Papers

Open-vocabulary segmentation enables rich semantic perception for UAVs, but frame-wise predictions can remain temporally inconsistent across repeated observations and changing viewpoints. We present PerSeM, a training-free persistent semantic memory framework for long-horizon open-vocabulary UAV mapping. PerSeM associates frame-wise semantic observations with persistent world-space voxels and constructs a majority-based semantic memory, which is conservatively refined through history-preserving spatial refinement, trust-aware replay, and context-guided verification. Experiments on the Forest and UAVScenes benchmarks show that persistent 3D memory provides substantial gains in semantic correctness and temporal stability over frame-wise predictions. Beyond this strong persistent-memory baseline, PerSeM provides consistent additional improvements, improving both semantic accuracy and temporal stability across all five evaluated UAVScenes sequences. Analysis using regions identified independently of the final PerSeM predictions further shows that these gains are concentrated in semantically difficult and temporally unstable regions, where majority-based memory is most likely to remain uncertain. These results demonstrate that persistent 3D aggregation provides a strong foundation for long-horizon semantic mapping, while conservative refinement of uncertain memory states can provide additional improvements without retraining or additional neural-network inference.

Conventional robot planning methods seek collision-free paths to a goal but fail when all paths are blocked. In these cases, the robot must determine which objects to relocate, in what order, and where to place them to clear a path—a problem known as Navigation Among Movable Obstacles (NAMO). Most NAMO planners assume a known environment, while existing approaches for unknown environments typically reason locally about relocations and cannot plan interdependent relocation sequences. We consider NAMO in unknown environments revealed through onboard sensing, where the robot must decide whether a blocked route requires relocation or a feasible path may exist through unexplored space. We propose an online framework that addresses this ambiguity by selecting between navigation and relocation using shortest paths that treat discovered movable objects as obstacles or as removable. Navigation relies on existing motion planners, while relocation uses a sampling-based approach that, unlike existing approaches for unknown environments, searches over interdependent relocation sequences and uses an LLM to bias sampling. Numerical experiments demonstrate scalability to cluttered environments requiring interdependent relocations and improved plan quality over existing baselines.

Active subspace methods provide a framework for quantifying predictive uncertainty in high-dimensional models by identifying and performing inference along parameter directions that have the greatest influence on the model output. However, the construction of active subspaces requires storing many full-dimensional model gradients, which becomes prohibitive as model size increases. We address this limitation by proposing Compressed Active Subspaces (CAS), a scalable approach that first maps the model parameters to a compressed space using a structured isometric embedding and then constructs the active subspace within this reduced parameterization. Our approach substantially reduces the memory required for active subspace construction and enables Bayesian inference for large models where standard active subspace methods become impractical. We demonstrate the scalability of CAS on neural networks of increasing size while maintaining predictive performance and robust uncertainty estimates.

Low-altitude wireless networks (LAWNs) are emerging as a key infrastructure for heterogeneous unmanned aerial systems that support concurrent services within a shared three-dimensional airspace. Their coexistence creates strong coupling among mobility, connectivity, and shared network resources, while heterogeneous services impose distinct and time-varying requirements. These interactions naturally form a dynamic non-cooperative game in which both operating conditions and coordination objectives evolve over time. Conventional optimization and learning-based controllers typically rely on predefined objectives, limiting their ability to adapt autonomously to changing service requirements and resource priorities. To address this challenge, we propose a hierarchical hybrid large language model (LLM)- multi-agent reinforcement learning (MARL) architecture organized as a dual-loop structure. Specifically, an outer adaptation loop employs LLM-assisted game orchestration to interpret service requirements and operator intent, and reconfigure objectives and resource priorities, while an inner loop executes decentralized, parameter-conditioned MARL policies under the configured game. A logistics-monitoring case study illustrates how the proposed framework facilitates coordinated coexistence among heterogeneous services, adapting to evolving operating conditions without retraining the underlying MARL policies. Finally, we discuss key challenges and research directions toward scalable, trustworthy, and adaptive agentic LAWNs.

