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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.
We prove that the domination number of the $2$-token graph of the path $P_n$ is $γ(F_2(P_n))=d(n)$ for every $n\ge 13$, where $d(n)=\frac1{10}(n^2+5n+c)$ and $c$ is an explicit constant that depends on $n \bmod 5$. This settles a conjecture by Leaños and the authors, who previously proved the upper bound. The lower bound is computer-assisted and follows the method used by Gonçalves, Pinlou, Rao and Thomassé for grid graphs.
Small area estimation (SAE) often requires both borrowing information across areas and benchmarking estimates to reliable aggregates. We develop a Bayesian framework that addresses these two objectives jointly through a new family of Benchmarking priors. The priors are induced by a benchmark-constrained regularization problem. The resulting family includes a Benchmarking Prior that incorporates the benchmarking restrictions without additional regularization across areas, and Single and Multi-View Laplacian Benchmarking Priors that introduce regularization through graph Laplacians constructed from area similarities based on external covariate information. For posterior computation under these degenerate priors, we develop tailored MCMC algorithms based on a reduced parameterization of the constraint space. We assess the proposed models using a data-based simulation and apply the framework to estimate Average Household Size (AHS) at the municipality level in Colombia in 2025. In this application, graph-based regularization improves model performance, with the Multi-View models generally producing more precise municipality-level estimates.
Precise shaping of surface acoustic waves (SAWs) on anisotropic piezoelectric substrates is complicated by elastic anisotropy and electromechanical coupling. Here we introduce a continuous diffractive acoustic lens (CDAL), in which weak phase-velocity perturbations produced by subwavelength metallization, together with diffraction, drive lateral field redistribution. An anisotropic thin-element propagation model enables efficient inverse design of the CDAL contour. Laser Doppler vibrometry verifies prescribed lateral field profiles and multichannel beam splitting with unequal widths. By combining continuous diffractive modulation with discrete source-phase encoding, we further shape the lateral field into a Bessel profile, demonstrating joint amplitude-and-phase control. This work provides a high-precision and fabrication-compatible mechanism for on-chip SAW field modulation.
Agents combine reasoning with tools to interact with external systems and complete real-world tasks. Early agents typically interleave reasoning and actions along a single execution chain. On complex tasks, this chain becomes unreliable because growing histories obscure intermediate dependencies and allow early planning errors to propagate. Recursively decomposing a complex task into smaller subtasks offers a natural solution, yet effective decomposition must account for the system's capabilities so that each subtask can be executed by the available tools. In realistic systems, however, tool libraries can be too large to expose in full. Injecting every tool description consumes substantial context while making relevant tools harder to retrieve and useful task boundaries harder to identify. We propose tool-aware recursive decomposition, which organizes tools by functional relationships into a hierarchy of capabilities. During execution, the agent discovers tools on demand and uses the hierarchy to recursively decompose a complex task into a subtask tree whose levels are aligned with the capabilities required at each stage. Experiments on complex real-world tasks show that the proposed method improves end-to-end task success rate by up to 40 percentage points over the compared baselines. The implementation of TaReD is available on GitHub: https://github.com/WeiXiang-Mao/TaReD.
In this work, we investigate the late-time expansion history and geometric diagnostics of logarithmic and exponential Finsler--Randers--Sasaki (FRS) cosmological models. We constrain both scenarios using cosmic chronometers, Baryon acoustic oscillations, and Pantheon+ Type~Ia supernovae, considering baseline fits as well as configurations calibrated with the local SH0ES distance-ladder prior. In the uncalibrated case, both profiles provide consistent descriptions of the late-time expansion history. Incorporating the SH0ES prior increases the inferred Hubble constant and modifies the inferred acoustic scale, reflecting the interplay between the local distance-ladder calibration and the BAO distance scale. Cosmographic reconstructions reveal a smooth transition from deceleration to acceleration at intermediate redshifts. Over the observationally relevant redshift range, both models exhibit a non-phantom, quintessence-like effective dark-energy sector. Finally, statefinder diagnostics distinguish the two FRS geometries: the logarithmic model remains relatively close to the canonical flat $Λ\mathrm{CDM}$ fixed point, whereas the exponential model follows a distinct dynamical trajectory. These results demonstrate that, despite their similar background expansion histories, the two FRS constructions can exhibit substantially different higher-order kinematic signatures.
