Papers

Satisfiability Modulo Theories (SMT) solvers are foundational to software verification, program analysis, and compiler testing, particularly over the theory of Quantifier-Free Floating-Point (QF_FP). While recent optimization-based SMT solvers have successfully applied gradient descent to continuous relaxations of logical formulas, they are fundamentally bottlenecked by gradient domination, a phenomenon where a small subset of difficult clauses hijacks the optimization trajectory, preventing the solver from satisfying the broader formula and trapping it in local minima. To overcome this, we present GradSAT, a novel framework that bridges optimization-based SMT solving with Multi-Task Learning (MTL). GradSAT reformulates the constraint satisfaction process by treating each SMT clause as an independent MTL task. By applying dynamic gradient normalization (GradNorm), GradSAT actively balances the gradient magnitudes across all clauses at runtime, systematically penalizing dominant gradients and accelerating lagging clauses to ensure uniform convergence. GradSAT implements this through a highly optimized, two-stage hybrid pipeline. First, a GPU-accelerated PyTorch backend leveraging symbolic compilation and operator fusion navigates the continuous relaxation to a high-quality basin. Second, the candidate assignment is handed off to a bit-precise local search engine to rapidly resolve the exact, rigorous assignment. By stabilizing the continuous search dynamics, GradSAT mitigates the brittleness of prior gradient-based solvers and provides a robust, highly parallelizable architecture for complex constraint solving.

Korean dialect corpora are available but not redistributable: weights may be released, while reproducing training and evaluation from the underlying data cannot be. We ask how much of that supervision synthetic data recovers, and whether that recovery can be measured independently of the synthesis pipeline. We contribute KoDialectBench, 1,000 items across five regions on three axes, released as identifier hashes and scoring code so users reconstruct the items from their own licensed copy. Recovery is strongly axis-dependent: our best synthetic arm reaches 91.2% of the real-data gain on region identification but 63.7% on comprehension. On generation the answer depends on the metric: the deployed marker lexicon reports 92.3% on dialectness and 119.3% on region match, the latter exceeding the real-data reference, whereas reference-based generation reaches 72.4%. We find the marker metrics' scoring inventory is entirely contained in the inventory our transformation rules can emit. We test the effect of construction access directly with an exact-form construction-disjoint arm that withholds 20% of marker types from the rules. At exactly matched training size (8,600 examples) it reduces dialectness recovery from 91.8% to 8.1% and region-match recovery from 101.9% to 25.6% on the held-out marker inventory, while the three pipeline-independent measurements do not fall at all. A complementary evaluator sweep defines metric-construction coverage (MCC) and finds measured dialectness recovery increasing monotonically as overlap rises from MCC=0 to MCC=1. Shared construction and evaluation inventories can therefore substantially inflate estimates of synthetic-data recovery.

Complex problem solving depends on acting effectively and understanding how a system works. AI advice may support these outcomes unequally. Two preregistered experiments compared participants managing a simulated clothing factory with and without an LLM advisor. Across studies, AI-supported participants reported greater confidence and understanding with less effort. In the first study (N=200), assistance increased company value but produced no detectable prediction-accuracy difference. After withdrawal, previously supported participants outperformed controls when decisions were scored against repeating previous choices, but not default settings. Within the AI-supported group, more frequent recommendation alterations predicted better unaided performance. In the second study (N=198), AI-supported participants went bankrupt less often and showed a small knowledge advantage in the registered analysis, largely associated with remaining solvent. More frequent recommendation alterations predicted higher knowledge within the AI-supported group. Applied HAI evaluation should assess users' understanding and independent capability alongside the performance achieved with AI support.

We propose a decoupled reconstruction framework that temporarily decomposes a NURBS representation into independent local Active Sections, enabling arbitrary local knot insertion, degree elevation, and basis modifications while preserving exact CAD geometry. However, these independent modifications inevitably violate inter-patch continuity, requiring a robust algebraic recovery of global admissibility. We introduce a novel reconstruction methodology that constructs a positive Hybrid Reconstruction Operator: anchor degrees of freedom are identified via QR pivoting, after which a sequence of linear programming problems with distance-based regularization generates strictly non-negative nullspace vectors, while a subsequent non-negative least-squares solve enforces a precise partition of unity. Crucially, to ensure computational efficiency and preserve locality, we implement a hierarchical pairwise condensation strategy that freezes columns already satisfying new interface constraints, confining the optimization exclusively to the active degrees of freedom at each merge step. The resulting hybrid basis is, by construction, strictly non-negative, spans the exact constrained nullspace, preserves partition of unity to machine precision, and reproduces the original geometry exactly. Numerical benchmarks, including a nonlinear diffusion problem on multi-patch curves with heterogeneous local polynomial degrees, confirm optimal convergence rates and demonstrate the framework's ability to seamlessly combine local geometric flexibility with globally consistent approximation spaces. By entirely decoupling local spline editing from the enforcement of continuity, this methodology provides a highly efficient, mathematically principled, and universally applicable tool for adaptive Isogeometric Analysis.

