Papers

We study the optimal gathering problem over a finite set of designated meeting nodes for asynchronous, anonymous, and oblivious mobile robots on an infinite grid under crash faults. The robots have global visibility and strong multiplicity detection, but share neither a coordinate system nor chirality. The objective is to gather all non-faulty robots at a Weber Meeting Node, minimizing the total Manhattan distance from their initial positions. Up to $n-2$ robots may crash permanently, and such crashes are indistinguishable from arbitrary delays. Existing approaches often rely on a designated robot to break symmetry, whose crash may block the remaining robots indefinitely. Instead, our approach enables every robot to independently select the same target from its snapshot, while target-dependent restricted shortest paths preserve the target as a Weber Meeting Node. We prove that, under strong multiplicity detection, optimal gathering is impossible from certain fully symmetric configurations. For all remaining configurations, our algorithm CrashTolerantWeberGathering() selects a unique common target, preserves its optimality throughout the execution, and allows non-faulty robots to progress without waiting for crashed robots, thereby guaranteeing gathering in finite time.

Medical image segmentation remains fragmented along two axes: segmentation paradigms and data dimensionality. Existing methods are typically developed separately for semantic, in-context, and interactive segmentation, and are further specialized to either native 2D images or 3D volumetric data. In clinical practice, however, segmentation workflows take many forms: a case may be initialized by semantic prediction, reference-guided segmentation, or user interaction. Regardless of how it begins, fine-grained refinement is naturally performed on 2D views; for volumetric scans, such 2D edits must propagate coherently to the rest of the volume. We present UniPro, a unified model that bridges segmentation paradigms and data dimensionality, using propagation to extend 2D segmentation to 3D volumes. Our key insight is that volumetric propagation and in-context segmentation share the same reference-conditioned prediction mechanism, differing only in whether the reference image-mask pairs come from other cases or from previously segmented neighboring slices. Building on this view, UniPro supports semantic, in-context, interactive, and propagation-based segmentation within a single slice-based framework, using class priors, reference exemplars, user clicks, and neighboring-slice predictions as mode-specific conditioning inputs. To improve propagation reliability, UniPro further incorporates bidirectional and 3D supervision to regularize slice-wise propagation beyond per-slice losses. Extensive experiments across diverse modalities and anatomies show that UniPro achieves strong performance across all segmentation settings, enabling annotation-efficient 3D segmentation from sparse 2D initialization and reducing slice-by-slice correction effort.

Reducing logic depth during FPGA technology mapping can leave fanout bottlenecks in the resulting LUT network. LUT replication redistributes these loads but consumes area and increases loading on shared fanins. We propose FAPO, a mapper-independent post-mapping optimizer that jointly refines sink assignments and LUT cuts under a final-area constraint. It evaluates replication, cut switching, and recovery by the resulting live LUT count and full-network timing. A necessary all-critical-path condition motivates minimum-cut proposals that complement greedy refinement. Within a fixed critical graph and a restricted same-cut action family, each proposal minimizes the number of copy actions needed to cover all current critical paths. Experiments on EPFL benchmarks show that FAPO reduces the geometric-mean fanout-aware area-timing product (ATP) by up to 14.48% with only a small increase in area. VPR evaluation gives a 6.82% geometric-mean routed-delay reduction relative to ABC if.

Irregular multivariate time series forecasting is a challenging yet important problem in real-world applications, where observations are often irregularly sampled and asynchronously recorded across variables. Existing time series foundation models are mostly built on regularly sampled sequences, making them difficult to generalize to irregular time intervals and asynchronous cross-variable dependencies. To address these challenges, we propose QiYao-I, a manifold based foundation model for irregular multivariate time series forecasting. Specifically, we introduce a novel sampling-conditioned temporal manifold attention mechanism that maps real timestamps into a learnable temporal manifold feature space and injects temporal manifold biases into attention layers, enabling the model to capture both irregular time intervals and local sampling structures. Further, we propose a dynamic variable interaction mechanism with frequency awareness. It selectively performs cross-variable message passing under asynchronous observations. Extensive experiments on real-world irregular multivariate forecasting benchmarks demonstrate that QiYao-I achieves superior performance compared with both time series foundation models and end-to-end irregular forecasting models, showing strong generalization ability in zero-shot and few-shot settings.