Personalized conversational AI relies on long-term memory systems that extract facts from user utterances and store them in persistent vector stores. Despite progress in retrieval, deduplication, and lifecycle management, the formation stage, the moment a fact is first written to storage has received almost no principled attention. We identify this as the binding constraint on memory quality in production systems. Critical contextual signals, such as the distinction between a permanent user attribute and a transient situation, exist only in the original utterance and are irreversibly lost the moment extraction produces a subject-relation-object triple. No downstream process can recover them. We propose Gated Memory, a lightweight, modular formation framework that interposes two decision checkpoints between conversation and storage: an admission gate that evaluates every candidate fact against the full utterance context before extraction runs, and a conditional enrichment stage that grounds admitted facts through an entity scope taxonomy with privacy constraints. The gate evaluates only the current exchange while using prior turns as read-only reference context, and produces a structured formation record. Admitted content is decomposed into atomic facts, each categorized, tagged with provenance (directly stated versus inferred), scoped to its condition of applicability, and grounded in resolved time and place, subject to a constraint that no entity absent from the context may be asserted. On the LoCoMo-10 benchmark with atypical emotional density in utterance data, Gated Memory achieves an overall +2.6% relative improvement in LLM-judge accuracy over a strong baseline with identical retrieval and generation, establishing formation quality as a measurable constraint on memory performance.
Let $\mathcal{P}_n$ denote the set of distinct permutations of length $n$ that arise from the flattening process applied to the partitions of $[n]=\{1,\ldots,n\}$. In this paper, we consider the problem of avoidance of a single classical pattern of length four by members of $\mathcal{P}_n$. Let $p_n(τ)$ denote the number of members of $\mathcal{P}_n$ that avoid the pattern $τ$. We show that $p_n(τ)=C_{n-1}$ for all $n \geq 1$ for seven patterns of length four yielding new combinatorial interpretations of the Catalan number sequence. Further, we show that $p_n(τ)$ corresponds to the binomial transform of Catalan numbers for three other patterns. To establish our results, we suitably refine the counting sequence $p_n(τ)$ in each case so as to obtain a system of functional equations satisfied by the corresponding generating functions. These functional equations may then be solved explicitly leading to a determination of $p_n(τ)$ in each case.
Target speaker tagging (TST) assigns enrolled speaker identities to diarized segments of multi-speaker recordings. The enrollment utterances of the other registered speakers are an attractive source of evidence for calibrating each verification decision: they share the deployment domain of the test material and require no external cohort set. We show, however, that they cannot serve as the cohort of conventional score normalization. Enrollments tend to cluster by recording session, so the per-speaker cohort statistics reflect enrollment proximity to the rest of the gallery rather than impostor behavior, and normalization then rejects entire speakers. We propose gallery affinity verification, a cohort-free calibration that exploits the gallery through two affine-invariant terms, score dispersion and enrollment-profile deviance, and is therefore immune to such per-speaker shifts. On a synthetic benchmark and an in-house meeting corpus, it improves tagging accuracy with and without conventional score normalization and adds further gains when combined with it.
We aim at studying the well-posedness of stochastic porous media equation problems under nonhomogeneous Dirichlet boundary. We obtain an unconventional homogeneous Dirichlet boundary stochastic porous medium equation by transformation under an additional assumption, and then use approximation problems to obtain the well-posedness properties of the equation with homogeneous Dirichlet boundary conditions under different initial conditions. Consequently, we obtain the corresponding solution to the original equation.
Conventional diffractive deep neural networks (D2NNs) treat polarization as independent channels and rely on scalar or semi-vectorial propagation models, which neglect cross polarization coupling and vector diffraction. Here we propose a vector D2NN (V-D2NN) that embeds the full vector angular spectrum method into the end-to-end training pipeline. This physically rigorous framework describes vectorial light-matter interactions across cascaded diffractive layers, enabling direct optimization of polarization conversion, spin-orbit coupling, and vectorial interference without external polarization optics. We demonstrate the V-D2NN on polarization-multiplexed tasks--ector beam generation, polarization dependent imaging and classification, and multiple channel optical encryption--where it consistently outperforms scalar and semi-vectorial counterparts. In longitudinal-field engineering, the V-D2NN actively shapes a prescribed longitudinal field with a normalized correlation of 0.839, a capability inaccessible to scalar-propagation models. An open-source training framework is also provided to support further development of vectorial diffractive optics for computing, sensing, and communications.
