Science & Mathematics

We study online assortment optimization under Markov chain choice and independent Bernoulli arrivals, with each period's request type known in advance. Each product may have multiple interchangeable physical copies, and each booking reserves consecutive service slots on a single copy. Customers choose among products, while the platform assigns purchases to feasible copies. We develop a sales-based relaxation that upper-bounds the optimal online revenue and use it to design a policy with two components: independent sampling and purchase--update coupling. We generate independent copy proposals and make a product eligible whenever at least one of its copies proposes. A general revenue-extraction bound for random candidate sets with independent product inclusions shows that optimizing over eligible products recovers at least half of each period's relaxation revenue benchmark in expectation. A purchase--update coupling reproduces the interval flows through independent virtual copy updates while preserving physical feasibility. Under general Markov chain choice, the policy uses a random gate to make the coupling feasible: it offers the selected assortment with probability \(1-1/e\) and the empty assortment otherwise. No gate is needed under multinomial logit (MNL) choice. The resulting policies achieve approximation ratios of \((1-1/e)/2\) and \(1/2\), respectively, relative to the optimal nonanticipative online policy, independently of product capacities. In the single-copy MNL setting, our policy improves the guarantee of \citet{huwu2026} from \(0.271\) to \(1/2\) under the same arrival convention. The \(1/2\) static extraction factor and the \(1-1/e\) uniform scalar-gate factor are separately sharp, and the \(1/2\) MNL guarantee is tight for the proposed policy.

Multi-threshold (MT) sampling records threshold-crossing times for parameter estimation in applications including positron emission tomography, oil well logging, and photon-counting X-ray imaging. We study whether the distribution of recorded crossings uniquely determines the signal parameters and how many thresholds are required for this identifiability. For a fixed MT sampler, we show that the ranks of distribution derivatives with respect to the parameters cannot increase through crossing, timing, and selection. Under suitable regularity assumptions, we characterize local identifiability by a full-rank Jacobian of finitely many event probabilities defined on recorded crossings and establish a necessary and sufficient global identifiability criterion under additional rank and topological assumptions. For a nonhomogeneous Poisson signal model with four intensity parameters, a fixed known single-photon response, and deterministic MT sampling, we prove that four cumulative probabilities of the first recorded crossing time establish local and global identifiability under their respective conditions using a single sufficiently small positive threshold. This attains the minimum number of thresholds for the specified model and sampler. Numerical experiments illustrate these results and reveal weak parameter sensitivity and substantial finite-sample estimation errors when estimation uses these probabilities. The results establish parameter uniqueness while highlighting the role of statistical sensitivity in accurate estimation.

Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models. We propose Neural Operator Splitting, a framework for learning fluid dynamics while preserving the physical structure of fractional-step numerical schemes. Instead of learning the full-step evolution monolithically, we decompose each time step into physically interpretable steps, and learn each operator separately using intermediate states from the underlying numerical solver. Guided by the linearity properties of the fractional steps, we introduce a conditional-linear Fourier neural operator (CL-FNO) whose linear state mappings are modulated by nonlinear conditioning on inputs such as boundary geometry. We further introduce two complementary strategies, symmetry sampling and corrective cycling, to mitigate error accumulation during autoregressive rollout. Experiments on 2D and 3D fluid flows with varying geometries and initial conditions show that our full model reduces mean relative $L^2$ rollout error by 68\% in 2D and 40\% in 3D compared with a single full-step neural operator. At comparable error levels, neural-operator inference is approximately $10^3$ times faster per step than the Monte Carlo solver.

Momentum is central to stochastic optimization in deep learning, including the training of large language models. Classical momentum methods typically rely on a fast exponential moving average (EMA) scheme, which discounts past gradients on a fixed timescale and may underweight older gradients that remain informative. This creates a trade-off between retaining long-term history and adapting to recent changes. We introduce Hybrid Momentum (HyM), which combines a linearly weighted average of past gradients with a geometrically discounted fast momentum. The former assigns weights proportional to the gradients' iteration indices and retains a growing span of history, while the latter emphasizes recent gradients. This hybrid construction is modular and can be combined with adaptive preconditioning and other update transformations. In particular, we propose HyMUON, which applies Newton--Schulz orthogonalization to the hybrid direction. Illustrative examples and controlled experiments demonstrate the benefits of combining gradient information across these two timescales. Across image classification, machine translation, and language modeling, HyM and HyMUON match or improve upon strong baselines. HyMUON improves over Muon on IWSLT14, and in both the 100k- and 600k-step GPT-2 124M OpenWebText regimes. For LLaMA-1.3B pretraining on C4, HyMUON achieves a final validation loss of 2.777, compared with 2.903 for Muon.