The metric traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization that asks for a minimum-cost tour covering all clients in a metric graph. The metric multiple-depot TSP (MD-TSP) is a natural extension, where the graph contains depots and clients, and the objective is to compute a minimum-cost set of tours covering all clients, with each tour starting and ending at the same depot. When the number of depots is part of the input, an adaptation of the Christofides–Serdyukov heuristic yields an approximation ratio of $2$. In this paper, we introduce a $(1+1/\sqrt{2})$-approximation algorithm. Like the Christofides–Serdyukov heuristic, our algorithm first computes a rooted spanning forest (RSF), then a matching to correct its odd degrees, and finally obtains a solution by shortcutting. However, instead of using a minimum-cost RSF, we construct an RSF by a primal-dual algorithm for a natural cut relaxation. The algorithm grows rootless components and the component containing all depots at different rates, adding an edge when its dual constraint becomes tight. Vertex labels record the times at which clients first become connected to a depot. The two-speed growth provides a joint bound on the forest cost and two label-dependent terms that also arise in bounding the parity-correction cost. Balancing the coefficients of these two terms by setting both to $\sqrt{2}-1$ yields the claimed approximation ratio.

Simultaneous localization and mapping (SLAM) is one of the services running on an autonomous robot. It is typically run to assist other tasks such as planning, manipulation, etc. All these tasks are run on edge hardware and are subject to severe resource constraints. However, most SLAM systems are built and tested in isolation, and their performance is reported as if they are the only task running on a system. We observe that existing benchmarks lack a common mechanism for comparing SLAM systems under realistic resource constraints. To address this limitation, we have developed SLAMSqueezeBench, a framework that allows testing of SLAM systems under realistic workloads on edge hardware. It does so by imposing constraints on compute and memory resources available for the SLAM system during execution. It also simulates realistic camera frame acquisition with frame drops when a finite buffer is full. Using SLAMSqueezeBench, we compare nine SLAM systems spanning classical systems, learning-based systems, and approaches for Gaussian splatting. Our testing framework will be available for use by the community upon publication.

We propose PaRID (PaRallel Instruction Duplication), a software-directed soft error detection framework that requires only compile-time effort for multithreading parallel programs. PaRID addresses two key challenges: supporting parallel programs with mixed serial and parallel regions and minimizing performance overhead without relying on costly dynamic profiling. It combines parallel-aware code transformation with LLM-tuned performance modeling, guided by eight generalizable findings from an offline characterization study, to enable fast soft error detection in parallel applications. Evaluation on NPB benchmarks shows that PaRID reduces protection overhead from 162.79% to 59.84% on average and achieves up to 5x speedup while maintaining full error detection effectiveness.

Hiring is bilateral: employers assess fit, while candidates present and defend evidence of their qualifications. Yet résumé screening, the first gate, is commonly automated as a static, one-call judgment over a résumé-job pair. We study a two-agent alternative in which employer-side and candidate-side agents represent these roles, exchange evidence, and update their judgments before deciding who advances. We compare procedures on 600 constructed résumé-job pairs using GPT-5.5 and Claude Opus 4.7. Two-agent screening advances more applications (33.3% to 39.3% for GPT-5.5; 34.0% to 35.5% for Opus 4.7). Across three runs on the common 191-pair borderline pool, pass-instance rates rise from 4.5% to 26.2% and from 6.5% to 16.1%, respectively. This is not a uniform relaxation: two-agent screening rejects applications one-call advances, changing decisions in both directions. At similar pass volumes, the procedures advance different applications, and no one-call threshold recovers applications consistently selected by two-agent screening. Among discovery-selected cases re-executed in fresh runs, two-agent-only selections recur less often than shared selections, clearly under GPT-5.5 and less certainly under Opus 4.7, while a separate one-call follow-up shows no comparable decline. As hiring becomes agent-mediated on both sides, the screening procedure, not only the model behind it, shapes who reaches human review and how reliably that access recurs.

Suppose we observe the first $n$ points of a sequence of random variables having length $n+1$, and wish to estimate a functional of the unobserved final point and the empirical measure of the $n$ observed training points. Such next-token functionals include the probability that the next token is novel (also known as the surprise probability), the tail probability of the minimum distance between the next token and training points, and the test error of a classifier trained on the observed points. All of these quantities are classically estimated by the leave-one-out method, which is inconsistent under temporal dependence. We propose a leave-a-window-out estimator, which deletes a window of length $\tau$ after each index before forming the empirical measure and reduces to leave-one-out at $\tau = 1$. Under natural assumptions, we show that the error of our estimator decays at a parametric rate for any stationary $\beta$-mixing process that also admits a Marton coupling. Our results thus cover several natural functionals on a large class of stochastic processes. We complement these upper bounds with a sharp minimax lower bound for estimating the surprise probability on mixing Markov chains. Simulations on Markov chains, moving-average processes, and autoregressive processes show that our estimator succeeds in many scenarios where leave-one-out and add-constant baselines fail.