Phoneme-level models transcribe or generate speech as a sequence of phonemes, the smallest sound units that distinguish words. These models enable fine-grained pronunciation control and understanding, yet often fail on input that does not match any single training language, such as speech alternating between two languages, known as code-switching, or low-resource languages absent from training. We identify a systematic failure mode behind this, phonological interference: models assume the input is in a single language and impose its phonology, overriding local phoneme-level decisions that conflict with the assumed language. We measure interference by how often a model retains phonemes that one language has but the other lacks. On code-switched input, two phone recognizers (speech-to-phoneme models) and a phoneme-conditioned text-to-speech model lose 32% to 79% of these phonemes, but lose far fewer of the phonemes both languages share. On unseen languages, we find that phone recognizers impose the phonology of the training language they assign to the speech, and the more confident the assignment, the more they lose phonemes the unseen language has but the assigned language lacks. We probe the models' language estimate from their internal activations, and trace interference to a low dimensional subspace. On monolingual speech, steering this subspace toward another language makes the model lose the phonemes that only the original language uses and produce phonemes that only the target language has. We introduce windowed language estimation (WLE), an inference time repair that replaces the model's language estimate in this subspace with one computed from a short window around each position. On code-switched input, WLE removes 34% to 69% of the interference in all three models, and in the recognizers it leaves monolingual performance essentially unchanged.
A reciprocity between multiplicities of projective direct summands for modular group algebras has been known for decades. Recently, the first author extended it to finite-dimensional symmetric algebras. We further generalize the reciprocity theorem to arbitrary finite-dimensional algebras by establishing a tensor-hom adjunction for stable and costable categories.
Point-of-Interest (POI) reranking in local search must model query-conditioned tradeoffs among lexical semantics, geospatial proximity, and numerical quality signals such as rating and review count, while remaining practical under real-time serving constraints. A close POI may only partially satisfy the query intent, while a farther one may offer stronger semantic and quality evidence. We present H2CE, a Heterogeneous Two-stage Cross-Encoder for latency-bounded POI reranking. H2CE represents numerical attributes in two complementary ways: bucketized natural-language descriptors are inserted into the cross-encoder input to support semantic--numeric attention, while exact scalar values are processed by dedicated MLPs to preserve magnitude information. The resulting semantic and numerical embeddings are fused through latent-space aggregation, enabling nonlinear interactions beyond scalar weighted sums. H2CE then applies a two-stage architecture: Stage 1 scores all candidates pointwise for scalable filtering, and Stage 2 performs head-to-head pairwise comparison among the top-$K$ candidates with Copeland aggregation, making fine-grained relative tradeoffs explicit while reducing pairwise cost from O(N^2) to O(N+K(K-1)). On a 5,743-query local search test set, H2CE achieves 67.48% NDCG@5, improving over XGBoost LTR by +22.82% absolute and over a zero-shot LLM reranker by +35.89%. The pairwise stage adds +1.98% NDCG@5 over the pointwise model alone. Ablations confirm the value of numerical features, latent aggregation, top-K pairwise reranking, and aligned training.
An online speaker diarizer maintains a growing inventory of speakers, and applications read it directly: a live transcript enumerates them as they appear. Existing systems either fix the inventory's size in advance, so speakers beyond that size are merged, or grow it on distance alone, so noise and turn boundaries split speakers. Scored on speaker count over nine public datasets, both failures appear where DER reports neither: on VoxSRC-23 the fixed-capacity systems return 44-46% too few speakers and the unbounded tracker with the lowest DER 63% too many. We build on that embedding-based tracker and change only what triggers a registration. A candidate speaker pool keeps unregistered embeddings apart and registers a speaker only once one candidate has gathered enough mutually compatible embeddings; commit-gated label assignment holds an output while its candidate is undecided, so no speaker appears in the output before it is confirmed. Across the nine datasets the macro speaker-count error falls from 225% to 21% of the reference and macro DER from 17.59% to 15.95%, at a mean added latency of 0.109s over all outputs; on VoxSRC-23 the tracker obtains both the lowest DER and the most accurate speaker count of the systems compared.
The recent e-closure method can recover every procedure that controls FDR (and other expectation losses). But the recovered e-collection is ``self-referential'' and gives no insight on how to improve the procedure (if improvable), and some recent improvements have been somewhat opaque. We introduce an elementary new technique called anchoring that exploits looseness in existing FDR proofs to enlarge a baseline multiple-testing procedure's self-referential local e-value. The resulting e-closure thus transparently retains every baseline discovery (and usually adding more) and controlling the false discovery rate under the same conditions as the baseline. To show that this principle is broadly applicable, we use it to improve a large suite of multiple testing procedures: (i) Anchored-BH dominates the Benjamini-Hochberg (BH) procedure under PRDS while being incomparable to Goeman's recent closed-BH, (ii) Anchored-BY dominates the Benjamini-Yekutieli (BY) procedure under arbitrary dependence while being incomparable to closed-BY, (iii) For two-sided Gaussian p-values (under appropriate covariance conditions), Anchored-2BH dominates running BH twice at half the level on two one-sided p-values, (iv) Anchored-dBH dominates dependence-adjusted BH, (v) Anchored e-BH dominates e-BH and is incomparable to closed e-BH, (vi) Anchored SeqStep+ improves the original (including selective and adpative variants) while preserving ordered rejection structures. All of these are accomplished in sorting or quadratic time. The appendix shows how to dominate Shifted-BH (for two-sided arbitrarily correlated Gaussians) and NDBH (under negative dependent p-values).