The emergence of increasingly sophisticated and evasion-resistant phishing attack strategies represents a significant threat to modern cybersecurity, particularly in cyber-physical systems and internet-based networks. Traditional probabilistic methods and certain machine learning approaches often struggle to detect novel attacks and may lack interpretability or portability. To address these challenges, we introduce CyberHull, a resource-efficient and deterministic framework for identifying malicious URLs through mathematically defined convex hull boundaries across multiple orthogonal feature domains, including structural content entropy, hyperlink graph topology, and semantic token distribution. CyberHull constructs compact convex hulls, referred to as vaults, using the QuickHull algorithm, with a training complexity of O(n log n) under suitable assumptions. URL classification is performed through point-in-polyhedron tests that impose relatively low computational overhead on standard CPUs. Experimental results demonstrate that CyberHull achieves 92 percent detection accuracy, substantially outperforming a baseline linear approach based on Principal Component Analysis (PCA), which achieves 32 percent accuracy. Furthermore, CyberHull offers a computationally efficient alternative to resource-intensive deep learning approaches for malicious URL detection.

In object goal navigation (ObjectNav), an embodied agent must find a target object (e.g., "find a bed") in a previously unseen environment, relying on spatial commonsense such as object co-occurrence. Large Language Models (LLMs) encode this commonsense, but deploying them on robots exposes a trade-off between reasoning quality and efficiency: cloud-based models incur latency and privacy risks, whereas small on-device LLMs are fast but prone to hallucinated spatial judgments. Hybrid reasoning LLMs offer both a fast non-thinking mode and a slow thinking mode, which raises a key question for embodied agents: when is slow thinking worth its cost? We propose CovNav, a training-free framework that answers this question with Conformal Prediction (CP), turning dual-process (System 1 / System 2) inference into an uncertainty-aware decision. Much like recent decision models such as Jev, CovNav casts each spatial query as a structured binary decision rather than free-form generation: a local LLM in fast mode judges whether the target is likely near an observed object, CP converts its token probabilities into a prediction set, and only ambiguous queries are escalated to slow chain-of-thought reasoning. The object-pair formulation keeps calibration tractable and supports open-set objects through off-the-shelf detectors. Experiments on Gibson and HM3D show that CovNav surpasses the strongest zero-shot baseline by 0.8 and 1.7 percentage points in success rate on HM3D v1 and v2, while invoking slow reasoning for only 12.4% of queries and retaining most of the gain of always-on thinking at a fraction of its latency. Real-robot experiments on a TurtleBot 4 further validate the approach. CovNav shows how calibrated uncertainty can decide when an embodied agent should think slowly, offering a principled form of adaptive test-time reasoning for LLM-based robots.

Electromyography (EMG) provides a non-invasive means of decoding silently articulated speech into text, but accurate decoding remains challenging due to limited availability of paired EMG-text data. We introduce PhonoBridge, a two-stage framework comprising a channel-aware EMG-to-phoneme frontend and a large language model (LLM) backend for text reconstruction. The frontend is trained on paired EMG-text data that consists of channel-wise feature extraction, cross-channel fusion, and electrode embeddings. With phonemes as the intermediate representation, we expand the backend's training data by converting LibriSpeech transcripts into phoneme-text pairs without additional EMG recordings. To adapt the LLM to frontend noise, we introduce Error-Profile-Guided Augmentation (EPGA), which perturbs transcript-derived phoneme sequences according to error patterns estimated from frontend predictions, generating additional training pairs for the LLM. On the Open Vocabulary silent-speech dataset, PhonoBridge achieves 24.77% WER, outperforming the previously reported best of 28.27% on the same test split.

Electronic health records are written to support care, not retrieval. Across years of oncology notes, the primary diagnosis is restated in report after report, while the events that shape a patient's course, such as a recurrence or a change in therapy, may be recorded only once. A retriever that ranks passages by similarity to the query keeps returning the repeated material and can miss these transitions, that is, it exhibits temporal redundancy across historical narratives. We argue that longitudinal clinical retrieval should be treated as allocating a limited evidence budget across time, not just ranking by relevance. We separate the task into three objectives: temporal evidence allocation, candidate reconstruction, and clinical validation. In Study A (13 clinical queries over 20 patient records, with two-stage reconstruction), the Temporal-15 configuration reaches a milestone slot recall of 0.538, compared with 0.388 for the Global-50 baseline. However, it also retrieves far more evidence (496 versus 50 indexed units per query), so the gain cannot be credited to allocation alone. When evidence is held fixed, removing prompted precedence rules raises schema-order reversals from 0.010 to 0.080. A five-patient, single-query pilot with fixed budgets finds that wider temporal coverage does not reliably yield more dated milestones. Together, these results suggest that how much a record says about a period is a poor guide to how useful that period is as evidence. Because no expert reference timelines are available, our measurements describe retrieval behavior rather than clinical accuracy. This position and technical report presents the retrieval analysis behind the Onco-CONSTRUE framework and sets out a research agenda for budget-constrained longitudinal clinical retrieval.