We consider the question of designing a universal family of sets $F \subset 2^{[n]}$ such that for any function $f:2^{[n]} \to R_{\geq 0}$ in a certain class, we have $$\max_{S \in F} f(S) \geq c(n) \cdot \max_{S \subset [n]} f(S).$$ We prove that there is a family of subpolynomial size such that for any nonnegative submodular function, $c(n) = \Omega(\frac{\log \log n}{\log n})$, and there is a family of logarithmic size such that $c(n) = \Omega(\frac{1}{\log n})$. We also prove that pairwise independence (which achieves a constant factor for graph cut functions), or even $k$-wise independence, does not imply a bound better than $O(\frac{1}{\sqrt{\log n}})$ for submodular functions. On the other hand, we prove that for any polynomially representable subclass of nonnegative submodular functions (such as the matroid connectivity functions for matroid representable over $F_q$), a constant-factor universal family of polynomial size always exists. For absolute XOS functions (a class that we introduce, in the form $f(S) = \max_i |\sum_{j \in S} w_{ij} + c_i|$ where $w_{ij}, c_i \in R$), we design a family of polynomial size such that $c(n) \geq \sqrt{\frac{\log n}{n}}$, and prove that there is no polynomial-size family achieving a factor better than $O(\sqrt{\frac{\log n}{n}})$.

Air-ground transportation research increasingly relies on co-simulation, yet constructing scenarios remains labor-intensive and difficult to validate. More importantly, a generated scenario may execute successfully while failing to realize the spatial, temporal, communication, or behavioral relationships requested by the user. This paper presents AURORA, a natural-language-driven agentic framework that treats air-ground scenario generation as a process of compilation with verification. Central to AURORA is the Air-Ground Scenario Graph (AGSG), a typed intermediate representation that explicitly connects agents, aerial missions, events, communication links, success conditions, and their cross-domain dependencies. This shared representation enables simulator-grounded parsing, joint road-airspace grounding, temporal planning, pre-execution feasibility checking, trace-based runtime verification, failure localization, and bounded repair within a unified workflow. We further introduce AURORA-Bench to evaluate not only whether generated scenarios execute, but whether they faithfully realize the requested interactions. Experiments across multiple language models show that structured execution substantially improves reliability, while runtime verification exposes silent failures that completion-based evaluation overlooks. Localized repair further resolves many violations without regenerating the entire scenario. The results show that reliable scenario generation requires verifying realized behavior, not merely executable code, and demonstrate the value of explicit intermediate representations for verifiable and repairable language-driven co-simulation.

Coding agents can recursively modify their own implementations, forming a loop of self-improvement. While prior work shows this can boost performance on coding benchmarks, existing approaches are costly and compute-intensive. We introduce a simple, sample-efficient self-improvement framework that significantly improves coding performance under strict budget constraints. We identify evaluation of candidate self-modifications as the main runtime bottleneck since prior approaches estimate their effectiveness by re-running a subset of benchmark tasks with the modified agent, which is time-consuming. We introduce Recursive Self Improvement via Fast Tree-search (SIFT), which augments these downstream task evaluations with an LLM-as-a-judge signal that performs pairwise comparisons between candidate patches, where the win-loss record is aggregated with a regularized Bradley-Terry model, and the resulting strength scores drive rank-based parent sampling inside a lightweight disaggregated tree search. Expensive downstream task evaluations are reserved only for the most promising nodes. Using a fully disaggregated tree search pipeline, the judge scores provide intermediate signal to guide exploration on promising candidate patches without being bottlenecked by slow evaluation runs. SIFT outperforms existing tree-search based self-evolution frameworks on the full Polyglot benchmark with significantly lower resource requirements in terms of CPU hours, wall clock time, and API cost.

