Machine Learning
Papers
Fresh from arXiv, typeset properly. Highlighted words trade on the market.
Monday 12 October
Clinical decision-making is a sequential process of information collection, clinical inference, and forecasting under partial observability, often without a uniquely correct treatment decision. Large language models (LLMs) have demonstrated strong medical question-answering capabilities but extending these advances to clinical reasoning remains challenging because many clinical tasks are only partially verifiable. Recent clinical reinforcement learning (RL) work has therefore largely focused on diagnostic endpoints, where correctness can be more directly verified. Oncology treatment decision making is a particularly challenging instance of this problem that extends beyond medical question-answering in which multiple decision trajectories can be clinically defensible for the same partially observed patient state. We formulate oncology treatment planning as an interactive RL problem under partial observability and construct patient-specific, process-aware rewards from decision processes observed in real world clinical records. The agent must learn to sequentially acquire information from a structured patient representation before committing to a first-line treatment recommendation, and is evaluated on information gathering, treatment selection, and reasoning alignment. Using GRPO and GDPO to optimize Llama-3.1-8B-Instruct within this environment, RL substantially improves the base policy beyond frontier model capabilities. The GDPO-trained policy increases Mean@3 scalar clinical reward by $79.60\%$ over base Llama and exceeds GPT-5.2 by $18.82\%$ under the same interactive environment, while reducing query count during training. Overall, our results show that patient-specific, partially verifiable rewards can provide an effective learning signal for interactive clinical RL when both the patient state and the underlying clinical decision process are only partially observed.
Machine Learning
When Sparsity Breaks Connectivity: Functional Reachability and Guided Topology Dynamics in Extreme Sparse Training
Dynamic Sparse Training (DST) periodically prunes and regrows connections, inducing a discrete dynamical mechanism over network topologies. At extreme sparsity ($\ge 99\%$), this dynamic tends to destroy input-output information pathways, and performance with standard magnitude/random updates degrades sharply. We formalize forward, backward, and functional reachability on layered sparse graphs, derive closed-form expectations for reachable neurons and edges, and show that Monte Carlo realizations match the theory. Guided by this reachability-based structure, we bias pruning toward non-functional edges and regrowth toward functionally consistent candidates. We introduce this reachability-driven modification of topology evolution as Reachability-guided in DST, referred to as guided DST. On CIFAR-10/100 and Tiny ImageNet, guided DST recovers large accuracy gaps versus unguided DST (up to $+14.4$ points at $99.9\%$ sparsity on CIFAR-100), and on MLP-Mixer guided DST remains trainable at $99.99\%$ sparsity while unguided random regrowth degrades sharply. These results cast extreme-sparse training as a connectivity-preserving dynamical process. Our implementation is publicly available at https://github.com/mzjaworski/ea_dst.
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Machine Learning
On Making $\mathrm{SE}(2)$-Invariant Networks Optimal
Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks are a canonical example, encoding translation equivariance. Extending this inductive bias to richer symmetry groups such as $\mathrm{SE}(2)$ in the most effective way possible is an ongoing architectural and computational challenge. Building on classical invariant theory, we derive invariant feature maps that are provably optimal: minimal and information-preserving with respect to the symmetry group. Our construction is designed to integrate seamlessly into standard architectures, requiring no modification to nonlinearities or normalization layers. As a concrete implementation, we introduce a plug-and-play module for convolutional neural networks that enforces $\mathrm{SE}(2)$ invariance, capturing both translations and rotations within standard architectures. The resulting models are both efficient and expressive. Experiments show competitive or improved accuracy compared to state-of-the-art equivariant methods at significantly lower computational cost. Finally, we provide a theoretical and empirical analysis of the relationship between equivariance and invariance, offering insight into their roles in controlling robustness and flexibility.
