Papers

Soft Actor-Critic (SAC) is widely used for entropy-regularised reinforcement learning with continuous action spaces, and practical implementations perform only a few actor steps towards an evolving target. In this work, we prove convergence guarantees when the target policy arises from policy mirror descent and compare it with the classical Gibbs target. We derive sufficient conditions for the strong convexity and smoothness of the actor objective, characterised by the curvature of the $Q$-function estimate through the Legendre differential operator, and establish an $\mathcal{O}\!\left(N^{-\frac{1}{5}}\right)$ best-iterate finite-time convergence rate up to actor and critic approximation errors. Moreover, the mirror-descent step size $\lambda$ directly controls the target drift and hence actor tracking error, whereas the analogous Gibbs bound contains a non-vanishing tracking term.

Leech-lattice quantization gives good quality at two bits per weight, but its codebooks hold more than 10^14 points, too many for a lookup table. Our earlier kernel expanded the codes at load time and read 4.804 bits per weight from GPU memory for 2 bits of code. We present Tetra, a new codebook on the same lattice. A 24-weight block still takes 48 bits, most of which index a 64-state trellis of the Golay code and one shared 16 KiB table. The kernel decodes a block with six table loads and two small lookups inside the matrix-vector product, and reads 2.148 bits per weight. For full models, we retrain one scale per matrix row, store the matrices that lose the most as 4-bit integers, and pay for them with 4-bit embedding tables. Our Qwen3-4B, 8B and 14B files hold 2.73, 2.70 and 2.73 bits per parameter over the whole model. They score 63.37, 69.58 and 75.66 on the full MMLU test set, 4.76, 4.21 and 2.46 points below 4-bit AWQ at 5.3 to 6.0 bits per parameter. They generate 113.8, 95.0 and 57.2 tokens per second in our engine. On GSM8K, through the served kernel, they lose 9.63, 4.62 and 3.26 points to FP16. At 4B our file scores 23.6 points above llama.cpp's IQ2_XXS (2.48 bits per parameter). Every number we measured for a table or figure comes from one NVIDIA L40S GPU. We preregistered the main experiments.

Images capture the world at one moment, whereas video reveals how it changes. Image self-supervision learns spatial structure from a single moment, while video methods commonly learn temporal relationships inside a representation computed jointly from several frames. We ask whether watching a scene change can instead improve features available from one image without sacrificing the ability to represent video. We introduce W2Rep, a masked feature-prediction framework in which an independently encoded source image participates in prediction at the same or another moment. The predictor is conditioned on visible video context, the queried location, and the signed time interval between source and target. This gives the cross-frame objective two complementary roles: the image path learns features that remain useful across time, while the video path must gather evidence that is missing from the source image. Across model scales and downstream tasks, W2Rep improves frozen and fine-tuned recognition under our comparison protocol, while joint video encoding provides further gains over frame-wise aggregation. Controlled experiments show that these gains depend on directly updating the source-image features and on using both video context and temporal displacement. Overall, change across a video can supervise a visual encoder whose representations remain useful at either image or video granularity. Code is available at~\href{https://wenooi.github.io/W2Rep}{https://wenooi.github.io/W2Rep}.

Creating believable vh requires the coherent integration of perception, reasoning, and action mediated by language. A central challenge is to combine these components into a control loop grounded in interactive 3D environments. To this end, we present A.D.A.M.O. (Agent for language-Driven Actions with Multimodal Observations), a visual-symbolic framework for language-driven vh that leverages a pretrained vlm with tool calling to unify perception, reasoning, and action within a single control loop. A.D.A.M.O. maintains a dual visual-symbolic world model that combines egocentric visual input and synchronized symbolic state to support grounded task-oriented behavior from natural language prompts. To support diagnostic evaluation, we introduce a controlled task suite organized by a cd taxonomy that breaks down spatial tasks into procedural and linguistic complexity. Experiments in controlled scenes show that semantic labeling strongly influences task completion and failure modes, reducing perceptual ambiguity while shifting failures toward downstream execution, whereas reasoning errors remain comparatively rare.