Clinical B-mode images are widely available as potential data sources for quantitative ultrasound (QUS) analysis for tissue characterization. However, standard clinical ultrasound devices apply unknown log-compression to RF envelope data before display and storage. Previous work has demonstrated estimation of the underlying RF envelope statistics in the presence of an unknown compression law. Using Fisher information analysis, we show that finite-offset log compression causes severe information loss when estimating the Rayleigh scale $\sigma$, which controls diffuse speckle. For a single image window, unknown compression raises the minimum achievable variance for unbiased estimation of $\sigma$ by a compression-independent factor of approximately 34.98. When $M$ equal-sized windows share the same unknown compression settings, the excess variance decays as $1/M$; even in the most favorable regime, reducing the variance inflation factor below 1.1 requires 340 windows. Our analysis treats the contrast parameter $a$ as unknown and the boundary offset $b$ as known; estimating $b$ experimentally shows even larger variance. We validate this theory using synthetic estimation experiments and demonstrate RF-scale recovery on real RF-envelope windows from the OASBUD dataset. Together, these results clarify the limitations of using routine B-mode images for QUS.

Benchmark scores alone provide an incomplete basis for assessing the trustworthiness of modern artificial intelligence systems. Large language models (LLMs), agentic systems, and multimodal models (MLLMs) require different forms of assessment, yet their evaluation evidence must remain interpretable for development and oversight. We propose a unified framework that connects output-level, trajectory-level, and cross-modal assessment through eight trustworthiness dimensions: capability, robustness, safety, fairness, transparency, governance, oversight, and efficiency. The framework preserves system-specific metrics while mapping native measurements to common performance bands, accompanied by uncertainty estimates and traceable evidence. A meta-evaluation layer examines the validity, reliability, and reproducibility of the evaluation itself. Multidimensional profiles expose strengths and weaknesses, while safety-critical overrides prevent aggregate scores from masking critical failures. Mappings to governance frameworks, international standards, and European Union regulatory requirements connect technical assessment with oversight needs. The framework provides a structured basis for assessing both system performance and the credibility of the evidence supporting it, with empirical validation across deployment contexts remaining an essential next step.

Web agents often revisit the same sites, yet most evaluations discard the procedures learned in earlier successful interactions. We introduce EconSkills, a skill library and evaluation framework that distills verified EconWebArena trajectories into parameterized standard operating procedures for retrieving live economic data. Each skill records its scope, navigation procedure, site-specific guidance, verification checks, and recovery steps while replacing source-instance values with placeholders. EconSkills separates two questions: whether a known relevant procedure transfers to a held-out task, and whether an agent can retain that benefit when selecting from a library. In controlled transfer, matched skills improve success over no-skill prompting and require fewer steps on paired successes. Under the evaluated prompt formats, the parameterized skill prompt substantially outperforms the corresponding raw-trajectory prompt. With the full 50-skill library, retrieval is competitive with the no-skill baseline overall and performs best on tasks with a direct family match; approximate matches on other tasks offset these gains. Browser trajectories further identify when procedural guidance shortens portal-specific navigation and when semantic verification remains necessary. These results establish that reusable economic web procedures can transfer across task instances and provide a concrete design target for match-aware selection and context delivery.

Recurrent-depth Transformers reuse one block across many steps, so information needed later must survive repeated rewriting of the hidden state. A natural remedy is to keep more history. We show that, in controlled cellular-automaton tasks, making history available is not the same as making it usable. Using Rule 30, where the correct state is known at every recurrent step, we test depth extrapolation and de- layed recall, the recovery of an earlier state after further computation. CoTFormer, which caches keys and values from every earlier step, extrapolates less far and recalls less accurately than a Block Universal Transformer (BUT) that keeps only its current state. Interventions show that its retained history can pull a corrected trajectory back toward failure, and that the cache block written at the requested step is neither necessary nor sufficient for recall. We introduce LSTM-UT, which adds a small, bounded, gated cell state to the shared block. Trained to depth 12, LSTM-UT keeps 99.7% exact-row accuracy at depth 60, where BUT gets no row fully correct, and one checkpoint stays above 99.95% at depth 1,000. It also improves delayed recall over both baselines, and the advantage largely persists at near-matched parameter counts. On these tasks, a small state under learned control proved more useful than a complete but unaddressed history. In OpenWebText2 language modelling, LSTM-UT outperforms BUT and, at equal width, reaches slightly lower perplexity than CoTFormer while CoTFormer needs up to 91% more training time per step; against a parameter-matched CoTFormer, LSTM-UT comes within 0.6 perplexity.