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Robotics
MIRROR: Reflecting Hidden Symmetries from Offline Robot Interaction Data
Symmetry-aware robot policy learning requires coupled observation-action transformations. For pixel observations, even simple physical symmetries can induce complex, viewpoint-dependent image transformations that are difficult to specify by hand. Existing symmetry-aware methods often rely on representations with predefined transformations, requiring preprocessing tailored to the sensing setup and task. We introduce MIRROR, a framework that learns how a known symmetry group operates jointly on observations and actions in partially observable Markov decision processes (POMDPs) from offline interaction data. MIRROR couples these transformations through adversarial tuple matching over one-step transition tuples, while explicit group-consistency regularization penalizes violations of the group-operation axioms. On four Robosuite tabletop manipulation tasks, MIRROR achieves the lowest aggregate error on three of four symmetry-quality metrics, including a 61% reduction in compatibility error (which measures consistency under transformation composition) relative to an adapted LaLiGAN baseline. Using the learned transformations in frame-averaged behavior cloning (BC) yields higher mean success rates than vanilla BC on all four tasks, increasing average success from 80.48% to 85.12%, with per-task gains up to 9.66 percentage points. We also repeat symmetry discovery and policy training in simulation with heightmap and segmentation-mask observations, then deploy the resulting policy zero-shot on a real Kinova GEN3 arm. Project page: https://pomdp-mirror.github.io.
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Data Structures and Algorithms
Thin matrix products up to D <= N^0.172 and lossless reductions for 3SUM, Exact Triangle and APSP, with 3SUM over abelian groups and a dichotomy for coordinatewise problems
Alman and Vassilevska Williams (arXiv:2610.06783) gave the first polynomial improvements over the textbook algorithms for 3SUM and APSP: deterministic algorithms with exponents 1.9992 for 3SUM, 2.9983 for Exact Triangle and 2.99942 for APSP. Their algorithm has two steps: a matrix theorem, computing N^2/sqrt(D) prescribed entries of the product of an N x D and a D x N integer matrix in time N^2/D^gamma, gamma > 0, when D <= N^eps, for every eps < 0.1204; and reductions from the three problems to the lopsided sparse triangle problem. We improve both. With Schönhage's five-term partial-product tensor, the matrix theorem holds for every eps < 0.172. The preprint's reductions keep a quarter of the matrix theorem's saving for 3SUM and a half for Exact Triangle and APSP; ours keep all of it, by calling the counting version of the triangle problem adaptively and building composite moduli one prime at a time. Together this gives deterministic 3SUM in n^{1.9945+o(1)}, and Exact Triangle, (min,+)-product and APSP in n^{2.9945+o(1)}. We also improve on the preprint's proof sketch for 3XOR and solve it deterministically in O(n^{1.99451}). Which other problems on three lists does the method make truly subquadratic? It solves 3SUM over F_p^d for every fixed prime p with 3XOR's exponents, and over every finite abelian group of exponent p^2, such as Z_4^d, in O(n^{1.99726}). For coordinatewise problems with a fixed relation P on every coordinate triple, a certified exhaustive computation shows that every Boolean P, and every functional P over three letters, either is the solution set of an equation over Z, F_2 or F_3, and the problem is then truly subquadratic, or has a gadget for Orthogonal Vectors, and the problem is then hard under the Orthogonal Vectors hypothesis. Over four letters, just four functional relations, up to symmetry, satisfy neither condition.
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Robotics
ClearNav: Perception-Aligned Quadrotor Flight Using Differential-Physics
Autonomous quadrotor flight in cluttered environment is an key capability for tasks like inspection and search. Navigation policies trained in simulation and transferred to hardware can fly at high speed in open space, but they can still collide as obstacle clearance shrinks. We attribute most of these collisions to a single mechanism, namely motion in directions the onboard camera does not observe. Heading that is not aligned with the direction of travel and lateral excursion during obstacle avoidance both carry the vehicle toward obstacles outside its field of view. We introduce ClearNav, a navigation policy trained with two reward terms that constrain motion to the observed direction, a forward-looking heading target and a penalty on lateral velocity. A third term penalizes speed near obstacles so that an obstacle entering the field of view remains avoidable. In simulation, across 18 held-out scenarios with 2304 paired flights per policy unseen in training, ClearNav improves success by 6.8 points, cuts the collision rate by 65% relative to the state of the arts, and flies at maximum 5m/s. For the proximity term alone under matched commanded speeds, the collision reduction still holds at 70%. The effect is significant on static scenes and consistent in direction on moving obstacles, though not significant there at the suite level, showing that safer flight in clutter is possible even on the limited sensors and compute of small drones. We also validate our navigation policy in a real-world cluttered environment, showing that it enables the quadrotor to navigate through the cluttered environment successfully and safely.