Patients often have several co-occurring clinical conditions, and the findings needed to identify and disambiguate them emerge over the course of a consultation. Evaluating clinical reasoning in this setting requires both multi-turn interaction and multi-label diagnosis. We introduce CLIMB, a benchmark in which a doctor model interviews a simulated patient to recover a ground truth set of co-occurring clinical conditions. Cases are synthesized from clinical decision algorithms and diagnostic datasets, grounding multimorbid presentations in structured clinical knowledge. Across six frontier and open models, none recovers the exact set of conditions in more than 10% of interactive cases. Diagnostic performance declines when conditions co-occur, even when models receive the full clinical record and the true number of conditions. Interaction reduces performance further. In controlled experiments, models behave like single-hypothesis trackers: they anchor on the diagnosis suggested by the opening findings, keep questioning around it, and recover a second condition mainly when a finding in view points to it. Questioning them further does not complete the set but adds mostly wrong diagnoses. We formalise this pattern with a theoretical reference model of single-hypothesis tracking. The benchmark, generator, and evaluation code are available at https://anonymous.4open.science/r/CLIMB-8340.

As Large Language Models (LLMs) continue to scale both in size and capabilities, their proficiency in the Arabic Language has seen significant advancement. However, a critical gap remains: the extent of their factual knowledge and cultural sensitivity to the diverse Arabic-speaking world remains largely underexplored. Current evaluation metrics often focus on translation or generic reasoning, failing to capture the rich historical, social, and regional nuances inherent to Arabic culture. In addition, most benchmarks rely on heavy work, with human intervention in some steps, making the evaluation of knowledge coverage expensive and slow. To address this deficiency, we introduce AraDynFact, a novel dynamic evaluation framework designed to rigorously assess the factual Arabic knowledge embedded in LLMs. Unlike static benchmarks, AraDynFact employs a dynamic approach to extract factual information and generate rich and answerable questions in a fast and automatic way. We apply AraDynFact to Arabic Wikipedia and audit the performance of several state-of-the-art models, ranging from Arabic-centric specialized LLMs to high-resource general purpose LLMs. In addition we found a high degree of correlation with existing, hand-crafted Arabic-centric benchmarks, confirming the potential of our dynamic approach.

We solve Conjecture 1.6 of Furio and Lombardo [On $7$-adic Galois representations for elliptic curves over $\Q$, Proc.\ London Math.\ Soc.\ (3) 133 (2026), e70193.]. As a consequence, we complete the classification of $7$-adic Galois images for non-CM elliptic curves over $\Q$. This is the first solved case in Problem 6.2 from Balakrishnan [Chabauty and beyond: Explicit p-adic methods for rational points, Proceedings of the International Congress of Mathematicians 2026 - Volume 3: Invited Lectures (Sections 1-4), 321-341, 2026]. The proof is the result of a long AI-training period by the author from June 2026 to September 2026. The author has been working on this project alone without the help of any other.

Large Language Model (LLM) reprogramming-based beam prediction demonstrates strong data efficiency by adapting pretrained language models for vehicle-to-infrastructure (V2I) beam prediction, yet the resulting model complexity makes such approaches impractical for latency-sensitive deployment. We propose LLMBP-Lite, a compact LLM-reprogrammed framework for beam prediction. It leverages structural redundancy through pruning along three complementary dimensions: Transformer depth, source-prototype vocabulary size, and prompt length. Additionally, knowledge distillation can be optionally employed to maintain the pretrained representational capacity after compression. Experiments on the real-world dataset demonstrate that LLMBP-Lite achieves a $65\times$ inference speedup over the uncompressed LLM-based baseline while maintaining prediction accuracy and consistently outperforming recurrent baselines under limited training data. These results demonstrate that the tradeoff between data efficiency and deployment efficiency can be substantially mitigated in vehicular networks.