Language-model agents are increasingly asked to carry out work spanning days or weeks, such as an operations remediation or a research programme. Such a task outlives any context window, any process and any interval at which a person can attend. In this paper, we argue that a long-horizon agent must run continually without forgetting before it can learn continually. This ability lies in the harness around the model rather than in the model itself. We derive seven bottlenecks from the long-horizon setting and answer them with a hierarchical architecture of three parts: (i) levels indexed by time scale, each keeping a bounded file summarising the level below; (ii) a clocked tick as the unit of autonomous action; and (iii) cascaded intelligence, where work is escalated to a more capable model only after failing review. We report on a ten-day campaign in which an agent built on this architecture reproduced a published reinforcement-learning result with a human attending once a day, and show (1) the agent kept the thread across every context reset and session boundary of the campaign, (2) operating knowledge written early changed later behaviour with no change to model weights, and (3) where learned components would enter such a system. Overall, our experience suggests continual learning for these agents needs a substrate outliving every context and process, and the checks the harness already runs are where a learner belongs.

We present AMB3R-SLAM, a real-time monocular SLAM system capable of reconstructing kilometer-scale trajectories over 10k frames on a single consumer-grade GPU. Our model couples a lightweight front-end for low-latency online tracking with a hierarchical backend that progressively enforces local, mid-level, and global consistency. By avoiding bundle adjustment that relies on the static world assumption, our system naturally handles complex dynamic scenes out of the box. Furthermore, we demonstrate that our method can be extended to leverage stereo, RGB-D, and LiDAR as additional inputs. AMB3R-SLAM achieves strong camera tracking performance across 9 datasets, reducing the absolute trajectory error (ATE) of previous state-of-the-art methods on VBR and Oxford Spires by over 70%. With additional LiDAR input, our model further reduces ATE to sub-meter level on KITTI and VBR datasets.

Verifier-based selection improves LLM performance by generating multiple candidate solutions and using a verifier to select the most promising one. However, existing methods typically treat verification only as a ranking step and discard its feedback once a fixed candidate pool has been evaluated. In this paper, we ask whether verification can also improve the candidate set itself. To this end, we introduce LLM-as-an-Improver and propose Verify–Repair–Reselect (VRR), which uses verification feedback to generate and reselect improved candidates. VRR retains the initial winner while conditionally generating three complementary alternatives: repaired versions of the winner and runner-up, and a solution based on a new approach. It filters invalid and duplicate candidates using only inference-time information and then reselects the final answer under the original evaluation criteria. Across diverse models and code-generation and reasoning benchmarks, VRR improves over fixed-pool verifier-based selection in many settings and can recover correct solutions even when all candidates in the initial pool are incorrect. These results highlight a broader role for LLMs as improvers: verification feedback can not only select among existing solutions but also construct stronger candidates beyond the initial pool.

Local-to-global techniques for establishing spectral gaps have played a central role in the modern theory of Markov chain mixing times and the theory of high-dimensional expanders. One of the most striking results in this burgeoning literature is that a spectral gap for the global down-up walk on the facets of a pure simplicial complex can be reduced to sufficiently strong spectral expansion of just the codimension-2 links of the complex, a phenomenon colloquially referred to as "trickle-down". These types of theorems have had many important applications, including rapid mixing of the exchange walk on the bases of any matroid. In this primarily expository article, we give streamlined proofs of two such theorems in the literature, one by Oppenheim (2018) and one by Leake and Oveis Gharan (2025), via an integrated Bochner method. Moreover, in the latter setting, we quantitatively strengthen the dependence of the global spectral gap on the dimension of the complex and the spectral influence, resolving an open question of Leake and Oveis Gharan. Disclaimer: The proofs were developed through a couple of rounds of interaction with GPT-5.6 Sol Ultra. We later discovered that Guo and Zhang (2026) had independently proven the same strengthening of the trickle-down theorem of Leake and Oveis Gharan using an extremely similar argument, also found by GPT-5.6 Sol Ultra. The focus of their paper is the complexity of approximating the partition function of spin systems on planar graphs, not on the trickle-down phenomenon itself. In contrast, our motivation is primarily expository, and we hope to bring Bochner-type methods and their connections with the trickle-down phenomenon to the attention of a wider community of researchers.