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Software Engineering
Why Agentic Workflows Fail: A Taxonomy Derived from Literature and Empirical Data
Agentic workflows combine large language models with planning, memory, tools, execution environments, and iterative feedback. Their failures are difficult to diagnose because the same user-visible symptom may originate from model behavior, workflow orchestration, external tools, infrastructure, or their interaction. This paper presents a source-aware taxonomy of agentic workflow failures and applies it to evidence from academic literature and GitHub. The taxonomy combines source attribution with three empirical dimensions: a concrete failure-type dictionary, workflow-stage localization, and agent-capability localization. Its central structure is a two-axis localization matrix: workflow stages form the horizontal process axis and agent capabilities form the vertical functional axis. This design moves beyond taxonomies that mainly classify final failure manifestations by localizing intermediate process states inside agent operation. Our empirical comparison shows that literature-derived failures emphasize planning, reasoning, learning, perception, and knowledge-related mechanisms, whereas GitHub-derived failures concentrate on execution-stage, actuation-related, tool, API, and infrastructure failures. The dominant hotspot is iterative execution and actuation. These findings indicate that agentic workflow reliability should be treated as a systems problem rather than only a model-output problem. The taxonomy provides a basis for structured evaluation, root cause analysis, failure injection, and engineering triage.
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Game Theory
Dynamic Run-Out Pricing for Perishable Goods
I study a dynamic pricing problem in which a seller with limited inventory must sequentially price a perishable product for arriving customers with heterogeneous valuations. The key difficulty lies in balancing immediate sales against future opportunities under capacity constraints and stochastic customer valuations. I propose a simple, interpretable, and asymptotically optimal dynamic pricing algorithm, called Dynamic Run-Out Pricing (DROP), that adjusts prices in real time based on current inventory and anticipated future demand. Under the assumption that customers' valuations follow bounded or exponential distributions, our theoretical results show that DROP's expected revenue converges to the optimal revenue as market size grows. Unlike traditional notions of near-optimality, where the ratio of the algorithm's revenue to the optimal revenue converges to 1, I show that the absolute difference between the two revenues converges to 0 as the market size increases, underscoring the algorithm's effectiveness. Furthermore, I extend our analysis to heavy-tailed valuation distributions, specifically the Pareto distribution, where standard run-out heuristics severely underprice inventory by ignoring the value of waiting for extreme valuations. To correct this, I introduce the Tail-Aware DROP (TA-DROP) heuristic, which intentionally inflates prices to protect inventory, and I prove that it restores asymptotic optimality with a strict polynomial convergence rate.
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Computer Vision
Bottlenecked semantic compression by representation reconstruction
Vision Transformers incur high computational costs when processing long visual token sequences. Existing reduction methods typically rank tokens independently and discard those deemed unimportant or redundant. We propose a reconstruction-guided framework for visual token condensation (ReConV), which summarizes the complete visual sequence with a compact Summary Bank (SMB) and retains tokens whose information is not adequately captured by the SMB, as indicated by their reconstruction residuals. At each compression layer, a lightweight position-conditioned decoder reconstructs the current tokens, leaving shared information compressed in the SMB while explicitly preserving poorly reconstructed details. Experiments on image classification and multimodal understanding demonstrate favorable performance-efficiency trade-offs: ReConV surpasses the uncompressed baseline with 48% fewer GMACs on ImageNet and enables reusable image-level representations for efficient multi-turn inference. Code is available at TokenDrop.