We consider a finite Ising chain in zero field and ask when the all-up configuration is as likely as zero magnetization (magnetization one for an odd number of spins). For both free and periodic ends, the crossing coupling of a long chain is half the logarithm of its length minus half the logarithm of that logarithm, up to a term that vanishes as the length grows. We compute further terms with explicit constants and, for free ends, bound the crossing at every length. The second term is missing from an earlier approximation and explains why an earlier numerical fit gives a slope below one half. To locate the crossing, we compare the known magnetization law with its Bessel approximation. The Bessel approximation is above the exact weight, and we bound its relative error for every length, coupling and magnetization. At the crossing this bound tends to zero. The central bin still has about as many domain walls as the logarithm of the length on average, so the crossing has a coupling width of order the inverse logarithm. In a fixed positive dimensionless field the last crossing comes from near the edge of the row, at a coupling of about a quarter of the logarithm of the length. For long chains it is the one-spin crossing when the field exceeds half the logarithm of two. Below that value another bin crosses later.

The radius of a neutron star is closely related to the equation of state (EOS) of asymmetric nuclear matter, particularly to the nuclear symmetry energy. At fixed stellar mass, the neutron-star radius and the nuclear-matter pressure near saturation density approximately satisfy a pressure–radius (R-P) scaling relation, linking stellar geometry to strong-interaction matter. In the presence of dark matter (DM), changes in the stellar geometry can modify this relation. We investigate how GeV- and sub-GeV-scale DM affects the R-P relation in DM-admixed neutron stars (DANSs) within a gravity-only two-fluid framework. We extend the Buchdahl analytic solution to a two-fluid configuration to demonstrate this scaling and then use 21 nuclear EOSs to fit the relation $R_{\rm NM}=\bar C P_{\rm NM}^{\eta}$ for $1M_\odot$ and $1.4M_\odot$ DANSs. The exponent $\eta$ and coefficient $\bar C$ jointly quantify the DM-induced modification and depend on the DM particle mass, stellar DM content, and self-interaction strength. For bosonic DM, changes in $\eta$ and $\bar C$ occur mainly in the sub-GeV range, whereas significant fermionic-DM effects persist up to about 1.5 GeV. Increasing the DM content or strengthening a repulsive self-interaction generally increases $\eta$ and decreases $\bar C$. The modified R-P relation therefore encodes information about the DM particle mass, abundance, and self-interaction, and affect the extraction of the nuclear EOS from celestial observations. At DM masses of several hundred MeV, both fermionic and bosonic DM can also produce DM-dominated low-mass ($1M_\odot$) DANSs with large radial extensions, for which the conventional scaling relation ceases to apply.

Braces play a fundamental role in matching theory, as they, together with bricks, constitute the basic building blocks of matching covered graphs in the tight cut decomposition. A brace is minimal if deleting any edge from it results in a graph that is not a brace. We prove that every perfect matching of a minimal brace of order at least six contains an edge whose ends both have degree three. Consequently, every such brace has at least three edges with this property. Combining this result with the forest structure induced by the noncubic vertices, we show that every minimal brace $G$ of order $n\ge6$ and size $m$, other than $K_{3,3}$, satisfies $n_3(G)\ge\max\left\{8,\left\lceil\frac{2n+8}{5}\right\rceil, \left\lceil\frac{m-n+4}{2}\right\rceil\right\}$, where $n_3(G)$ is the number of cubic vertices of $G$. Finally, we characterize the graphs attaining the constant lower bound: a minimal brace has exactly eight cubic vertices if and only if it is isomorphic to $B_8$, $B_{10}$, $Q_{10}^{+}$, or $Q_{12}$.

