Papers

We present a deterministic CRT-based sparse Fourier architecture for exact recovery of noiseless, on-grid, at-most-\(k\)-sparse spectra with an engineered transform length. The transform length \(N\) is selected as an exact product of small pairwise-coprime stage primes, allowing each stage to use transforms whose size scales with the sparsity rather than the ambient dimension. Three co-prime-increment time shifts provide a one-sided singleton-consistency screen: every genuine singleton passes, while passing collision bins remain provisional candidates. Each candidate bin is mapped by a total label-emission rule to at most one global frequency label, and per-stage label sets are intersected, yielding a deterministic \(O(k)\) candidate bound for every input. Candidate construction uses \(O(k\log N)\) samples. In a comparison real-RAM model with exact arithmetic and exact phase evaluation but without unit-cost root-index decoding, it requires \(O(k\log^2 N/\log k)\) arithmetic operations; in a stronger root-index-oracle model the arithmetic cost is \(O(k\log N)\). Under all-stage genuine-singleton survival, the candidate set contains the true support. Exactness, however, does not depend on that survival condition: a consecutive-sample residual verifier accepts a sparse reconstruction only when it is exact, and all failures route to a dense FFT. The resulting hybrid algorithm therefore returns the exact spectrum for every input in the stated noiseless, on-grid, at-most-\(k\)-sparse model, with \(O(N\log N)\) worst-case runtime. The verified sparse path additionally incurs an \(O(k^2)\) verifier cost in the root-index-oracle model. Neither computational model is a bit-complexity model.

Autonomous driving requires world models that can understand the physical world, reason and plan, and operate safely. In this paper, we first systematically evaluate existing action-conditioned joint-embedding predictive architecture (JEPA) world models, including LeWM, DINO-WM, and JEPA-WM for end-to-end autonomous driving (E2EAD). To isolate world-model quality from policy learning, we employ a goal-conditioned zero-shot planning setting that evaluates these models using ground-truth future observations as goals, without training any driving policy. We find that existing JEPA-based world models are either accurate for driving but computationally expensive, or computationally efficient but insufficient for planning. To address this trade-off, we propose AD-E2E-JEPA, which introduces a SIGReg-regularized learnable projector applied to projected patch embeddings. The projector reduces the number of planning patches by $16\times$ and the embedding dimension by $4\times$, achieving a $100\times$ inference speedup while retaining planning performance, with a 0.8-second runtime for an 8-frame rollout over 256 candidate trajectories. Without training any driving policy, the world model itself reaches the goals located 20 meters away on average within the displacement of respectively 4.0/2.8 meters, using world-model rollouts over trajectory vocabularies of respectively 256/8,192 candidates. On the NAVSIMv2 benchmark, it achieves 67.3/72.9 EPDMS with multiplicative safety metrics and 84.1/86.5 EPDMS$^{\dagger}$ without them in goal-conditioned zero-shot planning. Experiments further show that the self-supervised pretrained projector improves downstream imitation learning performance from 80.2 to 85.4 EPDMS. The source code is available at https://github.com/HaoranZhuExplorer/AD-E2E-JEPA

We investigate the spectral stability of quasinormal modes in nonconformal holographic QCD models using pseudospectral analysis. We first consider the soft-wall model, focusing on scalar and vector fields, and then extend the analysis to the analytic Improved Holographic QCD (IHQCD) model, where we study tensor glueball fluctuations. In both cases, the equations of motion are formulated as linear eigenvalue problems, allowing the instability of the quasinormal spectrum to small perturbations to be quantified through the pseudospectrum. We find that the spectral stability of the quasinormal modes exhibits a nontrivial dependence on temperature, reflecting the presence of intrinsic dimensionful scales in holographic QCD models. As the temperature increases, the magnitude of the imaginary part of the quasinormal frequencies grows, signaling an increasing decay rate and the progressive loss of coherence of the corresponding hadronic excitations. At sufficiently high temperatures, the quasinormal frequencies approach an approximately linear dependence on temperature, although this regime is reached only after the associated hadronic states have melted. We further compare the pseudospectral instability with the behavior of the corresponding spectral functions. Our results indicate that the growth of pseudospectral instability provides a complementary characterization of the loss of spectral stability and can serve as a useful diagnostic of hadronic dissociation and melting in holographic QCD.