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Artificial Intelligence
Agency as a New Organizing Abstraction for Computer Science
Advances in large-scale machine learning have enabled agentic AI systems: persistent, autonomous computational entities that pursue goals, initiate actions, and interact with open environments. These systems are often framed as applications of foundation models. We argue that this framing is incomplete: agency is also a candidate new organizing abstraction for computer science. What is new is not the concept of an agent, nor runtime policy generation per se, but its general-purpose, open-ended form, in which systems can synthesize courses of action from goals, observations, and memory, over tools and environments for which no complete task-specific model was specified in advance. Thus agency becomes a systems-level abstraction as well as an AI modeling concept. Where the process abstraction organizes computation around executing programs, agency organizes it around pursuing goals under bounded resources: a process executes a program; an agent pursues a goal. From this perspective, the recurring failures of deployed agentic systems (runaway resource consumption, behavior redirected by adversarial content, opaque continuous operation) are symptoms of structural abstraction gaps, not isolated engineering defects. We examine these gaps across six dimensions (execution, interfaces, correctness, oversight, coordination, and persistence) and argue that closing them requires coordinated advances in systems,
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Machine Learning
Position: Beyond Training Time, Test-Time Coordination is Essential for Cooperative MARL
We argue that cooperative multi-agent reinforcement learning (MARL) should treat test-time coordination as part of the problem definition rather than a deployment artifact. Our focus is on long-horizon, centrally monitored cooperative systems such as warehouse robotics, automated storage-and-retrieval systems, and cloud-resource scheduling, where teams share a reward, operate under shifting objectives, and already run with global telemetry at deployment. The dominant paradigm in this regime, centralized training with decentralized execution (CTDE), uses global information only during training and provides no coordination channel at execution. This is sufficient when agents are weakly coupled or the environment is stationary, but it fails when the team must realign after conditions change. The limitation is structural rather than algorithmic, and more training cannot add a channel that does not exist at execution time. We call this the recoverability gap. To address it, we name the underexplored design space of intermittent test-time coordination as centralized training with mixed execution (CTME), in which a coordinator observes global state and emits high-level signals while agents act locally. CTME is not a particular learning algorithm, but a cooperative MARL problem setting that makes test-time information structure explicit. It specifies team-level information, high-level signals, and update frequency after training, with CTDE recovered as a limit case. We do not argue that CTDE is obsolete. We argue that removing the test-time channel is a modeling choice, not a necessity, and the wrong default when global telemetry is available and teams must recover from drift.
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Machine Learning
Cross-View Time-Frequency Diffusion for Extreme-Aware Time-Series Generation
Generating realistic time-series requires faithfully reproducing rare but high-impact extreme events. Existing approaches often rely on specialized representations or extreme-focused training objectives, which may restrict the diversity of captured extremes or compromise overall distributional fidelity. We propose Cross-View Time-Frequency Diffusion (CrossTF), a framework that exploits discrepancies between time- and frequency-view denoisers for extreme-aware time-series generation. Our key empirical finding is extreme-sensitive cross-view asymmetry: moving along the direction connecting the two views' clean-sample estimates substantially changes extreme fidelity while having limited effects on overall generation quality. We further identify a late-stage cross-view window in which this discrepancy stabilizes and cross-view adjustments have a particularly strong effect on extreme fidelity. These findings motivate a staged optimization strategy in CrossTF: after training and freezing both denoisers, it only needs to learn step-specific fusion parameters within this window using an Extreme Value Theory-based objective under an energy-distance constraint. This formulation supports interpolation between and extrapolation beyond the view-specific estimates while limiting degradation in overall generation quality. Extensive experiments on seven real-world datasets against 11 baselines show that CrossTF improves extreme fidelity by 26.1% and overall performance by 7.4% relative to the strongest baselines. These results highlight cross-view discrepancy as an effective basis for low-dimensional optimization in extreme-aware time-series generation.