Accurate bus Estimated Time of Arrival (ETA) prediction is vital for urban mobility, passenger satisfaction, and transit efficiency, yet existing models falter against nonlinear spatiotemporal dynamics, data sparsity, and factors such as weather. This paper proposes HYB(nm), an adaptive hybrid ensemble framework that dynamically fuses five complementary models - a historical baseline (MST-AV), periodical temporal pattern analysis (GDRN-DFT), Koopman Neural Operators for nonlinear dynamics (KOOP-NET), weather-integrated feature-engineered neural networks (FENN), and real-time graph convolutional networks (MGCN) - via a meta-learner attuned to real-time context. Evaluated on GPS and weather data from three Kolkata bus routes comprising more than 4,000 trips, the framework leverages the individual strengths of its components (for example, the low-latency explainability of MST-AV, the weather resilience of FENN, and the network-dynamics capture of MGCN) to deliver the superior robustness of HYB(2), state-of-the-art accuracy rivalling leading graph neural networks, and balanced trade-offs in stability and efficiency across prediction horizons and operating conditions. The extensible HYB(k) architecture equips transit agencies with flexible tools, ranging from economical single models to tailored high-fidelity hybrids, advancing predictive, equitable urban transport.

Video diffusion transformers depend on temporal attention to coordinate information across frames, yet nearly everything known about this mechanism comes from analyzing trained models, so when and where temporal-attention structure forms during training remains poorly characterized. Population averages can also hide it, since a few specializing heads and a diffusing majority cancel in the mean. We therefore conduct a checkpoint-resolved census of every temporal-attention head across nine Open-Sora STDiT training runs spanning three model scales (306M to 1.03B parameters), scoring each head with an entropy-normalized measure of cross-frame attention concentration (CFAC) under a preregistered change-point and effect-size selection rule. The census reveals the sparse picture that averages obscure. Aggregate CFAC is flat or decreasing in every run, while a small minority of heads, roughly 4–13% in full-grid runs, develops pronounced concentration. Across seeds, the reproducible signal is positional but block-level. Selected heads repeatedly arise in the first temporal block, whereas individual head coordinates do not reproduce once block membership is accounted for. Among the analyzed 760M selected heads, attention maps converge to a small repertoire of local frame-routing motifs, self-frame diagonals and adjacent-frame bands, even when the responsible coordinates differ across runs. Correlation and ablation analyses do not establish a causal link to generated video quality, and we bound our claims accordingly. Beyond this STDiT family, the study contributes a transferable methodology. Checkpoint-resolved, per-head analysis under fixed selection rules can expose sparse temporal organization in other factorized video diffusion transformers and, with adapted routing metrics, in joint spatio-temporal architectures.

Sentiment analysis is a common tool for converting unstructured text into quantitative signals in finance and risk management. Yet most applications reduce the output to a discrete polarity label or a single predictive feature, overlooking the distributional structure of sentiment intensity in consumer complaint narratives. In this paper we treat negative sentiment in consumer complaints as a bounded continuous variable and study its full distribution rather than a single label. We score each narrative with a transformer classifier, model the scores with Beta distributions, and compare the fitted distributions of meritorious and non-meritorious complaints through the Kullback Leibler divergence and the squared Hellinger distance. The fitted distributions are then linked with dollar amounts and company response outcomes to construct anomaly diagnostics that flag complaints whose textual severity is inconsistent with the recorded relief. We find that the two groups have strongly overlapping distributions, so negative sentiment intensity is not a sharp classifier of outcomes on its own; combined with monetary and categorical attributes, it isolates unusually severe complaints for operational risk monitoring. Treating sentiment analysis as continuous distributional measurement, this study links sentiment extraction, bounded response modeling, and anomaly detection in a unified framework for consumer complaint assessment.