Recommendation models with sparse embeddings and a shared consumer often exhibit the one-epoch phenomenon: a second epoch lowers training loss while sharply degrading generalization. We present a view based on the violation of the prequential principle. On the first epoch, an example's label has not affected the embedding rows used to score it. On later epochs, those rows contain a displacement induced by the labels earlier update. This creates an incentive for the shared consumer to exploit this displacement in subsequent epochs, which fails to generalize. We call this self-influence asymmetry. Using an exact scalar model and local influence analysis, we connect this mismatch to the uncertainty in the embeddings and the consumers incentive to exploit it in subsequent epochs. We verify this hypothesis using an embedding-consumer-update interventions in deep recommendation models and propose uncertainty-weighted sensitivity regularization (UWSR) which counteracts this mismatch by augmenting the loss function to penalize the consumer for relying on uncertain embeddings. Unlike existing remedies, UWSR preserves the learned embeddings and across three benchmarks, four-epoch UWSR reduces test cross-entropy by 1.38%-6.78% and improves AUC by 0.0058-0.0231 relative to one-epoch training.

Interpreting architecture, engineering, and construction (AEC) drawings is hard for general Multimodal Large Language Models (MLLMs) and vision-language models (VLMs). We introduce K-OPSD, a VLM post-training methodology for improving AEC drawing understanding. Building on On-Policy Self-Distillation (OPSD) with verifiable supervision, we construct a teacher from the model's own best-of-N generations, certified by a process-level verifier, and rescue failed prompts by resampling under a hint that exposes the verified answer. We then perform an on-policy model update by training on verified completions with a cross-entropy inner-loss, outperforming the bounded token-wise generalized Jensen-Shannon divergence (JSD) used by on-policy distillation. Using K-OPSD, we fine-tune Qwen3-VL models on the AECV-Bench dataset. The resulting models attain the top average judge score (0.819) and combined accuracy (0.738), achieving competitive results against open-source baseline models. The recipe transfers to the out-of-domain ArchCAD dataset, where the 8B model gains most. We present the verifier suite and the continual learning and self-improving pipeline, our results provide preliminary evidence that verifier-guided self-distillation is a promising route toward more reliable machine reading of architecture drawings.

We prove polynomial-in-time Sobolev bounds on the approximation error between the twisted discrete nonlinear Schrödinger equation and its magnetic continuum limit. The analysis exploits complete integrability of the continuum flow through its Birkhoff representation to control approximation by a non-integrable Hamiltonian finite-difference lattice. We establish a focusing-defocusing dichotomy in uniform polynomial control: the bounds hold for arbitrary defocusing data and focusing data of sufficiently small mass, while modulational instability and aliasing yield an obstruction for large focusing data. The accompanying algebraic spatial rates are generically optimal in the Baire-category sense. The proof combines Birkhoff coordinates with modified energies for discrete Sobolev growth, while Fourier filtering recovers uniform spacetime estimates below the energy space despite degenerate lattice dispersion.