A Poisson's ratio near -1 indicates only that the bulk modulus is small compared with the shear modulus. In solid-void structures, the mechanism that frees the dilation usually weakens the resistance to shear as well, resulting in both moduli becoming small. In two-dimensional linear elasticity, we demonstrate that this loss is not inevitable. We consider a honeycomb of regular hexagonal blocks of a single incompressible isotropic elastic solid, joined along their whole edges by ideal interfaces that allow relative sliding along a direction inclined to the edge normal. Collective infinitesimal block rotations produce an exact dilational mechanism, so the effective bulk modulus vanishes, while sixfold symmetry ensures isotropy. The interfaces, however, transmit traction along their whole length. In a solid-void realization, each interface is replaced with fine solid plates separated by void, which bend easily yet retain their capacity to transmit axial force. Such dilational materials, which expand or contract freely while resisting every change of shape, could serve as interlayers that accommodate thermal or swelling mismatch while still transmitting shear, and as components in stents and deployable structures that change size without changing shape. An explicit, statically admissible stress field and the complementary energy principle yield a rigorous lower bound on the retained shear modulus, and a limiting argument transfers this bound to the solid-void mixtures. The honeycomb retains more than four-fifths of its constituent's shear modulus at zero bulk modulus: the supremum S of the normalized shear modulus of such mixtures satisfies S > 0.8528 > 4/5, exceeding the value attained by Milton's construction.
Large language models (LLMs) are commonly post-trained against LLM judges and other cheap surrogates because the true reward, such as human preference, is too expensive to query at scale. This practice often leads to reward hacking, where reinforcement learning against a miscalibrated surrogate leads to undesirable side effects. In this work, we study a setting in which a small number $n$ of model outputs are annotated with ground-truth labels (e.g., from expert review) and used to recalibrate the LLM judge before optimizing against it. Prior approaches to judge recalibration are costly or heuristic, and it is known that on-policy sampling fails when the surrogate is miscalibrated on a rare set of outputs. In this work, we propose envelope sampling, a theoretically-grounded method for judge recalibration that seeks to minimize an upper bound on the regret of the post-trained model under the assumption that the human reward and re-calibrated reward lie in an $L^2$ ball around the judge. We give practical algorithms to sample from the envelope by rejection or by fine-tuning against a modified reward, and experiments on clinical note generation and on a controlled sycophancy task show that recalibrating on envelope samples mitigates reward hacking where recalibrating on base-model samples does not.
Classical Schur--Weyl duality plays a fundamental role in the representation theory of general linear and symmetric groups. In this paper, we develop an affine Schur--Weyl theory for the Laurent polynomial loop semigroup. Let $\hat G_K(n)$ denote the Laurent polynomial loop semigroup inside the loop group $GL_n(K((t)))$ over a field $K$, and let $\hat S_K(n,r)$ be the affine Schur algebra. The natural action of $\hat G_K(n)$ on the affine tensor space $Ω_K^{\otimes r}$ induces an algebra homomorphism $K\hat G_K(n)\rightarrow \hat S_K(n,r).$ We prove that this homomorphism is surjective for every field $K$ satisfying $|K|>r$. Furthermore, we establish the double centralizer property for affine Schur algebras over unique factorization domains for all $n\geq2$. For $n\geq2$ and any field $K$ with $|K|>r$, this yields the corresponding centralizer property for $\hat G_K(n)$. In contrast, for $n=1$ and $r\geq2$, the corresponding natural homomorphism is not surjective over any field. For $n\geq 2$, we use the double centralizer theorem to determine the center of the affine Schur algebra and, when $K$ is a field with $|K|>r$, show that $\hatζ_{r,K}$ maps the center of $K\hat G_K(n)$ onto it. Over an algebraically closed field $K$ of arbitrary characteristic, we prove that every finite-dimensional irreducible $\hat S_K(n,r)$-module is a tensor product of evaluation modules. Moreover, we obtain explicit character formulas expressing these irreducible characters as products of characters of irreducible classical Schur algebra modules. Finally, we study polynomial representations of $\hat G_K(n)$ over algebraically closed fields $K$, and classify its finite-dimensional irreducible polynomial representations. For finite fields $\mathbb F_q$ with $q>r$, this yields a classification in the defining-characteristic setting.