In the context of precision physics, the resummation of large logarithms of the variable $x = Q^2/s$ is increasingly relevant at high energies. We report here preliminary results on the extension of the differential resummation formalism within the HELL framework to Higgs boson production via gluon fusion.

Most modern multimodal large language models (MLLMs) build on a pretrained visual encoder that provides a strong visual prior. Encoder-free MLLMs instead learn visual representations directly from raw pixels, offering a simple and unified architecture, but their scaling behavior has not been systematically characterized. To fill this gap, we compare scaling laws for encoder-free and encoder-based MLLMs and report three main findings: (1) Removing the visual encoder shifts the compute-optimal allocation for the multimodal objective toward larger models, while leaving that for text nearly unchanged. (2) The two architectures exhibit nearly overlapping loss–compute frontiers on the text objective, but diverge on the multimodal objective: encoder-free models underperform at small scales yet are predicted to catch up at around $10^{22}$ FLOPs, well within practical pretraining budgets. (3) Without a visual encoder, the language model learns to take over its role via vision-specific adaptation: bidirectional interactions among visual tokens become increasingly beneficial as training compute grows, visual processing shifts toward earlier layers, and expert routing for visual tokens becomes more concentrated. Overall, our results indicate that the advantage of the visual prior provided by a pretrained encoder diminishes with scale, positioning encoder-free architectures as a promising direction for multimodal pretraining.

EEG-based brain-computer interfaces support a broad range of applications, yet designing decoding architectures that perform well across diverse tasks remains challenging. We introduce AutoBCI, an agentic framework in which a Designer Agent and a Forecaster Agent support the discovery and selection of EEG decoding architectures across tasks. The Designer Agent performs Pool-Guided Architecture Discovery (PGAD), generating and refining architectures through training and validation across multiple EEG tasks, such as emotion recognition, motor imagery, and sleep staging. The Forecaster Agent performs Performance Estimation from Early Knowledge (PEEK), using architecture code, the training protocol, and early learning curves to predict full-budget validation performance and select promising candidates for continued training. Across 14 EEG datasets spanning motor imagery, emotion recognition, and sleep staging, we evaluate AutoBCI with six LLMs, including Opus 5.5 and GPT 5.6 Sol, and compare the architectures selected by the search procedure against ten baselines: six conventional EEG models and four foundation models. The architecture discovered by AutoBCI with Claude Opus 5.5 achieves 64.16% average test balanced accuracy (bAcc), compared with 63.87% for REVE, the strongest baseline on this metric. Using ten observed epochs, PEEK reduces mean absolute error in predicting average validation bAcc from 2.20 to 1.36 percentage points, a 38.1% reduction relative to the best-observed-score baseline. Code is available at https://github.com/Jiang-Muyun/AutoBCI

We study the asymptotic behavior of large-spin operators in conformal field theories by placing the theory on a pp-wave background. In this setting, the diagonal three-point coefficients involving two large-spin operators and a light operator are mapped to thermal one-point functions on the pp-wave. We predict these one-point functions in the two complementary regimes of high and low temperature, corresponding respectively to the total twist parametrically above and below an appropriate spin-dependent scale. In particular, at high temperature, we derive their asymptotic behavior using thermal effective field theory, while at low temperature, we obtain universal formulas that can be matched directly to predictions from the analytic bootstrap. We test these results in free theories on the pp-wave. Finally, we solve the large-$N$ $\mathrm{O}(N)$ model numerically, finding agreement with our predictions for both the one-point function and the free energy density in the high- and low-temperature regimes.