As LLM agents are increasingly deployed as commercial services, protecting proprietary orchestration logic and tool-use policies is important. We consider agent repackaging: an adversary integrates a protected agent into its own application via API and presents it under its own identity. It may modify parts of execution to obscure the source. The owner typically has only black-box access to the repackaged service, so black-box ownership verification is essential. Agent watermarking embeds ownership evidence into agent behavior for later verification. An effective watermark should satisfy two requirements: losslessness, preserving original functionality, and robustness, keeping ownership evidence recoverable after partial modification of execution. Existing methods often embed signals into behavior selection or execution trajectories, intervene in normal decisions, and offer limited robustness to behavior modification. We propose LoRo-Mark, a provably lossless and robust agent watermarking mechanism. For losslessness, it isolates watermarking into a cryptographically authenticated forensic branch that remains inactive during normal execution and is activated only by owner-authorized requests. By reducing unauthorized branch activation to standard MAC security, LoRo-Mark formally guarantees performance preservation. For robustness, it redundantly distributes ownership information across forensic behavior sequences, enabling reliable recovery under partial behavior substitution and sequence truncation. Experiments across multiple LLM agents show zero degradation on normal tasks and reliable ownership verification under sequence modifications.

Large language models (LLMs) have demonstrated strong capabilities in biological reasoning; however, genomic disease inference remains largely dependent on memorized gene-disease associations rather than understanding biological pathways. This shortcut learning undermines robustness and generalization, and breaks down when molecular identifiers are unavailable. We present GenoMorph, a multimodal genomic reasoning framework that shifts disease prediction from associative gene-disease mapping toward pathway-grounded reasoning. GenoMorph couples a frozen DNA foundation model with question-conditioned cross-attention fusion, self-adaptive latent reasoning (LatentSp), a residual reasoning gate for iterative genomic evidence reinjection, and rejection sampling fine-tuning regularized by hierarchical optimal transport (OT). Rather than learning direct gene-disease mappings, GenoMorph aligns genomic sequence representations with latent pathway dynamics, enabling reasoning trajectories that follow molecular interactions before producing disease predictions. LatentSp dynamically allocates computation according to reasoning confidence, reducing unnecessary reasoning steps and improving inference efficiency. We further construct an anonymized benchmark from the Kyoto Encyclopedia of Genes and Genomes (KEGG), replacing every gene and molecular identifier with anonymous symbols while preserving sequences and pathway topology, thereby removing memorization shortcuts. GenoMorph raises the weighted F1 from 0.7863 (BioReason) to 0.9412, and rejection sampling fine-tuning with self-adaptive latent reasoning pushes it to 0.9725 while cutting latency nearly 60%. On the anonymized benchmark it reaches 0.9465 F1, substantially outperforming prior systems and confirming that accurate disease prediction can arise from pathway reasoning rather than memorized gene-disease associations.

Domain adaptation is crucial for addressing distributional shifts that degrade model performance across domains. While most existing research has centered on classification, semi-supervised domain adaptation regression (SSDAR) for continuous-output tasks remains largely unexplored, particularly in practical scenarios with limited labeled target data. To address this gap, we propose semi-supervised domain adaptation regression through whitening transform and dual consistency (WhiteCon), which combines domain-specific whitening transform (DWT) and dual consistency regularization to enhance training stability and domain adaptation. DWT reduces the variance of the model parameters by transforming the feature covariance matrix into an identity matrix, thus stabilizing training under ordinary least squares assumptions. In addition, variance consistency regularization, as part of dual consistency regularization, aligns the variances of weak, strong, and mixup-augmented features to improve resilience against augmentation-induced perturbations. Empirical evaluations on various benchmark datasets under SSDAR settings demonstrate that the proposed WhiteCon achieves state-of-the-art performance compared to existing methods, effectively addressing domain shifts in regression tasks. The code for WhiteCon is available at https://github.com/sejin-sim/WhiteCon.

Mixture-of-experts (MoE) language models often exceed the memory of a single GPU. Expert offloading keeps most experts in host memory and loads them on demand, so decoding speed depends on how many experts each token must fetch. Caching and prefetching reduce this cost only as far as the routing allows. Router-only fine-tuning can reshape the routing to reuse experts, but it keeps the experts frozen, so they cannot adapt to the tokens the new routing sends them. We propose MaskCoFT, a masked co-adaptive fine-tuning method that trains routers and experts together with the cross-entropy loss alone. During fine-tuning, a learnable binary mask restricts the Top-K routing of each layer to a subset of experts, and the experts adapt to the tokens redirected to them. At inference, the learned mask becomes a soft prior that re-ranks experts, so every expert remains selectable. We simulate a GPU cache of 4 experts per layer for Mixtral-8x7B and 12 for DeepSeek-V2-Lite. MaskCoFT cuts expert fetches per token by 23.7% and 10.1% relative to the base model. In real offloading system serving, it lowers the time per output token by up to 16.4% and 5.5%, respectively. Its average accuracy over nine benchmarks stays above the base model by 0.92 and 0.53 points.