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Data Structures and Algorithms
Fast Forgiving Base64 Decoding with SIMD Instructions
On the Internet, we use the Base64 format to represent binary data (e.g., images or cryptographic keys) as text. The ES2026 JavaScript standard, following the WHATWG forgiving-base64 rules, requires decoders to ignore ASCII whitespace while rejecting other non-alphabet characters. Prior SIMD Base64 decoders assume whitespace-free input. We present a block-oriented decoding algorithm that removes whitespace inside the SIMD loop: clean 64-character blocks are decoded directly, while blocks with ignorable characters are compacted into a small stack buffer. We provide implementations for x64 (SSSE3 through AVX-512 VBMI2), ARM NEON, and LoongArch. Our C++ decoder reaches up to 94 GB/s on recent AMD Zen 5 processors. In Node 25, integration of our decoder raises Uint8Array.fromBase64 throughput by up to 6x compared with Node 19. The implementation has been adopted by major browsers and JavaScript runtimes.
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Artificial Intelligence · Cross-listed from physics.geo-ph
Event-Centric Earthquake Monitoring with a Multi-Station Transformer
Earthquake catalogs underpin studies such as fault structure, earthquake processes and seismic hazard, and their value depends on being both complete and reliable. Machine learning has improved individual tasks of earthquake monitoring, but processing stations independently discards the consistency of arrivals across the network, and running tasks in sequence fragments the information describing each earthquake. We present EQNet2, a geometry-aware multi-station Transformer that jointly predicts phase arrivals, first-motion polarities, source location and magnitude, and the association of arrivals into events. On a Northern California test dataset and on continuous waveforms from Ridgecrest and the San Francisco Bay Area, EQNet2 recovers more weak arrivals, produces fewer false detections, and associates more picks into located events. Its learned attention links information across stations along time–distance patterns consistent with seismic moveout. As seismic networks grow denser, exploiting multi-station coherence and event-centric prediction offers a path to more complete and reliable catalogs.
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Computation and Language
Evaluating Temporal Reasoning in Large Language Models: Event Temporal Relation Extraction with Allen's Interval Algebra, Logical Consistency, and Relative Time in Narratives
Understanding a narrative means knowing how every event relates in time to every other, yet large language models (LLMs) are mostly tested on isolated event pairs or coarse labels. We ask five LLMs to reconstruct the complete network of Allen's 13 interval relations for 360 English narratives whose events are placed relative to one another rather than by dates, and evaluate the outputs under a pre-registered protocol for agreement with our gold annotations, converse consistency and logical satisfiability. End to end, the best model clearly beats trivial baselines on macro-F1, our primary metric, yet under our pre-registered parser no model matches the accuracy of always answering "before", which the skewed labels inflate. Most of that accuracy gap is a parsing artifact: formatting errors in large matrices cost whole rows, and a post hoc parser that recovers the determined cells of malformed rows raises coverage from 0.60 to 0.84 and closes the gap to the baseline for the best model. On the cells they do answer, models recover precedence and containment but rarely overlap, and they fail most on flashbacks, where both the narration and the event list present the later event first. Logical consistency varies widely yet says little about agreement with gold: enforcing it raises accuracy mainly by filling empty cells, and is beaten there by the trivial control of guessing the majority label. Reliable structured output and robust handling of relative time are prerequisites for temporal reasoning over whole narratives.
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Artificial Intelligence
Generalizable field of view extension for diffusion MRI via conditional flow matching
Incomplete field-of-view (FOV) diffusion MRI (dMRI) acquisitions compromise whole-brain white matter analysis by excluding brain regions from tractography and connectivity studies. While deep generative models for dMRI FOV extension have been proposed, their generalizability remains limited by the acquisition-dependent nature of dMRI, where signal intensity varies with b-value, gradient direction, and scanner protocol, and the inherent 4D complexity of the data, making it difficult to train models that transfer across sites or acquisition schemes without retraining. We propose a flow-matching generative model that extends the dMRI FOV in both the superior and inferior directions by predicting apparent diffusion coefficients (ADC) in six directions, conditioned on the two nearest acquired slices and the full-FOV T1w image to enforce both local diffusion continuity and anatomical consistency. The ADC representation decouples the model from acquisition-specific b-values and gradient directions, providing a middle-ground across protocols. The model was trained on 3,103 subjects (5,105 sessions) across five different datasets spanning diverse acquisition schemes (b = 500 and 1000 s/mm$^2$; 21–192 gradient directions), four single-shell (b = 1000) and one multi-shell (b = 500/1000). Evaluated on 299 subjects across five independent datasets spanning b = 750–1500 s/mm$^2$ and 32–90 gradient directions, with single- and multi-shell schemes unseen during training, the proposed method achieves significantly improved bundle Dice score on downstream tractography (p < 0.01).