Flow matching (FM) learns generative dynamics through velocity regression. Geometric FM variants commonly assume a prior supported on the data manifold, requiring geometric knowledge that is often unavailable. Without such knowledge, low regression error alone does not guarantee manifold adherence. Adherence keeps generated samples within valid configurations and is empirically associated with better task performance. We introduce manifold-stable flow matching (MSFM), which can start from an arbitrary ambient prior, not necessarily supported on the manifold. Using tools from nonlinear dynamics, namely contraction theory, MSFM combines learned tangential transport with prescribed normal contraction. The construction uses analytical projectors for known manifolds and local affine proxies estimated by principal component analysis for unknown data geometry. By implementing contraction theory in both cases of known and unknown manifolds, we guarantee manifold invariance and transverse convergence to the manifold within a desired time window (e.g., one second). We derive a family of compatible probability paths and decompose the training loss into a learnable tangential term and a normal residual. An ellipse experiment attains a mean terminal off-manifold error of order $10^{-6}$. In Push-T robotic experiments, MSFM raises success from $74\%$ to $82\%$. In the Robomimic Square task, success increases from $60\%$ to $72\%$, while rotation-manifold deviation decreases from order $10^{-2}$ to $10^{-7}$. The MSFM terminal geometric errors are controlled by the chosen numerical tolerance. These results demonstrate stronger geometric adherence and higher observed task performance, supporting prescribed normal contraction as a complement to learned generative transport.

The Frieze-Jerrum rounding is a standard tool for rounding SDP relaxations of graph partitioning and clustering problems, assigning nodes to at most $k$ clusters using $k$ independent Gaussian vectors. Its analysis hinges on the collision probability $P_k(\rho)$ that two nodes whose SDP vectors have inner product $\rho$ are assigned to the same cluster. No tractable closed form for $P_k$ is known for $k\geq 4$, making it difficult to certify approximation guarantees and hindering the systematic search for better algorithms. We develop a Hermite-coefficient certification framework to derive accurate and tractable bounds on $P_k$. Using the Hermite expansion of Gaussian noise stability, we express $P_k$ as a power series with nonnegative coefficients, reduce these coefficients to one-dimensional Gaussian integrals, and certify finitely many of them, yielding rigorous bounds on $P_k$ over the entire correlation range. Our framework yields strengthened polynomial-time approximations for several clustering problems. For MaxAgree Correlation Clustering, we derive a $0.7818$-approximation, the first improvement in two decades over the $0.7666$ ratio of Swamy (2004). We also improve the best known ratios for the variant with at most $K$ clusters, MaxAgree$[K]$ (e.g., from $0.77$ to $0.8151$ for $K=3$). For Max $K$-Cut we resolve, via a structural property of the Hermite expansion, a conjecture of de Klerk et al. (2004) characterizing the Frieze–Jerrum approximation ratio for every $K\ge3$; we show that this ratio is tight, and determine it to within $10^{-6}$ accuracy for $K\le16$. Finally, we reduce the additive approximation error for modularity maximization from $0.42084$ (Kawase et al., 2021) to $0.3790$. On the hardness side, we show that approximating Maxagree within $0.802+\epsilon$ is Unique Games-hard via a construction in Gaussian space analyzed by Borell's inequality.

Courant–Hilbert (CH) deformations unify broad classes of solvable stress-tensor flows including $T\bar{T}$ and root-$T\bar{T}$. However, a gravitational action that systematically yields such general deformations has remained unknown. In this Letter, we construct a two-dimensional massive gravity theory whose on-shell action reproduces the complete CH deformation. The gravity sector is defined via an arbitrary function of the eigenvalue ratio $y$ of the relative zweibein. To bypass the technical difficulty of directly eliminating the auxiliary zweibein, we reformulate the matter sector using a $2 \times 2$ spectral decomposition involving $y$ and a rank-one projector $K$. Sequentially solving the equations of motion—first for $K$ and subsequently for $y$—naturally maps the system onto the Russo-Townsend form of the CH flow. Our work extends Tolley's massive gravity formulation of $T\bar{T}$ flows to the CH landscape, providing a clear geometric mechanism for solvable stress-tensor flows.