High-quality pre-training data is a critical bottleneck for educational and STEM-specific language models targeting edge AI and on-device deployment where token budgets are tightly constrained. While major organizations train ever-larger models on private corpora, the open ecosystem lacks STEM-focused synthetic datasets that deliver high per-token learning value efficiently for small models. To address this gap, we introduce QVAC Genesis III, a 191.43B-token, STEM-focused multi-domain synthetic corpus covering 19 domains across several difficulty levels and different educational styles. QVAC Genesis III is built via a dual generation strategy that performs targeted teacher distillation using a weak edge-scale student model as signal: the student's failures are converted into corrective explanations, while its successes are expanded into contrastive option-level reasoning over all answer choices. We further introduce an LLM-as-a-parser evaluation protocol that extracts final answers from free-form outputs and tracks both accuracy and answer validity. To validate the effectiveness of our QVAC Genesis III data, we conduct controlled from-scratch ablations with 1.7B-parameter models, showing that models trained with QVAC Genesis III consistently outperform both models trained with the open-source synthetic corpus Cosmopedia-v2 and the publicly released Cosmo-1B model across ARC, GPQA Diamond, and MMLU STEM benchmarks, achieving up to +28.57% on ARC-E and +21.35% on ARC-C, while reaching a Valid Answer Rate of up to 99.45%.

Robots can recall prior failures without knowing whether recalled evidence remains valid, conflicts with current observations, or is sufficient to guide a decision. We present CoreSense, a robot-system integration architecture that combines traceable episodic evidence with a conflict-aware belief gate and bounded, auditable recommendations. The gate checks scope, provenance, time, contradiction, and support before it permits PROCEED, requests re-observation, abstains, or escalates. Evaluation follows three complementary layers without commanding a physical robot: offline public real-robot data, a frozen signal-level simulation, and a live cloud deployment path. On CableTrace-120 and BotFails-200, belief gating reduces protocol-defined unsafe proceeds from 20% and 40% to 0%. A disjointly calibrated raw-video policy also reaches 0% unsafe proceed, but overblocks every nominal episode. On public data, a ViFailback-BotFails visual detector reaches 0.778 AUROC yet remains all-blocking, whereas cycle-disjoint UR3 telemetry for protective stops yields 0% unsafe proceed, 36.1% overblocking, and 61.9% coverage; grip-loss transfer remains a negative result. Controlled physical corroboration yields 3.3%, 0%, and 42.0%, while conflict-aware fusion yields 4.7%, 0%, and 42.8%. Finally, 20/20 cloud recalls validate a CockroachDB Cloud-Amazon Bedrock deployment path. The evidence supports an auditable integration pattern, not autonomous recovery or certified safety.

Large language models (LLMs) show strong zero-shot reasoning capabilities, yet their sensitivity to prompt context raises questions about reliability in deployment. This study investigates whether geographic context embedded in prompts influences LLM-based chronic kidney disease (CKD) screening, independent of any change in patient features. Using a community-based CKD dataset from Bangladesh (284 participants with 112 CKD and 172 non-CKD), we systematically varied the country attribute across 25 global contexts while holding all clinical inputs constant, and evaluated two open-weight LLMs (Qwen3 8B and Mistral 7B). Experiments were conducted on a common-correct subset of 156 participants for whom both models produced correct baseline predictions. Results show that non-CKD predictions were highly stable across geographic contexts, with both models maintaining consistent non-CKD predictions in nearly all settings. In contrast, CKD-positive predictions were considerably more sensitive. For Qwen3, CKD prediction dropped from a baseline of 65 to as low as 50 across country contexts, while Mistral showed smaller but non-negligible variation. Country contexts did not group according to known epidemiological or healthcare similarities; instead, groupings appear to reflect how country tokens are internally represented within each model. These findings demonstrate that geographic tokens can systematically shift clinical screening outcomes despite identical patient inputs, with implications for the deployment of LLM-based decision support in diverse healthcare settings.