Cache-based test-time adaptation (TTA) for vision-language models is often hindered by background bias in global representations and unreliable entropy-based cache admission under representation variations. To address these limitations, we propose RADC, which enhances prototype learning through reliable dual caching. RADC introduces a Semantic Foreground Cache that aggregates category-consistent spatial evidence from CLIP representations, yielding foreground prototypes that complement the global cache while mitigating background interference. To reliably manage both caches, Gaussian Risk Admission models multi-view representations as diagonal Gaussian distributions and jointly considers class separation and feature uncertainty to prioritize reliable cache candidates. RADC integrates zero-shot logits with complementary global- and foreground-cache predictions for robust inference. Extensive experiments on cross-domain and out-of-distribution benchmarks demonstrate consistent state-of-the-art performance.

In this paper, we study the sample complexities of value and policy learning in finite discounted Markov decision processes (MDPs) under recursive entropic risk preferences with risk parameter \(\beta\neq 0\), assuming access to a generative model of the MDP. We provide a refined analysis of model-based risk-sensitive Q-value iteration (MB-RS-QVI), a plug-in model-based method introduced in prior work, and derive \((\varepsilon,\delta)\)-PAC guarantees for both learning the optimal \(Q\)-value function and an \(\varepsilon\)-optimal policy. Our bounds improve the exponential dependence on the effective horizon \(1/(1-\gamma)\) compared with the best existing guarantees for this setting. In particular, they match the existing lower bounds in their exponential dependence on \(|\beta|/(1-\gamma)\), as well as in \(S\), \(A\), \(\varepsilon\), and \(|\beta|\), up to logarithmic factors. Consequently, our analysis removes the exponential gap between the previously known upper and lower bounds, leaving only a polynomial gap in the effective horizon.

Multivariate functional data arise in many modern manufacturing systems, where multiple sensors record densely sampled process trajectories. Monitoring such data is challenging because nominal variation is strongly correlated across samples, sensors, and time, while faults may appear either as isolated deviations or as structured departures concentrated within a limited number of sensor-specific temporal trajectories. We propose two unsupervised sparse tensor decomposition methods that preserve this multimode structure. Entrywise Sparse CP Decomposition (ES-CP) uses an entrywise \(\ell_1\) penalty to identify localized anomalies, whereas Fiberwise Sparse-Group Lasso CP Decomposition (FG-Lasso) combines entrywise and fiberwise penalties to detect both localized deviations and anomalies concentrated within temporal fibers. Both methods represent nominal process behavior through a low-rank CP decomposition and are estimated using alternating optimization with closed-form sparse-component updates. Two simulation studies evaluate performance under different fault structures, signal severities, noise levels, and missing observations. FG-Lasso attains or ties the highest macro F$_1$ score in almost all settings in the first study and achieves the highest macro F$_1$ score. In a multichannel forging-process case study, FG-Lasso and ES-CP obtain macro F$_1$ scores of 0.85 and 0.82, respectively, compared with 0.69 or lower for TRPCA and PCA-based anomaly detectors. The results demonstrate that explicitly matching the sparse penalty to the anticipated fault structure improves both anomaly detection and fault localization in high-dimensional functional processes.

Improvements in human-robot physical interaction (pHRI) can have major implications for physical therapy, search and rescue, and telemedicine. However, a major challenge concerns human constraints and safety in human-robot physical experiments. Concerns about human studies also include repeatability, scalability, and participant diversity. To conduct such experiments, an IRB and willing human participants are required. In this work, we present an improved phantom device, a physical twin, that enables real-world RL-type testing for physically interactive algorithms. The new device not only replicates the ball-and-socket motion of the shoulder but also renders scapular and protraction/retraction motions. The experiments showcase the device's ability to render multiple 3D joint limits and demonstrate a Franka Panda arm sensing limits and interacting with the device as an arm for ADLs (activities of daily living) and pHRI tasks.

We study how Vision Transformers ground abstract concepts (e.g., angry) when training data provide limited direct referential evidence. We hypothesize a metonymic grounding mechanism in which abstract predictions are driven by concrete, interpretable anchor concepts (e.g., fire) that bridge visual signals to abstract semantics. By applying Transcoders on CLIP and DINO vision encoders, we recover intermediate features that can be associated with semantic labels for more concrete concepts, and trace their contributions in circuits underlying abstract concept recognition. Experiments on a carefully curated icon dataset reveal structured metonymic circuits, in which perceptual primitives dominate early layers and object-like anchors precede abstract targets. Images containing rendered text instead recruit a distinct perceptual-to-textual route. Causal interventions further validate that metonymic intermediates are functionally involved in grounding abstract concepts.