We present Open-Qwen-Music, an open reconstruction of Qwen-Music and a fully specified research system for text-to-music generation that couples LLM-based semantic composition with diffusion-based acoustic rendering. The system comprises a 25 Hz single-codebook music tokenizer, a 3B-parameter autoregressive Music LLM, and a diffusion renderer producing 48 kHz stereo audio, following the cross-module interfaces reported by Qwen-Music. The strongest systems of this design remain closed, and prominent open music-generation projects release weights and inference code without their training corpora or end-to-end training implementations. This limits independent and controlled study of how information loss and prediction errors propagate from semantic representation through autoregressive planning to acoustic rendering. To our knowledge, Open-Qwen-Music is the first fully open release of an LLM-composition-plus-diffusion-rendering text-to-music system. Beyond model weights and inference code, the release includes the training datasets and provenance manifests, complete data-processing, annotation, training, inference, and evaluation pipelines, configurations, and pretrained weights for every learned module. Artifact manifests bind the identities of these artifacts across the complete workflow. Together, these artifacts establish a reproducible implementation of the modular architecture and provide an empirical basis for component-level analysis and future evaluation. We present the system as a transparent, executable research baseline and a starting point for the community, not as evidence of quality parity with Qwen-Music. Open-Qwen-Music is an ongoing effort, and we will continue to improve its generation quality, controllability, and robustness. All release artifacts are available at https://github.com/biang15343100-source/Open-Qwen-Music.

Historical manuscripts remain largely absent from modern vision-language benchmarks, leaving open how well multimodal large language models (MLLMs) handle culturally diverse, degraded, and non-Latin document images. We introduce PalmLeaf-VQA, a multi-script visual question answering benchmark for historical palm-leaf manuscript understanding across South and Southeast Asian traditions. PalmLeaf-VQA contains 923 curated manuscript images and 7,384 question–answer pairs from eight collection groups: Balinese, Grantha, Jathakam, Kambaramayanam, Kannada, Khmer, Sundanese, and Tamil. Unlike recognition-oriented resources, the benchmark targets manuscript-aware visual reasoning over preservation-relevant cues, including physical condition, line structure, material and coating, binding holes, margins, symbols, drawings, and localized visual artifacts. We evaluate recent proprietary and open-weight MLLMs under open-answer and constrained-answer prompting and provide fine-grained analysis across collections, question categories, and task types. The strongest evaluated model reaches only 58.00% exact-match accuracy on the held-out test split, revealing substantial limitations in current MLLMs for rare-script, degraded-layout, and preservation-oriented document understanding. PalmLeaf-VQA provides a standardized benchmark for advancing culturally grounded and layout-aware multimodal document analysis.

Scientific literature contains latent knowledge about materials behavior, but much of this knowledge is expressed through words, contexts, and recurring associations rather than explicit design principles. This raises a central question: how can large-scale scientific corpora be used for practical problems in materials discovery? Here, we present a literature-guided descriptor-based filtering framework for reducing composition search spaces. For a given performance metric, the framework selects two descriptors from a filtered vocabulary in a literature-trained word embedding model and uses the selected descriptors to construct a Pareto-based filter for candidate compositions. Across the evaluated performance metrics and composition search spaces, the framework filters out an average of 74.27% of the candidate compositions, with an average best-value error of 1.93% relative to experimental measurements. Compared with expert-chosen and random descriptors, our performance metric-dependent descriptors provide a more controlled balance between retained fraction and best-value error. These results show that literature-derived embeddings can support intuitive and reproducible filters for narrowing candidate composition spaces while preserving high-performing compositions.

Neural networks are becoming popular in solving mathematical problems, but stochastic models do not provide mathematical exactness by themselves. This study introduces a discovery-to-certification framework in which high-dimensional variational trial functions are learned in a compact separable representation, spectrally diagnosed and pruned, and then certified exactly through multimodular evaluation. Exact certification makes the numerical proofs fully explicit and independently verifiable. This framework can be run on a standard personal computer. Across three extremal problems, we show that neural optimization can contribute to rigorous mathematics in three distinct ways: by discovering improved constructions, by exposing empirical invariants that lead to proofs, and by revealing optimization barriers whose geometry motivates new analytic or numerical representations. More broadly, these results suggest a path toward AI-assisted mathematics in which flexible computational discovery and exact certification become complementary components of a single rigorous workflow.