Zhang and Yeung (IEEE Trans. Inf. Theory, 1998) established the first non-Shannon-type inequality that holds for all entropic vectors. Chan and Yeung (IEEE Trans. Inf. Theory, 2002) showed that there is a one-to-one relation between linear entropy inequalities and multiplicative inequalities involving cardinalities of subgroups of a finite group. The Shannon inequality admits a simple proof in the group theoretic setting, but a direct proof of the translation of Zhang–Yeung's inequality to the group-theoretic setting remained elusive. We resolve this open problem, giving a direct proof of the group-theoretic Zhang–Yeung inequality for cardinalities of subgroups of finite groups, using elementary group-theoretic and counting arguments.

Physical contact often determines how a humanoid should respond during loco-manipulation, yet vision and proprioception alone are often insufficient to characterize physical interaction, especially when the contact region is occluded. Unlike sparse force or torque measurements at predefined regions, distributed tactile sensing preserves spatially resolved contact patterns across the robot body. We therefore study how to integrate such whole-body tactile information into vision-language-action (VLA) policies for contact-rich control. Our approach, Uni-VLaT, introduces a tactile pathway whose latent state is trained not only for action generation, but also to predict future tactile, proprioceptive, and visual representations. This predictive objective builds a tactile-anchored multimodal context, encouraging a more structured understanding of the physical world. We evaluate Uni-VLaT on five real-robot tasks covering tactile-triggered locomotion, sustained physical interaction, human-robot contact, and loco-manipulation. Uni-VLaT achieves a 75% average success rate, outperforming a baseline without tactile input by 43 points and a tactile-input baseline without predictive supervision by 7 points. Across two pretrained VLA backbones, our method improves Table Sweeping by 30 points on both backbones and Back-Tap Walking by 85-90 points. Ablations further show that contextualized tactile prediction and absolute future targets are critical to performance. These results indicate that predictive tactile learning provides an effective route for extending pretrained VLA policies to whole-body physical interaction.

With limited annotation budgets, choosing which images to label determines how much a model improves. Data-selection methods that use features from a separately trained model, or scene descriptions written by vision-language models, have been successful, but those signals do not directly capture changes in the model being improved. The target model's own internal features reflect what it has learned so far and change with retraining, making them a natural cue for choosing the next training data. However, feature rarity alone does not reveal the errors that matter for performance. Here we link internal features to prediction errors and their expected impact on performance and select images for labeling and retraining without using labels for candidate images. We evaluated the method with an object detector on two datasets and two pairs of random seeds. Adding internal features improved the identification of prediction errors in 15 of 16 conditions. When performance was averaged over successive labeling rounds, the method outperformed selection based only on feature rarity in all four evaluation settings and ranked among the top two of six methods. With other conditions held fixed, performance after retraining was again higher than with rarity-based selection, even though the latter collected more errors. With longer retraining, the proposed method ranked first among six methods. These results suggest that linking a model's internal features to its errors and their effects on performance may help select training images that improve performance, thereby allowing the model's current state to guide which images are labeled next.

Refugee integration is a central policy challenge for host countries, and where governments initially place refugees shapes their integration trajectories. Yet placement officers often have limited information about where each case is most likely to succeed. Algorithmic refugee matching uses administrative data, machine learning, and constrained optimization to recommend employment-optimized placements in real time as cases arrive, with human placement officers retaining final authority. Between January 2020 and June 2023, the Swiss State Secretariat for Migration randomly assigned about 2,000 refugee cases to receive a canton recommendation either algorithmically optimized for employment or drawn to approximate existing procedures, with placement officers and refugees blinded to assignment. The two arms used identical but separate canton and origin-group quotas, so gains reflect better refugee-canton matching rather than reallocation toward stronger labor markets. The trial began just before the COVID-19 pandemic shifted labor-market conditions. For the pre-registered primary outcome – the share of months employed during the first three years – the pooled intention-to-treat (ITT) estimate across the 2020-2023 placement cohorts was +2.2 percentage points (about 10% of the 22.3% control mean; 95% CI [+0.05, +4.33]), rising to +3.9 pp (about 17%; [+1.11, +6.68]) for the post-COVID 2022-2023 cohorts. Effects grew over time: at 36 months, the pooled ITT on the employment rate was +5.2 pp (about 11%; 95% CI [+1.10, +9.25]) – comparable to the gains from hundreds of hours of intensive language training. Overall, the results provide rare field evidence that AI-based decision support can improve high-stakes public-sector allocation, offering a scalable, low-cost way to raise refugee employment.