The key-value (KV) cache of autoregressive transformers grows linearly with context length and dominates memory at long context. Most training-free remedies evict low-importance tokens, an irreversible choice along the sequence axis. We instead keep every token and store it more cheaply along the "feature" axis. We therefore propose AttSVD, a new "interpretable" low-rank compression whose basis is derived from each prompt's own attention geometry: an online, per-prompt truncated SVD that keeps only the directions attention actually reads, cutting persistent per-head KV memory in proportion to the retained rank. We propose two decode-time caching strategies, accumulating and streaming, for short and long generation regimes. Furthermore, we propose two refinements that make compression adaptive. A per-matrix energy rule sizes the logit space and the attention mass independently. An attention-aware basis truncates only in the spaces attention actually reads, preserving both the attention logits and the attention output. The same factors also provide free, per-head interpretability insights into the effective rank and the geometry attention consumes. Across multiple models, on both an agentic benchmark and the full LongBench suite AttSVD stays on par with the dense cache while using up to 50% of the KV-cache memory.

Robot manipulation systems using Vision-Language-Action (VLA) model backbones typically use just one VLA for task execution. However, individual VLAs do not perform well across different task states and environments. We introduce a framework for dynamically composing multiple VLA policies during execution: StepWise Action Policy Routing (SWAP). SWAP formulates policy routing as an offline reinforcement learning problem, learning a routing critic that selects the most appropriate policy at each decision step given the current observation. SWAP enables robots to select new policies to execute online rather than committing to a single policy for the duration of an episode. We evaluate SWAP on both real-world DROID manipulation tasks and LIBERO simulation experiments. SWAP improves over fixed-policy execution and routing baselines, giving absolute improvements in real-world task success up to 33% while reducing successful trajectory robot action step length by 28.3%.

In Divisor Nim, a player removes from one heap a positive number of stones that divides the size of every other heap. We prove that the Sprague–Grundy (SG) value satisfies $g(P)\le 2h_{\min}+\lfloor\log_2h_{\min}\rfloor$, where $h_{\min}$ is the smallest nonempty heap, independently of the number and sizes of the other heaps. The proof starts with odd heaps and classifies removals by their factors of $2$. The largest heap in a starting board then supplies an SG bound valid throughout every successor chain. When one heap varies, we sharpen Morisawa's eventual-period bound: the smallest fixed heap controls the SG value range, the number of consecutive values compared, and an increase in the varying heap that repeats legal moves. The remaining dependence on the fixed board lies in the SG periods of direct successors. Using the largest fixed heap, we derive an explicit common period for all these recursive layers. Its possible prime divisors belong to a fixed finite set, independent of heap count; their exponents remain controlled by the total fixed stones. Finally, joining boards under one shared divisor rule preserves and can tighten the SG ceiling. Minimum 2-adic depth and its count parity determine every joined outcome, and a join with at least two odd heaps has exact SG value $0$ or $1$. We close with two conjectures: $g(P)\le2h_{\min}$, and that the least eventual SG period, when one heap varies, divides $2\operatorname{lcm}(1,\ldots,h_{\max})$. Here $h_{\max}$ is the largest fixed heap, excluding the varying heap. The second claim would remove heap-count dependence from the period bound as well.

One-step real-world image super-resolution (Real-ISR) offers efficient inference, but recovering realistic and perceptually rich details often relies on score distillation or adversarial learning, introducing additional trainable components and making optimization more cumbersome. To this end, we propose DriftSR, a one-step Real-ISR framework that leverages pretrained diffusion priors through distribution drifting. Specifically, we perform drifting in the frozen intermediate representation space of a pretrained diffusion model, without introducing an additional task-specific feature encoder. Building on this space, we introduce Spatial Feature Drifting, which treats spatial features rather than entire images as distributional samples, enabling denser supervision for distribution alignment. To mitigate structural deviations, we further introduce Structure-Modulated Guidance, which adaptively refines drifting guidance according to local structural consistency with the LQ input. Consequently, DriftSR optimizes only the one-step generator, without auxiliary distillation branches or adversarial discriminators. Extensive experiments on three real-world benchmarks demonstrate that DriftSR delivers high-quality super-resolution reconstruction with efficient one-step inference.