Although diffusion-based methods have substantially improved the controllability of multimodal face synthesis, their semantic alignment remains suboptimal because most existing approaches rely on implicit latent-space objectives to model the relationship between denoising variables and multimodal conditions. Such implicit modeling is often insufficient to enforce precise correspondence between synthesized faces and conditional inputs, especially under long-tailed semantic mask distributions where rare attributes receive weak optimization signals. To address these limitations, we propose EC\textsuperscript{2}Face, a multimodal face synthesis framework that improves semantic alignment through explicit semantic supervision and distribution-aware optimization. First, we introduce Explicit Conditional Consistency Guidance (ECCG), which imposes direct consistency supervision in pixel space by decoding an approximate reverse estimate of the clean latent and explicitly aligning the synthesized image with textual descriptions and semantic masks. A temporal dynamic modulation function is further designed to adapt the supervision strength according to the timestep-dependent reliability of reverse estimation. Second, we propose Long-Tail Adaptive Flow Matching (LAFM), which reweights spatial optimization signals based on semantic attribute frequency, with normalized weights to maintain numerical stability during training. Importantly, all additional modules are used only during training and introduce no extra inference overhead. Extensive experiments show that EC\textsuperscript{2}Face consistently outperforms competitive baselines in both generation quality and semantic alignment, achieving a 29.38% improvement in mask accuracy on rare attributes.

The Isabelle/HOL dataset of Benzmüller and Scott's study of Gödel's ontological argument and Scott's variant (Monatshefte für Mathematik, 2025) is carried to Lean 4 and from there back to the automated provers, as a benchmark independent of either proof assistant. The port covers all thirty theories, structure and names preserved: 548 statements compare identical as parsed, every named result is proved again, and five results the original reports without replaying them are proved here. For every theorem, #print axioms gives the postulates its proof consumes: Scott's necessary existence and modal collapse need only a symmetric frame, confirming that KB suffices. The benchmark, in TPTP THF and SMT-LIB, turns the steps of an argument debated in philosophy into 294 theorems, alongside 45 statements the original refutes or leaves open, ten left open there. Five THF provers, and cvc5 on SMT-LIB, prove 227 theorems within ten seconds on one core and 232 within sixty, and none proves any of the 45. E and Leo-II solve the most, although Leo-II's calculus has been unchanged for about a decade and was only repaired and modernised here, as release 2.2. Vampire, whose later version won the higher-order division of CASC-30, solves the most in no configuration. Only E and Leo-II are measured in their own automatic mode: Zipperposition proves 101 in a single mode and 213 with its developers' portfolio, Vampire 174 without options and 209 with a higher-order schedule that its CASC mode does not select, and Leo-III 159 alone and 177 with E as partner.

Medical vision-language models can propose how urgently a skin lesion should be reviewed, but the local service retains authority to accept or replace that proposal under referral policy, capacity, and locally held patient context. Proposal quality and selected-action quality are therefore distinct evaluation targets, and benchmark evidence transfers between them only when local review preserves the expected action score. We introduce AuthEval, a logging and evaluation framework that records both actions, scores the selected action under declared local criteria, and, where feasible, scores the declined proposal under the same rule. It reports the resulting authority gap only when the record supports it. Because the gap is the product of the proposal-change rate and the mean score change on changed cases, that rate alone determines neither its magnitude nor its sign. On ISIC 2019, with MedGemma and simulated local review, two constraint regimes with similar change rates produced an optimistic image-equal gap under capacity ($+0.744$ simulator units) but no detectable gap under safety. The declared evaluation unit also mattered: under mixed constraints the gap reversed from $+0.374$ to $-0.206$ when weighting shifted from image to lesion-aware cluster. AuthEval thus clarifies whether a study's records support claims about the model, the workflow, or both.

When a robot faces unfamiliar physical conditions, a common approach is to collect evidence about what changed and adapt. For such diagnosis to improve behavior, six ordered empirical conditions must hold: a meaningful reference, identifiability of the physical condition, use of the acquired evidence, decision value, selection value over a fixed alternative, and safe realization. We test this chain in controlled and public environments. In our controlled environments the frozen policy chooses correctly on every decision, but which evidence it buys is fixed by how the panels assign decisions to evidence strata. On three mechanisms absent from training, the frozen decoder fails its registered transfer gate. On all 96 decisions of the transfer panel, its full-trace input lies far outside its training range, and on such inputs it returns one answer whatever the trace contains. All 15 of its errors fall in the 30 decisions from which cheaper evidence was removed by design, a split hidden by aggregate accuracy. None of three primary public tasks passes its registered qualification gates. Before attributing a failure to how a frozen model uses evidence, evaluation should therefore check whether its deployment inputs lie inside its training range.