Isoflux control in spherical tokamaks requires coordinated plasma-current and boundary regulation under coil-voltage and computational constraints. This study develops observer-based constrained model predictive control (MPC) for EXL-50U. Vacuum-vessel spatial coarsening reduces a 538-state linearized model to 40 states while retaining control-relevant responses. A Kalman observer provides full-state estimates, and MPC jointly optimizes current and boundary-flux tracking with explicit voltage bounds. Matrix precomputation, specialized solver code generation, and structured linear-system solution reduce online computation. Nonlinear free-boundary Grad–Shafranov evolutive simulations evaluate nominal operation, measurement noise, configuration mismatch, a one-step delay, and combined noise and delay against proportional–integral–derivative (PID) control and a linear–quadratic regulator (LQR). Nominal MPC root-mean-square errors are 1.126 kA for plasma current, 0.0164 m for last-closed-flux-surface geometry, and 2.463 mWb for the worst flux channel, all below both baselines. With noise, the boundary error is 0.0199 m over the common evaluation window, and regulation is sustained throughout the test. MPC completes a limiter-to-divertor transition without relinearization or retuning and maintains regulation under delay and combined disturbances. Across all five cases, mean MPC computation times are 0.413–0.441 ms, with all 99th percentiles below 1 ms. These results support joint current and isoflux regulation and millisecond-scale computational feasibility, providing a basis for future EXL-50U experiments.

We give a dynamical characterization of the Chandrasekhar mass for cold white dwarfs governed by the radial Euler–Poisson equations with the exact Chandrasekhar equation of state. This mass is the infimum of masses for which a finite-energy classical solution with a physical vacuum can contract its entire support to a point in finite time. Below it, conservation of energy prevents complete collapse. For every mass in a sufficiently small interval above it, we construct a solution whose support shrinks to the origin and whose density concentrates there with the full mass of the star. The interior approaches a collapsing Goldreich–Weber profile. Near the vacuum boundary, a different rescaling gives a limiting profile that connects the high- and low-density regimes of the pressure law. We determine this profile and show that, after adding the electron rest energy, the conserved energy equals that of the Goldreich–Weber reference solution. The proof combines matched asymptotic expansions with local existence and energy estimates that extend solutions backward from times approaching collapse to a common earlier time.

In school choice, a lottery number is often used by the matching mechanism to break ties when there are more students who prefer the same school than the number of seats available. There has been growing theoretical and empirical interest in understanding the impact of revealing the lottery number to students. In practice, in recent years, the NYC Public Schools started revealing the lottery number to students to improve transparency. Theoretical findings from prior literature also suggest that revealing the lottery number strictly improves the number of matches under the deferred acceptance algorithm. However, these theoretical results are based on the over-simplifying assumption that all students share the same preference ranking for schools. In this work, we relax this assumption and allow students to have heterogeneous preference rankings. Under a game-theoretic model where student strategies form a Bayesian Nash equilibrium, we characterize scenarios where revealing the lottery number can either improve or worsen the matching outcome, measured by two metrics of match rate and social welfare. We further consider revealing partial information about the lottery, and demonstrate non-monotonic effects in the amount of information available to students. These results together illustrate complex tradeoffs induced by the lottery revealing policy.