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Machine Learning
Learning to Detect Shifts in Unstructured Data Streams via Monitoring-by-Betting
Continuous monitoring of generative AI systems requires detecting distribution shifts in the unstructured data they ingest and generate. Existing monitoring methods typically control false alarms by requiring the discrepancy measure used to detect shifts to be *pre-specified*. However, for unstructured data, pre-specification creates a sensitivity–breadth trade-off: a narrowly defined measure is sensitive to the anticipated shift but may miss unexpected changes, whereas a broadly defined measure may detect a wider range of shifts but with reduced sensitivity. Although adaptively hypothesizing the shift direction can overcome this limitation, such data-dependent adaptation generally invalidates conventional false-alarm guarantees. We reconcile adaptivity with statistical validity through testing-by-betting, reframing sequential changepoint detection as a betting game in which the bettor continually updates its hypothesized shift direction, or witness function, as new observations arrive. We introduce *asymptotic e-detectors*, which approximate the pre-change distribution using a calibration set of size $m$, and prove that they asymptotically control the average run length to a false alarm as $m$ increases. Empirically, calibration sets as small as $m=30$ provide effective control. We then develop adaptive monitoring strategies ranging from black-box bettors that learn from embeddings to interpretable bettors based on LLM-proposed concepts. Across three real-world datasets, including data from a clinical AI scribe deployment, adaptive monitors detect shifts faster than fixed monitors at the same false-alarm level. Further, when the true shifts are sparse and interpretable, LLM-concept monitors provide the fastest and most interpretable detection, while also guiding root-cause diagnosis for complex shifts.
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Numerical Analysis · Cross-listed from math.AP
Fresnel scattering for open waveguide networks
This paper concerns the Helmholtz scattering problem for open waveguide networks, extending the analysis from [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674] to plane-wave incident data. We first reduce the problem to a Fredholm second-kind integral equation on an infinite interface. This produces an integral representation of the solution to the original scattering problem, which is then used to obtain detailed asymptotic estimates of the solution at infinity. To leading order and away from the waveguides, the scattered field is itself a plane wave. Its amplitude and phase shift exhibit a jump across a critical polar angle depending on the direction of the incident plane-wave. Our estimates also imply that the scattered field is outgoing in a weak sense, allowing us to establish a uniqueness result. We conclude by calculating the waveguide-mode contributions to the scattered field in a perturbative regime.
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Machine Learning
JustOPD: On-Policy Distillation from Autoregressive to Diffusion Language Models
On-policy distillation (OPD) is a post-training approach for large language models (LLMs) that enables a student model to learn a teacher model's distribution from sequences sampled from the student's own policy. Despite its promising capability, OPD for diffusion language models (DLMs) remains underexplored and existing studies primarily focuses on DLM-to-DLM distillation. The limited availability of strong teacher DLMs and the flexible generation order of DLMs impose additional technical challenges as well. However, it remains unclear how to effectively distill knowledge from a strong autoregressive language model (ARM) into a weaker DLM, given the mismatch between the left-to-right decoding of ARMs and the flexible decoding order of DLMs. Inspired by Ni et al. (2026), we propose JustOPD, an ARM-to-DLM on-policy distillation method that uses autoregressive rollouts during training to align the student's generation process with the ARM teacher's left-to-right decoding. This alignment enables effective distillation from ARM teachers while preserving the DLM's flexible generation-order capability at inference time. Experiments using Qwen3-14B as the teacher and Dream-7B as the student demonstrate that JustOPD consistently improves mathematical reasoning performance over the base DLM across multiple divergence choices.