Event pipelines often discretize asynchronous timestamps before learning. This step looks harmless, but its stability depends directly on temporal resolution. We study this dependence at the representation level. We first show that hard temporal binning is discontinuous: an arbitrarily small timestamp shift near a boundary can move unit event mass between bins. We then define a class of nonnegative, mass-preserving, resolution-faithful continuous encoders and prove that every encoder in this class has global L1 sensitivity at least 2/Delta, where Delta denotes bin width. Linear two-bin interpolation attains this limit. Local support and first-moment preservation also make it unique. Experiments on SHD, N-MNIST, and DVS128 Gesture support the analysis. Across uniform timestamp budgets, linear interpolation lowers mean representation drift by 47-72% while keeping clean accuracy nearly unchanged. On DVS Gesture, it produces zero prediction flips across all tested budgets and three seeds. On SHD, measured drift follows 1/Delta with R^2 = 0.992.

Underwater Optical Wireless Communication (UOWC) has emerged as a promising technology for high-speed underwater data transmission, offering significantly higher bandwidth and lower latency compared to acoustic and Radio Frequency (RF) technologies. However, the underwater medium introduces severe impairments that degrade link performance and limit communication range. The growing complexity of these challenges has increased research interest in Machine Learning (ML) and Deep Learning (DL) approaches, which offer powerful tools for channel modeling, signal processing, and system adaptation in ways that conventional analytical methods struggle to achieve. This survey provides a comprehensive review of ML methods applied across the full UOWC system pipeline, covering channel modeling, transmitter design, receiver detection and equalization, link alignment, and emerging applications, including wireless power transfer, semantic communication, object detection, optical sensing, and localization. Finally, we discuss open challenges and future research directions to motivate further work in this rapidly growing field.

Vision-language models (VLMs) and vision-language-action models (VLAs) are increasingly deployed in real-world applications. There, a small perturbation to the recorded camera image may change a decision significantly. However, existing benchmarks for these models only sample perturbations, which does not guarantee the absence of a failure in the untested region. We present the first robustness validation of six VLMs (drawn from the Gemma, InternVL, LLaVA, and Qwen families) and five VLAs (drawn from the GR00T, OpenVLA, and $\pi$ families) over entire continuous regions of photometric and geometric image perturbation: brightness shifts, camera rotations, and their composition. To this end, we build on the validation framework H$^2$V and introduce H$^2$V-M, a margin-aware convergence rule that makes validation affordable at the 32B parameter scale. We demonstrate that H$^2$V-M outperforms H$^2$V by an order of magnitude in model queries and that it finds counterexamples faster than random sampling while providing soundness guarantees. Our VLM and VLA robustness validation shows that robustness is mostly dependent on the perturbation type, rather than the model, and that VLMs are more robust to large camera rotations than VLAs. For VLAs, even perturbations as small as $\pm1^\circ$ can change the commanded action in many cases. We also show that robustness depends more on model family than on model size.

Unmanned aerial vehicle (UAV) swarms deployed in mission-critical applications must simultaneously track a mobile aerial target and maintain reliable data links. However, active integrated sensing and communication (ISAC) operation imposes a dual energy burden on propulsion and transmission, threatening mission continuity through premature battery depletion. In this paper, we propose a two-tier UAV swarm architecture in which mission UAVs (MUAVs) execute cooperative ISAC for mobile aerial target tracking while dedicated charging UAVs (CUAVs), equipped with solar harvesting panels, replenish low-battery MUAVs via aerial UAV-to-UAV wireless power transfer (WPT). We formulate the joint minimization of the cooperative posterior Cramér-Rao bound (PCRB) over MUAV trajectories, per-slot sensing-communication time splits, WPT scheduling and admission, and CUAV rendezvous trajectories, subject to minimum uplink rate, dual-tier energy causality, WPT proximity, collision-avoidance, and speed constraints, yielding a non-convex mixed-integer program (MIP) that, to the best of our knowledge, is the first to jointly couple cooperative ISAC sensing quality with aerial WPT and dual-tier energy management. To solve it efficiently, we propose Receding-Horizon Alternating Optimization (RHAO), a four-block per-slot algorithm that decomposes the problem into: charging admission via the Hungarian algorithm, MUAV trajectory and time-split via successive convex approximation (SCA), CUAV rendezvous, and WPT power allocation, with monotone convergence guarantees. Simulation results demonstrate that RHAO reduces the mean PCRB by 16.8 times over a fixed-time-split baseline and 5.4 times over a static-trajectory scheme, while the aerial WPT subsystem sustains all MUAVs above the energy-critical threshold throughout the full mission horizon.