Boson Sampling is a prominent candidate for the demonstration of quantum computational advantage but it remains unclear whether a large-scale boson sampler can find useful computational applications. The challenge is that to use a boson sampler to estimate, for example, a physical observable, it is necessary to coarse grain the outcome distribution, owing to the exponential size of the outcome space and the anti-concentration properties of the Boson Sampling distribution. In this work, we analyse the complexity of a specific type of coarse-graining of Boson Sampling distributions based on linear functions of the output photon occupation numbers, which we refer to as linear statistics. We present an efficient classical algorithm for approximating linear statistics of boson samplers within additive error for different kinds of input states, such as Fock states and squeezed states. This allows us to unify in the same framework recent results on efficient quantum-inspired classical algorithms for simulating molecular vibronic spectra, or efficient classical approximations of coarse-grained distributions based on detector binning. Additionally, we show how our algorithm can be used to classically evaluate a proposed one-way function based on Boson Sampling, while other proposals for cryptographic applications escape our classical simulation techniques. We leave open the question of classical simulability of non-linear statistics and connect it to the problem of computing transition amplitudes of linear-optical circuits with one layer of interactions.

We establish a fully static, dissipation-only primitive for Gaussian state transfer in which collective coupling to a shared environment fixes a single transfer time without coherent transport or time-dependent control. The dynamics close in a bright–dark decomposition, yielding an analytic transfer time $t^{*} = \pi / g_{a}$ and a real interference factor that eliminates dynamical phase accumulation, so that all phase sensitivity arises solely from the Gaussian fidelity metric. This defines a fixed-time Gaussian communication channel in which dissipation mediates information transfer without active control. Ensemble analysis shows that channel performance remains robust to amplitude-level asymmetries, which act as uniform-rate dressing, whereas phase-level system detuning disrupts the fixed-time mechanism via dynamical phase winding and produces revival behavior. Incorporating finite Ornstein–Uhlenbeck memory via a zeroth-order O-operator expansion yields only rate and phase renormalization without introducing new dynamical pathways. In the fast-memory regime, environmental correlations are rapidly suppressed, rendering the channel insensitive to environmental detuning and restoring the Markovian limit. These results show that collective dissipation alone is sufficient to support fixed-time Gaussian state transfer, challenging the assumption that coherent transport or active control are required for continuous-variable communication.

Effective central nervous system (CNS) intervention requires more than predicting biological responses: a scientific system must determine which intervention, observation, or additional evidence can improve a decision under uncertainty. However, in partially observed neuronal microenvironments, identical predicted outcomes may correspond to different exposure states, biological mechanisms, and intervention risks. We propose NeuronSifter, a decision-centric Agent-in-Twin framework, where an AI agent operates with an evolving biological digital twin rather than a fixed predictive model. NeuronSifter compiles interventions into state-conditional target-occupancy representations, propagates them through a mechanism-grounded World Action Model (WAM), and selects informative measurements based on their expected reduction in decision uncertainty. A shared probabilistic belief state couples intervention simulation, observation selection, and outcome assimilation, enabling the digital twin to continuously refine its decision-relevant representations through externally verified evidence. We evaluate NeuronSifter in Alzheimer's disease intervention scenarios using mechanistic neuronal microenvironment simulations and retrospective clinical endpoint references. The evaluation framework examines adaptive evidence acquisition, uncertainty-aware intervention planning, and robustness under model discrepancy through controlled environments and independent comparisons. NeuronSifter demonstrates how an AI system can actively identify missing evidence, refine biological hypotheses, and optimize intervention decisions under limited experimental budgets. Code is available at https://anonymous.4open.science/r/NeuronSifter.