We investigate some aspects of holography in de Sitter space, pertaining to the proposal for the dual theory residing on the late-time boundary [arXiv:astro-ph/0210603v5], including a Fermionic field that satisfies the Dirac equation. The modes of the solutions near the boundary are found to possess equal and oscillatory fall-off, similar to the scalar field belonging to the principal series representation of the isometry group of de Sitter space. We evaluate, by suitably adding a boundary term to the Dirac action, the wavefunctional of the Bunch Davies vacuum in path integral formalism in terms of the projections of the field on the eigenspaces of the time-like ${\gamma}$-matrix. We validate our path-integral construction of the wavefunctional by reproducing the two-point function between the field operators in the vacuum state as computed in the canonical formalism. By appropriately identifying the boundary sources in terms of the projected components of the bulk field, we find that a single Dirac field in the bulk corresponds to a pair of primary spinor fields in the boundary theory and show that the resulting wavefunction coefficients satisfy the conformal Ward identities. We check the robustness of our holographic map under the addition of a Yukawa interaction considering the two cases where the scalar field in the interaction term belongs to the complementary series and the principal series representations of the isometry group of de Sitter space respectively.

Multimodal large language models (MLLMs) are increasingly envisioned as core components of scientific and engineering agents, yet their ability to interpret physical fields remains poorly understood. Existing physics benchmarks largely emphasize textbook problem solving or intuitive physical reasoning, leaving open whether MLLMs can infer physically meaningful information from continuous field observations. We introduce PhysFieldBench, a benchmark comprising 24 tasks and 1,160 evaluation examples across controlled equation fields, simulated physical fields, and observed physical fields. The tasks assess three forms of inference: identifying physical mechanisms, comparing latent control variables, and predicting outcome properties. Across representative open-source and proprietary MLLMs, zero-shot performance is low: the best model achieves a chance-normalized score of 29.3, while several open-source models remain near chance. In contrast, a task-specific supervised vision transformer performs substantially better, demonstrating that the inputs contain learnable physical information. To diagnose these failures, a structured self-explanation analysis attributes most errors to missed visual patterns and incorrect visual-to-physical mappings. Further, to explore whether post-training can improve physical inference and generalize to unseen tasks, we compare supervised fine-tuning with final answers or chain-of-thought supervision and reinforcement learning. Final-answer supervision performs best overall but transfers less effectively, whereas reinforcement learning after chain-of-thought supervision achieves the best generalization. Together, these findings highlight the need to improve visual-to-physical grounding and cross-task generalization for MLLMs to reliably interpret physical fields in scientific and engineering workflows.

Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250 $\times$ faster than iterative samplers.

Long-horizon micromagnetic simulation remains expensive because conventional and learned solvers typically propagate Landau–Lifshitz–Gilbert (LLG) dynamics step by step. Existing learned approaches generally retain stepwise integration or model deterministic evolution, leaving full-field, direct-horizon stochastic prediction largely unexplored. We propose FLARE, a flow-matching framework that recasts stochastic finite-time magnetization prediction as conditional transport over anchor-relative local axis-angle rotations. This rotation-space formulation respects the intrinsic geometry of magnetization dynamics and preserves pointwise unit norm by construction. By explicitly conditioning on the physical prediction horizon, FLARE directly generates full-field stochastic endpoints across multiple target times without stepwise integration. Against the strongest single-checkpoint external baseline on each metric, FLARE achieves 29.9% lower angular energy distance ($15.30^\circ$), and a 37.3% lower fair energy score (0.393). On a representative composed 5-ns two-segment protocol, FLARE achieves a $3{,}062\times$ best-batch speedup over the widely used GPU micromagnetic solver MuMax$^3$ on a single GPU.