Scaling exponents of neural dimensionality are read as properties of the code, and used to compare representations and benchmark models against cortex. Yet one recording of 11,311 mouse V1 neurons gives 0.25, 0.30 or 0.35, depending only on how it is subsampled. We show that such an exponent measures the population and the probe together. We split it exactly into a floor, which random subsets of the same sizes give, and a shift, which a declared axis of stimulus classes adds. The usual random-subsample exponent is almost all floor. Stimulus direction lifts the exponent in every grating recording by reading both symmetry sectors of the code: orientation, which repeats every half turn, and direction, which does not. The lift lives in trial-to-trial fluctuations that differ between directions, while the class means, which linear decoders read, pull it down. Two measured terms, how much the classes' fluctuations overlap and how the means sit against them, account for the shift. They give its sign where it changes: in Allen Neuropixels recordings, whose class means mostly raise the exponent, and in macaque V1. In an XY lattice whose classes stay on one orbit, temperature flips the sign as the two terms say, and in GPT-2 the shift ranks the indirect-object circuit's name-mover and backup heads. Reported with its path, its floor and its shift, an exponent says how much structure a probe finds and what carries it. Our open tool, rung, reports all three for any labelled neural recording or language-model layer: https://github.com/adilamin89/structure-in-the-zoom

Constructive classifiers add structure while they train: a level to a tree, a unit to a hidden layer, a split at a leaf. This paper asks what each of four such growth decisions buys, measured under one protocol on 24 datasets, and gives an exact diagnosis and fix for the one that buys nothing. The diagnosis concerns the natural way to deepen a soft decision tree: turn every leaf into a gate whose two children inherit the parent's class distribution, so the function is unchanged. I prove that this leaves the gradient of every new gate identically zero and with the gate at 1/2, gives the two children identical gradients, so under this construction the added level can never learn. That predicts where it costs: nothing on two-class problems, where two leaves already suffice and a great deal where more classes need more leaves. Measured, the cost is -0.2 points over 13 binary datasets and 40.2 points over 7 multi-class ones, and it tracks the number of classes (Spearman 0.64), not the number of features (0.03). The fix is any perturbation of the children. Neither its size nor its direction matters: a residual-directed initialisation changes accuracy by +0.20 points against noise. The other three decisions each buy one thing. Fitting a new hidden unit to the residual before installing it buys a smaller network but not a more accurate one. Splitting one leaf at a time buys sparsity; it lost accuracy until I found that the split started its two children identical and untrained, the same defect in another place; with the children inheriting the parent and the symmetry broken, per-leaf growth comes within 2.3 points of a complete tree using 23% of its splits. Requiring statistical significance before a node gets a more expressive split buys nothing. Every number comes from the measurement scripts.

Traditional dynamical system models, including Koopman operator representations, are fundamentally equality-based, whereas many analysis and control tools rely on inequalities. This mismatch motivates representations that are intrinsically aligned with certification tasks involved in the analysis and control synthesis problems. In this paper, we propose a data-to-certificates (D2C) paradigm that bypasses explicit model construction and directly learns certificates from data. We introduce supereigenfunctions of the Koopman operator as an inequality-based generalization of eigenfunctions that define exponential growth envelopes encoding stability, safety, and uncertainty propagation, thereby serving as certificates for a range of control objectives. We establish their theoretical foundations and show that the associated rates recover intrinsic dynamical quantities such as Lyapunov exponents. Two complementary constructions are developed: a geometric approach based on the multiplicative ergodic theorem (MET), and a resolvent/Gramian formulation that enables computation directly from trajectory data. The resulting framework yields certificates that can be used for stability and contraction analysis, as well as stabilizing and safety-critical control synthesis via convex quadratic programming-based optimization program. Numerical examples demonstrate the effectiveness of the proposed data-driven certification approach for stabilization, contraction, and safe control design.