Robust skeleton-based action recognition requires representations that capture a wide spectrum of motions, from subtle to moderate and strong ones. Existing methods often focus on strong motions. This paper introduces DiMoP, a masking- and diffusion-driven motion representation learning method with frame-level pseudo-classification to explicitly learn the distribution of joint motions rather than regressing deterministic coordinates, as existing methods often do. By diffusing masked joints with progressive noise and denoising them conditioned on visible joints, DiMoP learns through controllable noising and denoising processes, enabling uniform learning of weak, moderate, and strong dynamics. To enable the masking-based generative diffusion learning with a discriminative capability, a pseudo-frame classifier is proposed that enforces the learning towards sequence-consistent and temporally coherent pseudo-labels without manual annotations. Together, these strategies provide a principled mechanism for joint generative and discriminative motion modeling. DiMoP achieves state-of-the-art performance across NTU RGB+D 60/120, and PKUMMD, including a 1.1 percentage point gain over prior works on NTU RGB+D 120 with the cross-subject protocol.

Large-scale routing problems are difficult to solve efficiently as their search spaces grow rapidly with problem size. Existing approaches primarily improve the optimization procedure itself, often at increasing computational cost. We instead shift the focus to a useful initialization that can be refined into a high-quality solution with limited downstream refinement. We propose Just Initialize, a training-free and solver-agnostic initialization component for large-scale routing optimization. Just Initialize compresses a large routing instance into a compact surrogate space, optimizes its global routing structure, and recovers the resulting solution as an optimization-friendly starting point in the original space. Extensive experiments on Traveling Salesman Problems (TSPs), Capacitated Vehicle Routing Problems (CVRPs), Vehicle Routing Problems with Time Windows (VRPTWs), and Prize-Collecting Traveling Salesman Problems (PCTSPs) demonstrate that Just Initialize achieves high-quality solutions comparable to or better than state-of-the-art methods while substantially reducing computational cost across instances ranging from 1K to 100K nodes, including an average speedup of approximately 70$\times$, sub-second runtimes on 10K-node instances, and runtimes within tens of seconds on 100K-node instances.

Let C be a non-singular real algebraic curve of genus g. The real structure on C induces a real structure on the configuration space of n distinct unlabeled points on C. We prove that this configuration space is maximal (in the sense of the Smith-Thom inequality) if and only if C is maximal or the genus of C is zero and n is even.

State space models (SSMs) achieve efficient sequence processing because their affine state updates are closed under composition and can therefore be evaluated with an associative parallel scan. Nonlinear recurrent models can provide richer, state-dependent dynamics, but generally lose this compositional structure: parallel evaluation then requires iterative methods that repeatedly linearize and scan the recurrence. We ask, what state-dependent nonlinear dynamics can be designed to remain exactly composable? We answer by introducing RiccatiSSM, a nonlinear SSM, in which each state dimension follows an input-conditioned Riccati differential equation. Its quadratic state dependence makes the local Jacobian explicitly state-dependent, while its exact per-step flow under piecewise-constant inputs is a Möbius transformation. Since Möbius maps are closed under composition and compose through $2\times 2$ matrix multiplication, the complete nonlinear state trajectory can be evaluated exactly with a single associative parallel scan, without iterative linearization. We further derive a constrained parameterization that ensures bounded, contractive dynamics, and avoids poles in the fractional-linear state update. Across long-sequence classification, regression, and forecasting tasks, RiccatiSSM achieves competitive predictive performance while reducing runtime by $22{-}33\%$ compared to the nonlinear LrcSSM under matched architectures. These results demonstrate that state-dependent nonlinear dynamics can retain exact composability and be evaluated efficiently within a single parallel scan.