The upgrade and rewriting of large scientific codebases has traditionally been a major challenge. While evolutionary search with large language models (LLMs) can port and accelerate legacy code, repair feedback in prompts alone does not prevent subsequent candidates from repeating the same errors. We introduce Certificate-Driven Evolutionary Search (CDES), which extends evolutionary search with enforceable restrictions derived from failed candidates, recorded as certificates of assumptions, checker evidence, and justified restrictions. Its control logic enforces these restrictions through rejection, backtracking, and targeted repair while preserving compatible edits. We apply CDES to CPU-to-GPU translation of two particle-simulation functions from the Geant4 toolkit, evaluated with a harness that goes beyond unit tests to combine formal checks, numerical comparisons, physics checks, and GPU safety tests. Generated implementations achieve 13.78x and 23.54x function-level speedups over CPU code, including data conversion and transfers; for one function, GPU throughput exceeds an expert implementation by 14.9%, reaching 16.1% when complementary components are combined. In an ablation over execution settings, certificate feedback increases the fraction of candidates passing required correctness checks from 55% to 90%.

We prove that every acylindrical action on uniformly locally finite product of trees induces the hyperfinite orbit equivalence relation on the Roller boundary. As a byproduct, we construct an example of a standard Borel space and two commuting bounded-to-one surjective partial Borel maps that generate a universal countable Borel equivalence relation. This contrasts to Shinko-Weilacher-Yu's theorem on hyperfiniteness of bounded-to-one actions of commutative monoids.

Motivated by the structure of various standard statistical arrays, Bailey, Praeger, Rowley and Speed (1983) described the automorphism groups of poset block structures as generalized wreath products. We observe that these are exactly the groups used to define DAG exchangeability in Jung, Lee, Staton and Yang (2021), and we restate the representation theorem of the latter work in this language. As a concrete example, we write out the resulting representation for block matrices whose block rows and block columns are separately exchangeable, and whose rows and columns may also be permuted independently inside each block.

We study a one-dimensional nonlinear stochastic wave equation driven by Gaussian noise that is white in time and rough in space. We prove a bi-parameter local linearization for mixed increments along the two characteristic directions. The proof combines characteristic cancellation with a localized fractional-energy estimate that controls boundary interactions caused by the rough spatial noise. As an application, we establish quadratic-variation limits on arbitrary anisotropic rectangular meshes and construct a consistent estimator of a multiplicative diffusion parameter. Numerical experiments illustrate the finite-sample performance of the estimator.

Names are personal identifiers, but they also carry social meaning and are widely used to evaluate how language models treat different people. Such evaluations typically assume that matched names are comparable model inputs. We show that this assumption often fails at the lexical interface: matched names are not necessarily matched inputs. Some names receive direct single-token access, while others are assembled from multiple subwords, creating unequal name-surface support. Across nearly half a million first names and 12 LLM-associated tokenizers, direct lexical access is highly selective, model dependent, and uneven across race- and gender-associated name metadata. We introduce NameTrace, a model-native, fine-grained, pre-behavioral framework for measuring whether unequal name-surface support remains a vocabulary property or becomes visible in task-relevant internal representations. NameTrace measures concept accessibility from the model's own probabilities over task-specific adjective axes with continuous task-aligned weights. On matched atomic and short-fragmented names within the same race/ethnicity–gender-associated strata, support predicts systematic differences in concept accessibility across fellowship, hiring, clinical assessment, and lending. These differences persist across all eight matched strata, extend across model families, and transfer to unseen names. Hidden-state interventions further show that the measured task directions have downstream leverage, shifting later constrained choices. Unequal lexical support is therefore demographically structured at the input and remains visible in task-relevant model computation. NameTrace makes lexical comparability measurable, supporting a broader principle: behavioral comparability begins with lexical comparability.

Reinforcement learning (RL) has become an effective post-training paradigm for long-horizon large language model (LLM) agents. However, we find that the resulting policies can be sensitive to various policy perturbations, such as hidden-state noise, pruning, and quantization. In this work, we study how to improve perturbation robustness during policy optimization. We first introduce the notion of a perturbation robust policy and analyze conditions under which perturbed policy updates preserve stable monotonic improvement. Based on this analysis, we introduce Stable Perturbation-Robust Policy Optimization (SPrPO), which applies adaptive and sensitivity-aware perturbations during RL training. We evaluate SPrPO on ALFWorld and WebShop and conduct systematic experiments across multiple perturbation types and scales, showing improved perturbation robustness while maintaining stable policy optimization.