Healthcare providers lose substantial revenue to systematic payer underpayments and claim denials, yet identifying the recurring, correctable patterns behind them remains largely manual and does not scale to hospital claim volumes. We present Pattern Intelligence, a deployed system that discovers such patterns without supervision by clustering claims on their adjudication behaviour rather than their identity. Each claim is embedded in a 130-dimensional vector combining per-line expected-versus-actual payment ratios, claim adjustment reason (CARC) codes, denial and payment signals, and service composition. Payer and contract identity are deliberately excluded from the distance metric - we show they dominate the geometry and collapse clusters into trivial per-payer groups - and are reintroduced only as a post-hoc segmentation (by contract and visit type) that keeps every surfaced pattern coherent and actionable. We cluster with HDBSCAN, recover structure from the noise set via second-pass sub-clustering, and gate low-confidence memberships. A large language model translates each centroid into an analyst-ready description of dominant procedures, adjustment reasons, and failure mode. We report a recurring finding: roughly one-third to one-half of high-dollar denials, depending on tenant and segmentation, form an irreducible long tail that no density-clustering configuration or representation we tried groups - a domain property, we argue, rather than a modeling deficiency. We evaluate validity through cluster-coherence analysis and quantify impact with a recoverable-opportunity ($) metric on two production tenants (approx. 10K and 157K claims) within a six-tenant deployment. Rather than a new algorithm, the contribution is a problem formulation, a representation-design insight, and empirical findings from production.

Bipedal humanoids can change their effective footprint by adjusting body yaw, enabling both narrow-passage traversal and socially aware yielding. This paper presents a posture-aware navigation framework centered on \emph{Adaptive Traversal Tubes} (ATT), \emph{Interval Velocity--Heading} (IVH) control, and a sidestep-enhanced AMP locomotion prior. ATT represents a behavior-feasible corridor width field along a reference path, unifying geometric clearance and social comfort into a continuous signal. IVH maps this width to a continuous frontal-to-sidestep posture schedule and omnidirectional velocity commands. A velocity-conditioned AMP policy, trained with GVHMR-retargeted frontal/sidestep motions and coupled \((v_x,v_y)\) tracking rewards, is designed to improve transition stability over a generic locomotion controller while remaining interchangeable with the default onboard policy. This preprint presents the full method; a planned evaluation protocol on a Unitree G1 is outlined, with quantitative results to follow. Demo videos of MuJoCo simulation and real-robot deployment are available at: github.com/lborogzj997/Humanoid-Navigation-in-Crowds-and-Narrow-Spaces.

We introduce the target-response Jacobian $J = [\partial \hat y_i/\partial y_j]$, which measures how model predictions respond to changes in individual training targets. $J$ complements training-data attribution (TDA) methods, which characterize sensitivity to the weights placed on training observations in the loss rather than to their targets, and can be computed matrix-free at the same cost as influence-based TDA methods. We show that sample-weight influence $\mathcal{I}$ and $J$ follow from the same implicit differentiation argument and differ only by a per-example multiplier: for pointwise losses, $\mathcal{I} = J\operatorname{diag}(m)$ exactly at any stationary point with an invertible Hessian. For canonical-link losses (squared error, logistic, Poisson) the multiplier is the training residual, $\mathcal{I} = J\operatorname{diag}(r)$, and softmax cross-entropy obeys a multiclass version. The identity predicts three ways in which influence fails when used in place of $J$: small residuals shrink its predicted shift towards zero (interpolation collapse), residuals of mixed sign wash out its direction (direction washout), and under softmax cross-entropy it collapses a training point's per-class sensitivities towards its own true class (true-class collapse). We score both operators against refitting with a per-prediction $R^2$ across target perturbations, with no rescaling. On tanh networks trained with squared error (Friedman #1) and logistic loss (MAGIC, HIGGS), with $N$ from 2,000 to $10^6$, $J$ reaches $R^2$ between 0.99 and 1.00, whereas influence's $R^2$ is negative on every dataset. On an MNIST softmax classifier, influence's $R^2$ is again negative, while $J$ reaches 0.92. On HIGGS, one row of $J$, holding all $10^6$ sensitivities of one prediction, takes under 0.2 seconds on an RTX 3090 after a one-time setup of under five minutes, whereas refitting would take $10^6$ refits.