Large language models are trained with backpropagation, whose global gradient coordinates all layers but forces each to hold its activations and wait for the gradient to pass back through every deeper layer. Conventional local learning removes this update locking by training each module to predict the target through its own readout, but has not scaled to billion-parameter pretraining. We identify these private readouts as a key weakness, since they leave each module without information from deeper modules. We propose Shared-Output LOcal learning (SOLO), which replaces them with a shared, read-only copy of the final module's readout, the only one trained on the output of the whole network. Taken from the previous step, the copy transmits information from the final module without passing gradients between modules or reintroducing update locking. SOLO approaches backpropagation on Transformers of 340M to 2B parameters pretrained on 15B tokens, staying within one point in average zero-shot accuracy with a perplexity gap that narrows with scale. Readout ablations attribute SOLO's improvement over private readouts to sharing. Without update locking, each of p pipeline stages holds activations for O(1) micro-batches instead of O(p). The freed memory permits larger micro-batches, which reach up to 1.44x the best measured throughput of pipeline backpropagation on the same partition. To our knowledge, SOLO is the first local learning method to show such memory and throughput gains in billion-parameter language-model pretraining. Local learning thus becomes a practical alternative to backpropagation for large-scale pretraining.

World-action models use predicted visual futures to condition robot actions, yet execution feedback can invalidate parts of a prediction while leaving its task structure useful. We propose Revisable Temporal Planning (RTP), which maintains the visual future as a persistent action condition and revises it after feedback. Its central mechanism is a learned revision bridge: it resumes an intermediate state saved during visual generation and adapts its continuation to current observations. Visual and action supervision connect this revision to subsequent control. Time-aware history supplies observed evidence, and an adaptive policy selects retention, bridge revision, or fresh replanning from new noise before decoding the next action. On RoboMME and RMBench, RTP achieves task-averaged success rates of 48.6% and 84.8%, respectively. Matched comparisons support learned continuation; estimated checkpoint-source and action-prefix effects are positive but less precisely resolved. These results connect feedback-driven visual-plan revision to closed-loop task performance. Project Page: https://PLACEHOLDER.github.io/RTP/

Pólya and Szegő conjectured in 1945 that the disk achieves the largest electrostatic capacity among all planar sets with given logarithmic capacity. This question generalizes naturally to balls and Newtonian capacities in higher dimensions. The conjecture remains open. This paper establishes a conditional result: the conjecture would follow if among all lower dimensional sets in a horizontal strip with Neumann boundary conditions, the transverse component of the Dirichlet integral of the equilibrium potential could be shown minimal for the lower dimensional ball. As supporting evidence toward this latter property, the paper shows extremality of the ball for $L^p$-norms of the potentials, via Baernstein star-function symmetrization techniques.

Quantitative characterization of lymph node morphology is important for assessing axillary lymph node metastasis in breast cancer. However, surfaces reconstructed from computed tomography (CT) segmentation may contain geometric and topological defects that compromise subsequent analysis, while conventional shape descriptors predominantly characterize global morphology. To address these issues, we developed an integrated framework combining topology-aware surface processing with multi-resolution spherical harmonic (SH) analysis of CT-derived axillary lymph nodes. The processing pipeline produced topology-valid genus-0 surfaces with improved mesh quality, which were then represented at multiple SH degrees and characterized using 20 predefined geometric feature families. Geometric fidelity increased with SH degree, whereas predictive performance peaked at intermediate resolutions. Preferred SH degree also differed across feature families. A family-specific mixed-resolution model achieved an AUC of 0.918, compared with 0.884 for the conventional PyRadiomics Shape14 baseline, corresponding to an improvement of 0.0344. Controlled perturbation experiments showed that higher SH degrees transmitted more fine-scale geometric variation and yielded lower stability of curvature-based predictions. Representative geometric descriptors provided interpretable characterization of metastasis-associated surface morphology. Independent validation further supported the framework's transportability: label-free replication in a multicenter lymph node cohort reproduced the family-specific resolution effects, while a labeled LIDC-IDRI lung-nodule experiment reproduced the resolution-dependent relationship between SH degree and predictive performance. Altogether, the framework provides a topology-valid basis for quantitative characterization of lymph node morphology and metastasis-associated imaging phenotypes.