Residual completion augments query-aware sparse attention by estimating the contribution of tokens omitted from the exact sparse computation. We ask whether improving a layer's attention-output reconstruction on the same incoming Q/K/V and selected support necessarily improves the fidelity of the final model output. We study training-free RESA and learned Top-K+$\phi$ with frozen backbone language models. A prespecified single-layer screen yields two Qwen3-0.6B/Multi-LexSum interventions for which direct-runtime measurements show positive prespecified request-aggregate local reconstruction gain but worse final KL fidelity than the corresponding all-abstain Exact Top-K baseline on both discovery and prompt-token-disjoint holdout requests. Exact restoration at the same layer instead improves final fidelity, showing that the reversal is specific to approximate completion in these cases. In complementary multi-layer experiments, a task-independent local diagnostic often repairs the tested completion estimators, although the repaired models do not consistently outperform Exact Top-K. Together, these results show that better local reconstruction need not translate into better final-model fidelity.

Good design is often synergistic, creating super-additive value by linking goals so that existing resources produce greater outcomes. However, finding these synergistic opportunities in sparse design spaces is difficult, and current LLM-supported ideation tools largely default to additive paradigms such as feature blending, variant generation, or local patching. We present Scanvas, an AI-supported system for systematically discovering and developing synergistic design opportunities. Scanvas operationalizes synergy through a two-step computational process: first, it decomposes seed ideas into explicit properties (components, behaviors, surpluses, and issues) to enrich the design space; second, it systematically searches across enriched ideas using three theory-grounded strategy operators: unlocking or strengthening goals, turning weaknesses into resources, and sharing components across functions. We instantiate Scanvas as an auto-generation pipeline and an interactive system. Pipeline ablations and a user study with 12 professional designers demonstrate that Scanvas enables users to surface and develop significantly higher-quality, synergistic concepts compared to LLM ideation baselines.

Vision-Language-Action (VLA) models integrate pretrained Vision-Language Models (VLMs) with action heads for robot control. Common action heads have distinct limitations: point regression provides only a point estimate of the action distribution, while standard flow-matching samplers require costly iterative sampling. To address these limitations, we unify regression and flow matching under a shared objective and extend it to derive a quantile objective. This quantile objective guides the design of our Quantile Head, which predicts a median and positive gaps to form ordered marginal action quantiles in one forward pass. These quantiles support multiple sampling strategies without retraining and are jointly supervised to train the default median policy. Our local analysis of this joint supervision shows that, with calibrated nearby quantiles, fixed gaps, and matched correction speed, direct median updates have lower variance than under median-only supervision. Experiments show that this jointly supervised median policy achieves the highest average success rates among the compared methods on LIBERO, LIBERO-Plus, LIBERO-Pro, and two real-robot tasks, together with the shortest mean episode time among matched LIBERO baselines; code is available at https://github.com/xwangrs/Quantile-Head-for-VLA.

Prompt-specialized multi-agent systems enable multiple agents to share a model while performing complementary roles to solve complex tasks. However, agent-specific prefixes change the KV cache generated for the same shared context, causing each agent to repeatedly prefill the growing context and construct a separate cache with high computation and memory overhead. Selective recomputation reduces this redundancy but still retains substantial model execution, while existing delta correction methods either support only recurring context relations or maintain memory-intensive online correction states for dynamically changing context. For first seen shared context, these methods also construct a reference cache outside the agent workflow, and an approximate correction at the first agent affects the outputs passed to subsequent agents. We present KVCMAS, an online KV cache correction framework that represents cross-agent cache deviations using compact low-rank states and seamlessly chains corrections along the agent workflow without an additional reference prefill. This design supports dynamically changing shared context while preserving an exact first-agent cache. Across multiple language and vision-language workloads, KVCMAS matches or improves the accuracy of prior KV cache sharing methods while achieving the lowest TTFT under highly concurrent serving. Under controlled serving traces, it provides a 2.0x TTFT speedup over inference without KV cache sharing and reduces peak GPU memory by up to 3.7x relative to a prior KV cache correction method. These results establish KVCMAS as an accurate and scalable KV cache sharing approach for prompt-specialized multi-agent serving.