Function secret sharing (FSS) underlies two-party private inference and private information retrieval, with cost dominated by generating, moving and evaluating distributed point function (DPF) keys. A trusted GPU-integrated distributed function accelerator (DFA) removed key movement by generating and consuming keys locally, but tolerates only semi-honest adversaries. A malicious host or GPU can tamper with shares, replay one-time material, swap buffers after checking, request early outputs, or abuse the accelerator as a forgery oracle, while malicious FSS ships large authenticated keys or multiplies DPF work. We present VIGOR-DFA, protecting the chain from authorized input to authorized output release with three mechanisms: a fresh authentication epilogue using three field multiplications per DPF output, 3.8-4.0 times faster per gate than per-lane DPF tag trees; a freeze-before-challenge check of every opening with t = 3 independent MAC lanes over F_{2^61-1}; and a role-bound one-time resource ledger with a release guard, in a protected datapath beside the GPU L2 cache. We prove stand-alone static malicious security with abort in a protected-module model, with statistical error Q(2/p)^t approximately 2^-148 for Q less than or equal to 2^32 checked batches. Our DFA-calibrated model shows that, against dealer-based malicious FSS modeled after the protocol family of Shark, VIGOR-DFA removes 21.8-563 GB of per-query offline authenticated material and, mainly by generating it in-module, lowers LAN latency by 10.1-14.0 times (1.5-1.8 times excluding offline distribution) and energy by 3.0-3.9 times. Malicious security costs 2.5-3.5 times LAN latency over semi-honest DFA and 0.145 mm^2 at 7 nm. We have completed the verification of specifications and the functional CPU reference model, including GPU/RTL conformance verification, protected runtime evaluation, and deployment-related tests.

Recent experiments suggest that strong light-matter coupling between molecules and cavity modes can significantly modify chemical reaction rates and yields. Despite multiple proposed mechanisms, a clear microscopic understanding of how vibrational strong coupling alters reaction kinetics remains incomplete. Here, we employ a general quantum-dynamical framework for analyzing competing reaction pathways in polaritonic chemistry by considering reaction coordinates with multiple relevant transition frequencies and general harmonic environments. We extend on a tensor-network formulation of the hierarchical equations of motion (HEOM) method to compute probability currents between vibrational states, leveraging a concise formulation for effective spectral densities and a controlled compression of Markovian bath modes into system-level jump operators. This allows us to decompose the resulting state-to-state probability currents, revealing how cavity-induced changes in individual transitions propagate through multistep reaction networks. We find that these local modifications can alter kinetic bottlenecks and selectively redistribute reaction flux between competing pathways, changing branching ratios under irreversible conditions without substantially affecting the equilibrium yield in the reversible regime. Finally, for coupled reaction-coordinate, spectator-mode, and cavity environments, we find structured, asymmetric rate profiles arising from interference between hybridized decay channels. Together, these results provide a mechanistic framework for understanding pathway-specific chemical reactivity under vibrational strong coupling.

Landing on small celestial bodies is challenging because the spacecraft must satisfy safety and actuator constraints despite gravitational forces that are difficult to model accurately. This article presents an optimal control for safe landing with gravitational uncertainty and strict actuator limits. The approach addresses spacecraft pose control with attitude represented on SO(3), where there are actuator constraints and state constraints on position, attitude, velocity, and angular velocity. The approach combines several key techniques. First, the gravitational force uncertainty is estimated using an extended high-gain observer, and we present a new dynamic upper bound on the estimation error. This gravitational estimate and dynamic bound are then used to compute optimal control forces and torques that satisfy state and actuator constraints while tracking a landing trajectory. Optimal forces and torques are obtained from the closed-form solution to a quadratic program that has a single control barrier function constraint constructed by composing multiple control barrier functions that are designed to enforce each state and actuator constraint. Finally, an optimal allocation maps control forces and torques to actuator commands that satisfy actuator constraints. The method is demonstrated in simulation using 2 vehicle configurations with severe gravitational uncertainty.