Simulation-ready world reconstruction demands physical interactivity beyond visual realism, which existing black-box 3D generation fails to deliver. We present NeoWorld-3, a coding-agent framework that reconstructs interactive 3D worlds from visual observations via tunable, executable programs. At its core, NeoSDK provides the underlying computational engine for low-level geometries, part composition, differentiable parameter refinement, and physics validation. At the same time, NeoMCP exposes these capabilities as structured, tool-callable APIs for vision-language agents to visually inspect, edit code, and iteratively refine programs. Through a hierarchical coordinator-worker architecture, the framework scales seamlessly from standalone articulated objects to complex compositional scenes. Evaluations across object-level and scene-level reconstruction benchmarks demonstrate that NeoWorld-3 achieves state-of-the-art geometric fidelity and physical readiness. Crucially, manipulation trajectories planned within our reconstructed twins achieve successful zero-shot execution on a physical dual-arm robot, completing the Real-Sim-Real loop.

Modern industrial ranking systems increasingly adopt generative recommendation (GR) paradigms, in which user behavior sequences and non-sequential (NS) features are tokenized and jointly modeled by Transformer-style backbones. This unified formulation provides a scalable interface for modeling long histories and heterogeneous features. However, sequence and NS representations often carry asymmetric semantics: historical representations may combine environment context with observed-action semantics, whereas candidate-side NS representations contain no observed action but incorporate richer supplementary context, such as user-item interaction features and recent behavior lists. Direct interaction between such representations can make query-key dot products compare different semantic objects, limiting meaningful cross-token interaction. To fill this gap, we propose EASformer, an Environment-Action-State disentangled architecture for industrial app ranking. EASformer constructs an explicitly aligned context environment space shared by historical and non-sequence tokens, while disentangling user actions from historical token and candidate-specific context form non-sequence tokens. Based on this aligned space, EASformer enables complementary historical action retrieval and state-conditioned action prediction. Furthermore, the disentangled design supports a Cloze-style self-supervised objective by masking historical actions and reusing the candidate prediction pathway. On an offline benchmark from a real-world industrial app marketplace, EASformer achieves an AUC of 0.89411, yielding a 0.88% relative improvement over the deployed baseline. Online A/B tests further support this advantage, with relative eCPM lifts of 1.26% and 3.94% across two real-world ranking scenarios.

Long-video understanding with multimodal LLMs is fundamentally constrained by the mismatch between video length and the model's limited visual context budget, making frame selection essential for practical reasoning. Existing query-aware methods typically rely on heuristic pipelines: they assign one-dimensional query-conditioned scores to frames and then apply sampling, ranking, or extraction rules to form the final subset. While effective in practice, such methods are generally not derived from an explicit optimization objective and struggle to capture the heterogeneous evidence required for complex reasoning. In this paper, we revisit long-video frame selection from a principled optimization perspective. We formulate it as a structured evidence-allocation problem and propose OTFS, an optimal transport framework that maps multiple evidence sources onto video frames. To reflect the asymmetry of this problem---important evidence should be preserved, whereas redundant frames need not absorb mass---we instantiate this view with a semi-unbalanced entropic optimal transport objective and an efficient solver, OTFS-Sinkhorn. Combined with an exact dynamic program for coverage-aware subset extraction, OTFS yields a practical two-stage training-free pipeline. We further show that, in the single-source case, our formulation induces a Gibbs-type distribution over frames, making Q-Frame's temperature-scaled distribution a special case of our framework while also providing a broader perspective for understanding related prior methods. Experiments on three long-video understanding benchmarks show that OTFS consistently outperforms strong training-free baselines. Codes are available at https://github.com/barry664/OTFS.

For millennia, knowledge has been carried by language, and large language models still put language at the center. Yet the coding agents built on these models mostly write code. This paper is a contribution to epistemology, which asks what kind of knowledge code is and how it is obtained. We define knowledge as code as knowledge written in a programming language or in a machine-parsable data format, whose validity can be checked by executing it. We define thirteen epistemic properties of knowledge media and show that code is the first medium to have all of them. We distinguish two ways in which knowledge enters code, encoding and learning by execution, where code is both the experiment and the record of its result. Agents make learning by execution observable, since their trajectories record every probe, observation and line of code they keep. Code is thus not only a tool of knowledge work but a knowledge medium in its own right, the first that can check what it holds.