Successive cancellation perturbation-enhanced (SCP) decoding improves the performance of finite-length polar codes by performing multiple SC decoding attempts with receiver-side perturbations. However, many existing perturbation schemes generate or update subsequent perturbations according to the outcomes of previous decoding attempts, resulting in additional decoding latency. In this paper, we propose an offline variance design (OVD) method for parallel SCP (PSCP) decoding of short- and medium-length polar codes. First, we formulate the exact recovery objective conditioned on ordinary SC failure and classify failed frames by the position of the first genie-aided intrinsic error and the number of subsequent intrinsic errors. We also derive a consistent Gaussian representation of the perturbed channel that preserves min-sum SC hard decisions. Second, we construct a class-based approximation of the recovery objective using Gaussian approximation and backward recursions, accounting for both error correction and new errors introduced by perturbations. We prove that both the exact and analytical objectives are nondecreasing and exhibit diminishing marginal gains as independent branches are added. Third, we develop a greedy algorithm to select variances from a finite candidate set for a given code, signal-to-noise ratio (SNR), and number of perturbation branches. All variances are determined offline, allowing the original SC branch and all perturbation branches to start simultaneously. Simulations for rate-$1/2$ polar codes of lengths $64$, $128$, $256$, and $512$ show that OVD-PSCP achieves lower block error rates (BLERs) than conventional SCP with the same number of perturbation branches. The gains are larger for shorter codes and increase as the number of perturbation branches grows.

AI systems often feel brittle and fragmented. A large language model (LLM) may correctly explain a concept but fail to apply it, or follow safety instructions in one context but not another. This behavior suggests a general failure to lift local information to a global understanding. To gain fundamental insight, we frame "understanding" as learning constraints and propagating their consequences. We construct learning tasks on monoid worlds, sets of states connected by action transitions, where observed training transitions and an unseen constraint jointly determine held-out transitions. Measuring generalization tests whether models can learn global constraints from local transitions and propagate their consequences. We consider inverse, commutativity, composition, and periodicity constraints relevant to spatial and semantic structure. Across attention, recurrent, and state-space architectures, next-state training fits the data but fails to propagate non-trivial constraints. Compositional training, which uses identical paths but hides intermediate states from the input, achieves 96% accuracy on inverse, commutativity, and composition constraints across architectures, yields corresponding improvements in geometric generalization of world models trained on embodied environments and relational generalization in Wikidata-finetuned LLMs. How far do models propagate constraints when inferring an unseen fact may depend on first inferring others? We define proof depth d of a held-out transition, measuring the minimum number of inference rounds to infer the transition, and find that model generalization decreases sharply with proof depth. Increasing compositional path length T improves generalization. These results provide a formal way to investigate global understanding in language and world models and demonstrate that compositional training promotes information propagation and integration.

We prove that if $G$ is a residually finite group, $\widehat{G}$ is its profinite completion and the map $H_2(G, \mathbb{Z}) $ $ \to H_2(\widehat{G}, \widehat{\mathbb{Z}}),$ induced by the canonical map $G \to \widehat{G}$, is injective, then the non-abelian exterior square $G \wedge G$ is residually finite. We show that if $G$ is a finitely presented centre-by-metabelian group then $\nu(G)$, the non-abelian tensor product $G \otimes G$ and the non-abelian tensor square $G \wedge G$ are residually finite. Furthermore we prove that if $G$ be a finitely presented metabelian group then the weak commutative construction $\X(G)$ is residually finite. We discuss a criterion for the $q$-exterior square $G \wedge^q G$ to be residually finite.