A Moore graph simultaneously asks for two things that normally pull in opposite directions: every vertex should have many neighbors, while every pair of vertices should remain close. For diameter two and degree $k$, the Moore bound is $k^2+1$, and equality forces a remarkably rigid graph: it is strongly regular with parameters $(k^2+1,k,0,1)$. Hoffman and Singleton showed that such a graph can exist only for $k=2,3,7$, and possibly 57. The degree-57 case on 3,250 vertices remains open. This paper is not an attempt to settle that open problem. Instead, we ask a more algorithmic question: How efficiently can the defining Moore structure itself be searched exactly? We begin from a human-developed exhaustive search based on the radius-two Moore tree. Leaves fall into $k$ groups of size $k-1$, and the edges between every pair of such groups form a perfect matching - a permutation. For efficiency, a partial construction is abandoned immediately when it creates a triangle or quadrangle. We then describe a sequence of exact algorithm-engineering improvements developed through a human-guided AI process and accepted only after mathematical checking and controlled regression tests. The main steps are reversible short-cycle forbid counters, bit-parallel domains, minimum-remaining-value branching, singleton propagation, matching-based AllDifferent filtering, balanced replayable parallel frontiers, residual-symmetry orbit pruning, and canonical deduplication of frontier states. On the principal $k=9$ benchmark, stronger symmetry cuts wall time from 47.6 to 17.9 seconds on a six-core laptop setup. Further parallelization speedup is reported separately; on a 16-core/32-thread machine, median wall time is reduced to 5.28 seconds. Degrees 10 and 57 are used as stress tests, and a five-minute degree-57 run uses only 161 MiB peak resident memory, showing that state size is modest.

Segment-based explanation methods such as LIME return a single explanation for each prediction, computed from one fixed image segmentation. This hides two important facts: a prediction can be supported by many different sets of image segments, and the segmentation itself shapes which explanations can be found. We introduce MOXIE (Multi-Objective eXplanation Imaging Engine), an evolutionary framework that searches for segment subsets that preserve the classifier's confidence while keeping as little of the image as possible. Instead of one explanation, MOXIE returns a Pareto front of alternative explanations that range from compact to highly faithful. We evaluate MOXIE with NSGA-II and four segmentation methods (SLIC, Felzenszwalb, Watershed and Voronoi) on BloodMNIST and HAM10000 datasets, using the same evaluation budget as LIME. Results show that MOXIE achieves a higher hypervolume than LIME on every image. LIME's explanations often appear convincing, yet the classifier's confidence collapses when only the highlighted segments are shown. MOXIE's fronts reveal how much of the image is needed to preserve the model's confidence and which contextual regions influence it. We also find that segmentation strongly affects evaluation: methods with unequal segment sizes appear most compact when segments are counted. These results show that alternative explanations provide a more complete view of a model's decision than a single explanation.

Rugby Union's continuous play, variable-length possessions, and multiple scoring outcomes make it difficult to model with standard approaches. We present a Markov Chain framework that represents Rugby Union as a finite state space over score differential, remaining time, and pitch location, with transition probabilities estimated from historical match data. The resulting model supports simulation and analysis of in-game trajectories, including win probability and expected point estimates from any given state. We validate the model through calibration analysis and comparison to models that predict only final outcomes. Our state-space approach produces well-calibrated, competitive estimates while additionally enabling analysis of how games evolve between states.

We study domination of the bi-parameter Hilbert transform by $(1,1)$-type sparse forms over axis-parallel rectangles, and show that such domination fails even for smooth test functions compactly supported in $(0,1)^2$. Our proof combines an explicit construction of two finite lattices based on the arithmetic of $\mathbb Z[\sqrt2]$ with a randomization argument.

For $n\geq2$ and $p\in(n-2,n)$, we prove that closed balls maximize the ratio of Riesz $p$-capacity to Newtonian capacity among all compact subsets of $\mathbb{R}^n$. This resolves the classical Pólya–Szegő capacity ratio conjecture and its higher-dimensional extensions. For $n\geq4$, a sharp inequality for the ratio of Newtonian capacity to logarithmic capacity is established. All equality cases are characterized.