This paper presents a comprehensive experimental evaluation and detailed analysis of state-of-the-art multi-object tracking algorithms, with an emphasis on quantifying the individual contributions of detection and association components to overall tracking performance. Unlike existing surveys that primarily offer theoretical categorizations or taxonomies of tracking methods, our work adopts a rigorous experimental perspective grounded in publicly available implementations, providing practical guidance for researchers and practitioners in method selection and system design. We introduce a unified pipeline diagram that consolidates the core components across the two main branches of visual multi-object tracking: tracking-by-detection and end-to-end deep learning paradigms, and systematically analyze the object detection, feature extraction, and data association modules. Through extensive empirical studies on standard benchmarks, including MOT16, MOT17, MOT20, SportsMOT, DanceTrack, and CrowdTrack datasets, we reveal critical insights: (1) detection quality dominates association strategy performance, with detector improvements yielding more than 10% gains compared to less than 5% from refined association strategies; (2) modern deep learning detectors paired with specialized re-identification models significantly outperform joint detection and embedding approaches; and (3) transformer-based end-to-end methods exhibit greater robustness to detection quality variations but at a substantial computational cost. Our findings from extensive experiments provide key insights into component-level effects in MOT, particularly the dominant influence of detection quality relative to association, while offering practical insights for designing and optimizing MOT systems under varying performance and robustness requirements. Code and experimental setups are available at github.com/linh-gist/VisualMOT.

AI agents increasingly orchestrate long-running activities with users, tools, and system resources for days and weeks. To improve agent quality, safety, and cost efficiency, developers need to determine where failures happen, what triggers unsafe effects, and which tasks consume the most budget, then optimize those tasks. In systems software, profiling answers similar questions by aggregating resource consumption and attributing it to responsible code paths to identify hotspots. Yet existing agent observability tools focus on per-execution debugging and tracing rather than cross-run, long term profiling, making these questions difficult to answer at scale. Agent observability needs profiling, not only debugging, but profiling agents is challenging: the responsible entities are task intent like diagnose authentication, compare branches rather than code paths, and lack stable identifiers for aggregation. We propose a semantic operation stack model that adapts profiling to agent trajectories. Uniform operations represent all activities, and operation stacks replace the runtime call stack, enabling hierarchical attribution at different granularities. We observe that an agent's task occupies a contiguous span and decomposes into subtasks, so we introduce recursive operation segmentation, which recursively splits trajectories at task boundaries. AgentPProf is a profiler that aggregates agent trajectories into pprof-compatible profiles, enabling flame graph visualization and analysis. AgentPProf reaches 0.764 $B^3$ F1 against human annotations on CodeTraceBench. On three problem-localization benchmarks, the profile raises MAP by up to 56%, demonstrating that it effectively attributes resources, locates problems, and helps optimize token cost at practical profiling cost. AgentPProf is available at https://github.com/eunomia-bpf/agentsight.

For every $n\ge9$, we construct a strongly connected synchronizing automaton with two input letters and $n$ states whose shortest word merging some three distinct states has length $\lfloor4n/3\rfloor$. One letter is a permutation; the other has an image of size $n-1$. We give complete transition maps and an explicit word attaining the bound. For the lower bound, we assign an integer to each unordered pair of states and prove that applying either input letter can decrease it by at most one. For $n\not\equiv0\pmod3$, the same construction contains a specified state whose shortest merging word, with its partner chosen freely, has length $\lfloor4n/3\rfloor-1$.

Emphatic temporal-difference learning (ETD) stabilizes the expected off-policy TD update and changes its projection geometry, but neither property determines constant-stepsize sampled dynamics. We construct an ergodic two-state counterexample in which the ETD mean map contracts while the sampled product has a positive top Lyapunov exponent. Regenerative-cycle analysis separates this sign from the infinite variance of the follow-on trace. We introduce regularized emphatic TD (RETD), a normalized first-order post-shock repair that leaves the trace and importance ratios unchanged, stores the emphatic TD signal in a leaky scalar state, and releases a delayed correction. RETD's raw equilibrium is an affine shift of the ETD equilibrium; single- and two-regularization readouts recover the ETD fixed point exactly. We prove almost-sure convergence for harmonic diminishing stepsizes and a conditional constant-stepsize moment-contraction result from a Markovian random-product bound. RETD has certified negative exponents on the two-state construction and one Baird point, whereas the positive Baird ETD sign remains numerical. Paired 10,000-run experiments validate both separations, fixed-point recovery, a nonmonotone stability region, and task dependence. RETD changes post-shock dynamics; it does not reduce the shared follow-on-trace variance.

