{-}$ via the $DK^{*}$ and $D_{2}^{*}K$ intermediate states is consistent with the experimental value $R_{\text{exp}}=1.27^{+1.29}_{-0.95}$ within uncertainties. These results support the assignment of $D_{s1}(2933)$ as the $2P_{1}$ excited state of the $c\bar{s}$ system with final state interactions.