Real-time agents are often evaluated with the world paused, or with decision time rounded to whole ticks (tick conversion). Tick conversion predicts almost no loss for a learned decider whose hit accuracy falls by 14.8 percentage points (pp) on the same games in asynchronous play. We instead split the decider's gap to a zero-latency teacher into time and quality components. In ViZDoom, we train a small decider by imitating a scripted teacher, run the game on wall-clock time, and add a control in which the teacher waits for a call to the decider's server before deciding. On a Windows host, three preregistered studies put the time component at 6.5-8.7 pp and the quality component at 6.3-8.6 pp. On a Linux host that skips 0.08-0.09% of ticks, the time component disappeared (-0.1 pp; paired 95% bootstrap interval [-0.4, 0.0]) while the quality component remained (5.6 pp [3.7, 7.5]). Retraining on teacher-labelled states from the decider's own play (DAgger) improved it on new games on both hosts (2.6 pp [0.4, 4.9] and 3.1 pp [1.1, 5.2]), a preregistered partial success. Imposing one delay schedule on every arm in live play left a quality component of 5.8 pp [4.0, 7.5] on 100 new games, and retraining cut the decider's disagreement with the teacher on its own states from 22.7% to 14.9%. In a conveyor simulator with a 400 ms deadline, delay past it erased the quality component. A latency-matched control whose delays match the decider's shows which remedy to try.

Given an $n\times n$ matrix $A=(a_{i,j})$ and subsets $I,J$ of $[1,n]:=\{1,\dotsc,n\}$, let $A_{I,J}=(a_{i,j})_{i\in I,j\in J}$ denote the $(I,J)$-submatrix of $A$. We prove that, for every totally nonnegative matrix $A$ and every $h=1,\dotsc,n-1$, \begin{equation} \operatorname{perm}(A_{[1,h],[1,h]}) \operatorname{perm}(A_{[h+1,n],[h+1,n]}) \;\geq\; \operatorname{perm}(A_{[1,n]\cap 2\mathbb Z,[1,n]\cap 2\mathbb Z}) \operatorname{perm}(A_{[1,n]\smallsetminus 2\mathbb Z,[1,n]\smallsetminus 2\mathbb Z}). \label{eq:absmain} \end{equation} In particular, these inequalities hold for the $0$-$1$ totally nonnegative matrices arising as antiadjacency matrices of unit interval orders. Our proof is based on explicit Bruhat-order comparisons between two distinguished families of permutations. Let $\mathfrak{A}_n$ be the Young subgroup $\mathfrak{S}_{1,\ldots,\left\lfloor\frac{n}{2}\right\rfloor} \times \mathfrak{S}_{\left\lfloor\frac{n}{2}\right\rfloor+1,\ldots,n}$ and let $\mathfrak{B}_n$ be the set of parity-alternating permutations \begin{equation*} \{w=w_1\cdots w_n\in\mathfrak{S}_n \mid i \text{ and } w_i \text{ have the same parity}\}. \end{equation*} For the balanced case $h=\left\lfloor\frac{n}{2}\right\rfloor$, we construct a bijection $f_n:\mathfrak{A}_n\rightarrow\mathfrak{B}_n$ satisfying $w\leq f_n(w)$ in Bruhat order. We then extend this construction to arbitrary $h$ by means of maps $g_{n,h}$ satisfying the corresponding Bruhat-order comparison. These maps yield the inequalities for all totally nonnegative matrices.