In the Steiner Point Removal problem, we are given a graph $G=(V,E)$ with an edge-length function $\ell_G: E\rightarrow \mathbb{R}_+$ and a subset $T\subseteq V$ of terminals. The goal is to find a minor $H=(T, E_H)$ of $G$ on vertex set $T$ such that the shortest path metric derived from $G$ on the edges of $H$ preserves the distance between every pair of terminals within a small multiplicative stretch. Filtser proved that a stretch of $O(\log |T|)$ can be achieved (in polynomial time), while Chen and Tan more recently proved a lower bound of $\Omega\left(\sqrt{\frac{\log |T|}{\log\log |T|}}\right)$ on the achievable stretch. Their lower bound is via a simple construction involving low-degree high-girth graphs. The existence of such graphs is guaranteed through the existence of low-degree high-girth expanders. In this work, we improve the lower bound to $\Omega(\sqrt{\log |T|})$ using the same simple construction of Chen and Tan but with a more careful analysis that exploits the expansion property.

Breast cancer is a significant contributor to female mortality across the world, displaying one of the highest oc currence rates among the various cancer types. In response to the need for early breast cancer detection, researchers have increasingly turned to association rule-based classification as a favored method. Association Rule mining is a data mining approach which offers the benefit of yielding results that are readily understandable for medical professionals. This paper introduces a novel association rule-based data mining technique for breast cancer classification based on a weighted classification approach. This implementation employs three core algorithms: Rule Generation, Rule Pruning, and Rule Prediction. Rule Generation identifies frequent itemsets and creates association rules. Rule Pruning eliminates rules using specific criteria and separates them into major and minor groups based on their influence on training data. Rule Prediction applies the pruned rules to classify test data. The final prediction algorithm was tested on several testing samples to show the feasibility and performance of the approach.

We study commercial intent inference that runs entirely on the user's device, under three constraints frozen before the work began: the downloaded payload under 3 MiB, Tier-0 inference under 20 ms at p95, and no raw text, content embedding, or stable identifier leaving the device. Under them we build a retrieval path over a 6,020-leaf commercial taxonomy: a static embedding table distilled from a Korean sentence transformer, quantized to 4 bits, no inference runtime. Our main result is where that constraint costs accuracy. On real Korean commerce text labelled by others (22,900 AI-Hub shopping reviews), mid-category top-5 on real product names is 75.0% against an 18.4% permutation baseline, but splits on one observable: a query containing some leaf name as a substring scores 83.5%, one containing none 45.2%. A generic 196.6x larger teacher seemed to localize the gap (+20.1 pp without an anchor, +0.1 with). That null was two effects cancelling: the same teacher fine-tuned on the student's own contrastive pairs reaches 0.8586 and beats the pure-encoder student by +10.6 pp with an anchor and +20.9 pp without. The cost is not uniform, but it is not free anywhere; where the anchor is absent, task adaptation buys the teacher nothing, so what the constrained encoder lacks there is capacity. The expensive regime is detectable on-device from the ranker's own score margin: declining the least confident fifth lifts the rest to 0.8296. A second axis we first reported, a manufacturer model code, does not survive source-category fixed effects (-4.0 pp, p=0.51); the anchor does (+13.0 pp). Payload is 2,942,652 bytes, all three library links measured. Tier-0 p95 is 4.431 and 3.670 ms on two iPhones (A14, A16) and 5.080 ms on a budget Android tablet (Snapdragon 695), all slower than three server CPUs on the same code. Taxonomy supervision is mostly synthetic Korean utterances.

Natural turn-taking in full-duplex voice interaction requires determining from partial speech whether a pause reflects hesitation or a completed conversational intent. Acoustic voice activity detection lacks this semantic information, while cascaded ASR-based endpointing introduces transcription dependence and additional processing stages. We formulate semantic endpoint detection as a causal audio-language reasoning task and introduce FD-VAD, an ASR-free streaming endpointer that maps bounded causal audio windows directly to Continue/Stop decisions. FD-VAD combines a frozen speech encoder with a lightweight modality adapter and a parameter-efficiently adapted language model, using a last-chunk training objective for streaming inference. We further introduce confidence-gated endpoint commitment to control interruption versus delay and boundary-focused hard-negative sampling to improve decisions around ambiguous turn boundaries. Across in-domain and conversational evaluations, FD-VAD outperforms strong streaming and non-streaming semantic turn classifiers, and achieves the highest EOT recall among qualifying systems on TurnBench dev set $0.853$ (at FP<=0.10) in a zero-shot setting. These results show that semantic endpointing can be performed directly from streaming audio without intermediate ASR or dialogue state tracking.