Whole genome sequencing (WGS) is essential for precision oncology, yet its clinical adoption remains limited by prohibitive computational costs and multi-day turnaround times. This work presents a fully localized low-resource framework enabling stable deployment of a trillion-parameter biomedical LLM on a single consumer-grade RTX 4060 laptop with 32GB system memory and 8GB VRAM, as well as on routine clinical workstations in general hospitals, completing the entire tumor-paired WGS workflow from raw FASTQ input to clinical-grade full-variation-spectrum report output. Under standard 30X depth configurations, our implementation finishes a single tumor-paired WGS analysis within 18 hours, achieving 99.62% F1 score for somatic variant detection with over 99.9% concordance to the industrial-standard A100 cluster pipeline, fully meeting clinical oncology accuracy requirements. Quantitative profiling shows adaptive heterogeneous memory scheduling accounts for 71% of total execution time, while model optimization introduces less than 9% of total detection error. This work is the first engineering implementation of trillion-parameter biomedical LLM-driven clinical-grade genomic analysis on consumer-grade hardware, breaking the industry paradigm that trillion-scale genomic LLMs require hundred-thousand-dollar GPU clusters and multi-day turnaround, establishing a low-resource pathway for global primary medical institutions to adopt whole-genome precision oncology at zero additional cost.

Deep spline superposition networks face a tension between approximation order and stability across depth. We study approximation under a hard layerwise Lipschitz budget, and organise it around two quantities: the factorisation stability complexity of a given deep factorisation, and the budget-compatible approximation complexity of a discretisation operator. First, we solve exactly the finite-depth diagonal balancing problem for a fixed chain of nonnegative envelope matrices: the optimal uniform layer budget equals $\|M_{L-1}\cdots M_0\|_{\infty\to\infty}^{1/L}$, attained by an explicit one-pass minimiser, for rectangular layers, with a complete treatment of degeneracies and non-attainment. The optimum can be arbitrarily larger than the Lipschitz constant of the network itself, because passing to envelopes destroys sign cancellation. Second, we give a constructive spline discretisation theorem preserving the budget up to a controlled slack, with an explicit grid threshold. Conversely, for linear spline-valued operators that preserve the budget exactly, we prove budget-compatible minimax lower bounds on classes constrained simultaneously in the first and third derivative norms – a constraint pair that is forced by the problem and that rules out the usual scaling escapes. Finally, we show that the corresponding layer errors need not cancel under composition: for every operator of the class there is a stable depth-$L$ tower realising a constant fraction of the accumulated error, so the linear-in-depth accumulation of the upper bound is not a proof artefact.

We determine the degree-distortion tradeoff for polynomial approximation of the $d$-dimensional cross-polytope $B_1^d$. For every $1\le t\le d$, every globally nonnegative degree-$2t$ form that is positive away from the origin has multiplicative sandwich distortion at least $(2e)^{-1/2}\sqrt{d/t}$, while an explicit sum-of-squares (SoS) form achieves distortion at most $(2e)^{1/2}\sqrt{d/t}$. Hence both the nonnegative-form and SoS optima are $\Theta(\sqrt{d/t})$, and degree $\Theta(d)$ is necessary and sufficient for constant distortion. The lower bound is representation-free. Averaging over signed permutations and evaluating on flat points of the $\ell_1$ sphere reduces every candidate to a support-size profile $V(k)=k^{-2t}Q(k)$ with $\deg Q\le t$ and $Q(0)=0$. After the substitution $u=1/k$, Lagrange interpolation shows that this degree budget cannot keep the profile nearly constant across $d$ support scales. A matching SoS construction averages even powers of sign-vector facet normals and reduces the upper bound to a Rademacher moment. We also isolate a weighted reciprocal-grid lemma, derive consequences for $\ell_p$ balls, and contrast the polar cube. For a general symmetric polytope, weighted facet powers yield a one-sided certificate whose boundary-floor objective is concave and whose worst-direction oracle reduces to convex dual-norm problems; at degree two, its optimizers recover classical optimal design and the John ellipsoid. This is an oracle-model certificate optimization, not an end-to-end complexity result or a characterization of the full SoS optimum.

Zero-shot object counting aims to estimate the number of objects specified by a text query without category-specific training. Recent approaches primarily rely on density regression or detection-style instance prediction. While effective, density-based models often suffer from spatial ambiguity and background leakage due to weakly regulated mass allocation, leading to fragmented or part-biased representations that increase counting error in complex scenes. In this work, we propose an instance-aware dual-decoder framework that structurally couples density and point representations for zero-shot object counting. Instead of treating density estimation as independent pixel-wise regression, we interpret it as a structured mass allocation problem over a latent set of object instances. Predicted instance centers induce a soft instance-wise decomposition of the density map, upon which we enforce two geometric constraints: (1) per-instance mass conservation, ensuring each object contributes approximately one unit of density mass, and (2) center-of-mass alignment, encouraging each density component to concentrate around its corresponding predicted center. These constraints introduce instance-level geometric consistency and lead to more accurate mass allocation, thereby reducing counting error. Extensive experiments on FSC-147, PUCPR+, and CARPK show that our approach consistently reduces counting error and establishes new state-of-the-art performance in zero-shot object counting.