Ultra-low-latency machine learning and data processing pipelines operating on the sub-microsecond level often contain static dataflow kernels that require fine-grained bitwidth control, arithmetic optimization, and fast hardware performance estimation. This works introduce Alkaid, a free and open source domain specific compiler that translates sub-microsecond latency dataflow kernels into platform agnostic Register Transfer Level (RTL) or High-Level Synthesis (HLS)-ready code in seconds. Alkaid targets ultra-low-latency ML pipelines, especially those addressed by existing ML-to-hardware flows such as hls4ml, while also supporting the surrounding pre-processing, post-processing, and control logic. At its core, Alkaid uses an arithmetic centric intermediate representation, Alkaid Low-level IR (ALIR), to preserve fixed-point semantics, heterogeneous bitwidths, and operation level structure for optimization and code generation. Alkaid further provides comprehensive hardware-aware optimization passes and an interpretable white-box analytical performance model for rapid design space exploration without synthesis in the loop. Across representative ML workloads, including MLPs, GNNs, and transformers, Alkaid achieves 20-30% lower LUT usage than the best prior flows for bit-exact equivalent designs, with up to 40% lower latency in some cases. Beyond typical neural networks, Alkaid achieves comparable performance to the state-of-the-art method for synthesizing boosted decision trees, while also enabling the implementation and integration of non-ML kernels such as sorting networks and histograms.

We investigate a class of dynamic percolation models on a lattice, in which connections are added and removed by a set of local stochastic rules. In particular, the removal of any connection that can result in one connected cluster becoming two (or more) separate clusters is strictly forbidden. These models include and are inspired by a model for local quantum error correction for a toric code studied by Chirame, et al., PRX Quantum 6, 030363 (2025), who identified a phase transition with first-order characteristics, such as bistability and a discontinuous order parameter. We show numerically that this transition is a hybrid percolation transition (HPT), having characteristics of a continuous percolation transition such as diverging critical clusters while at the same transition having discontinuities like a first-order transition. We then modify this model to be fully isotropic, showing that the HPT remains. In both of these models, the steady state on one side of the HPT is an absorbing state; by turning on additional isotropic local stochastic moves, we remove the absorbing state and strongly suppress or remove the first-order transition, leaving an apparently continuous percolation transition. Curiously, the numerically-observed percolation critical exponents do not change significantly between the models with hybrid transitions and the model with an apparently continuous transition. These exponents are significantly different from known percolation transitions, indicating that this may be a new universality class.

We introduce an algorithm for efficiently preconditioning log-concave and log-smooth distributions that scales logarithmically with the condition number of the underlying distribution. Based on Gaussian cooling, our multistage method approximately samples from a sequence of well-conditioned distributions to construct a preconditioner for each subsequent stage of the cooling schedule. This method is motivated by existing practical approaches for mass matrix estimation in Markov chain Monte Carlo (MCMC), in which an effective preconditioner for the target distribution is estimated from samples produced during a warm-up period. However, our approach is conceptually distinct from existing approaches and moreover permits theoretical analysis. Our algorithmic framework is flexible, allowing essentially any log-concave sampling algorithm to act as the subroutine within each cooling stage. For instance, using first-order rejection sampling (FORS) as the sampler, the first-order query complexity of our method is $\tilde{O}(d^{4/3} \log \kappa)$ for a large class of log-concave and log-smooth distributions with condition number $\kappa$ and $\tilde{O}(d^{1/3} \log \kappa)$ for translation-invariant distributions. In the translation-invariant setting, we provide numerical experiments for the lattice $\phi^4$ model, a simple lattice field theory.

Three-dimensional perception is critical for robotic manipulation, particularly for high-precision tasks, as recovering metric depth and precise 3D object positions from monocular RGB observations is inherently ill-posed. However, many Vision-Language-Action (VLA) models rely solely on RGB observations for perception. Leveraging recent advances in foundation models for stereo matching, we introduce ExStereo, a stereo module that augments pre-trained 2D VLAs with 3D perception. ExStereo reconstructs scene geometry from stereo image pairs and renders multi-view observations as an explicit stereo representation for stereo feature extraction. The action tokens from the action expert selectively attend to the resulting stereo tokens through our proposed action-stereo cross-attention mechanism, enabling the policy to generate robot actions conditioned on 3D scene information. To learn robust 3D representations, we introduce a mid-training stage before task-specific post-training, using a self-supervised learning objective on large-scale stereo data. We validate our approach by fine-tuning two publicly available VLAs, $\pi_{0.5}$ and SmolVLA, and evaluate them in simulation and on a real-world bimanual PiPER platform. Across both settings, VLAs fine-tuned with ExStereo consistently outperform baselines, demonstrating the effectiveness of stereo perception for robotic manipulation. Our project website is at: https://exstereo-vla.github.io/ExStereo/.