The hulusi is a wind instrument that was invented in Yunnan Province, China, and has become tremendously popular in recent years. It consists of a mouthpiece, a gourd, and three bamboo tubes, all with free reeds made of copper. The main bamboo tube in the middle has seven finger holes. In this instrument, the pipe length, not the free reed's eigenfrequency, determines the instrument's pitch, unlike, for example, with the Western accordion or the blues harp. In this study, a machine learning model implemented in the COMSAR framework (https://github.com/ifsm) was used to investigate the timbre characteristics of the hulusi to cluster different instruments and pitches. The measured hulusi pitches C, B, A, G, and F were analyzed according to seven psychoacoustic features, among which only the spectral centroid, sharpness, and fractal correlation dimension are shown to form pitch clusters. These timbre features were used to train Kohonen self-organizing maps (SOMs) for clustering. Brightness and sharpness analysis revealed that the highest pitches were less bright and less sharp than mid- and low-range pitches were. Furthermore, the fractal correlation dimension, which mainly determines the chaoticity of the initial transients, was the best-clustering timbre feature for the hulusi, with the highest pitches showing the least chaoticity. This result is supported by defining a cluster quality index for the SOMs.

We study libraries of cross-sectional signals: at each date, a forecast vector over $d$ assets intended to predict the next period's cross-sectional return. Demeaned and unit-normalized, a signal is a point on a sphere and its $T$-date history a point on a product of $T$ spheres. A pairwise correlation cap on histories is a minimum angular separation on that product, so growing a library under such a cap is a packing problem. If a large library is not too pairwise correlated and is equally weighted, does the equally weighted sum (EWS) tend to a known principal-component quantity as it grows? We answer this under explicit assumptions on how the library is filled. Separation alone guarantees nothing: it fixes no limiting distribution; a saturated library covers the sphere yet can carry a biased count; and near-maximum packing on a fixed domain forces uniform volume, which on the unrestricted sphere gives zero mean and no distinguished principal component (PC1). Alignment depends on the admission rule and candidate distribution. Under the uniform product-volume benchmark, screening on positive average information coefficient (IC) yields a nonzero, target-aligned mean but an isotropic second moment, whereas a positive IC margin $\beta$ makat every finite $T$, with athree-level spectrum whose leading eigenvalue tends to $\beta^2$ while residual levels decay as $1/T$; margins of order $T^{-1/2}$ keep a positive admission rate but a vanishing eigengA finite residual-spectrum criteS-PC1 alignment.Gilbert-Varshamov codes show separation permits both outcomes: exponentially large positive-IC libraries exist whose EWS is PC1, and others whose EWS is orthogonal to PC1. $\log J=o(T)$ suffices for uniform estimation among $J$ candidates from $T$ iid dates. Derived results are proved and checked numerically; no market data are used.

Developmental encodings are often motivated by the expectation that a structured genotype-to-phenotype process can improve evolvability, robustness, and adaptation. Yet an encoding that expands phenotypic variation may simultaneously make useful parental structure harder to preserve under mutation and recombination. We test this trade-off in a controlled evolutionary-robotics benchmark comparing three matched representations: direct encoding, a static generative encoding, and a temporal zygotic developmental encoding. All three conditions use 34 genome parameters, 34 adult-controller parameters, identical initial genome matrices, the same optimizer, the same mutation and crossover operators, the same environments, and the same number of fitness evaluations. Across 30 paired evolutionary runs per representation, developmental encoding does not reliably exceed direct encoding in final training or out-of-distribution fitness. It does, however, substantially increase final population phenotypic diversity and mutant-reachable phenotype diversity. The same representation exhibits lower mutation viability, lower genotype–phenotype locality, sharply reduced crossover offspring fitness and viability, and increased recombination novelty. Continued developmental dynamics also attenuate damage applied early in development relative to otherwise identical late damage. These results identify a representation-level trade-off: development can enlarge the neighborhood of reachable phenotypes and provide within-development damage attenuation while degrading the local inheritance of already-adapted structure. We argue that developmental encodings should therefore be evaluated not by performance alone, but by a joint geometry of generativity, locality, robustness, and inheritance compatibility.