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Systems and Control · Cross-listed from q-bio.OT
Model-Based Cortisol Replacement Strategies for Patients With Adrenal Insufficiency
Cortisol is an essential hormone secreted by the adrenal glands. Abnormally low level of cortisol is referred to as adrenal insufficiency. This paper focuses on devising treatment strategies for patients suffering from adrenal insufficiency using a model-based approach. Two conditions of adrenal insufficiency are analysed. They are hypothalamic-pituitary (HP) and adrenal gland disorders. The hypothalamus, pituitary, and adrenal glands constitute the hypothalamus-pituitary-adrenal (HPA) axis, which regulates stress and maintains physiological homeostasis through cortisol secretion. A comparative analysis of the existing mathematical models of the HPA axis is conducted. Based on this analysis, a novel model of the HPA axis is proposed that incorporates endogenous circadian rhythm. This proposed model is used to design effective cortisol replacement strategies. In addition, hydrocortisone replacement therapies are proposed and validated with clinical data from the literature. The results presented in this paper are applicable to patient-specific treatment strategies for individuals with adrenal insufficiency.
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Numerical Analysis
A Method for Exact Enforcement of Boundary Conditions on General Curved Triangular Domains: Algorithm and Application to Scientific Machine Learning
We present a method for enforcing exactly Dirichlet, Neumann, and Robin conditions on general triangular domains with arbitrarily curved boundaries. The algorithmic constructions developed here complements those in a previous work for general quadrilateral domains. Our method combines (i) the exact mapping between a general curved triangular domain and the standard triangle, (ii) TFC constrained expressions, and (iii) Barnhill transfinite interpolations, to provide explicit closed-form trial ansatze that mathematically satisfy the imposed boundary conditions exactly. Corner compatibility induced by the boundary conditions is pivotal, and enforcing exactly the imposed boundary conditions hinges on the exact enforcement of the induced compatibility constraints. The corner compatibility associated with the acute vertices of the standard triangle and the coupling between gradient components when the hypotenuse corresponds to a Neumann/Robin boundary pose particular challenges. Two strategies are critical to resolving these issues, by reformulating conditional corner constraints into equivalent unconditional forms and by introducing a separate TFC-style auxiliary edge construction together with an associated linear solve on the hypotenuse. We analyze the corner compatibility constraints and present formulations for the general form of functions that exactly satisfy the imposed Dirichlet, Neumann, or Robin conditions on curved triangular domains. The proposed method has been implemented using extreme learning machine type randomized neural networks for solving PDE problems. We present ample numerical experiments with linear/nonlinear PDE problems on a variety of domains with complex boundary geometries. Numerical results show that the current method has enforced the Dirichlet, Neumann, and Robin conditions on curved domain boundaries to the machine precision.
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Artificial Intelligence
Learning to Play: Reinforcement Learning and Games
Amazing breakthroughs in reinforcement learning have taken place. Computers teach themselves to play Chess and Go and beat world champions. There is talk about expanding application areas towards general artificial intelligence (AI). The breakthroughs in Backgammon, Checkers, Chess, Atari, Go, Poker, and StarCraft have shown that we can build machines that exhibit intelligent game playing of the highest level. These successes have been widely publicized in the media, and inspire AI entrepreneurs and scientists alike. Reinforcement learning in games has become a mainstream AI research topic. It is a broad topic, and the successes build on a range of diverse techniques, from exact planning algorithms, to adaptive sampling, deep function approximation, and ingenious self-play methods. Perhaps because of the breadth of these technologies, or because of the recency of the breakthroughs, there are few books that explain these methods in depth. This book covers all methods in one comprehensive volume, explaining the latest research, bringing you as close as possible to working implementations, with many references to the original research papers. The programming examples in this book are in Python, the language in which most current reinforcement learning research is conducted. We help you to get started with machine learning frameworks such as Gym, TensorFlow, and Keras, and provide exercises to help understand how AI is learning to play.
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Machine Learning
Cross-Market Meta-Learning for Electricity Price Forecasting
Day-ahead (DA) electricity price forecasting is usually posed per market, with a separate model fitted to each grid's own history. This caps accuracy: statistical and tree-based baselines saturate, while higher-capacity sequence models need more training data than a single market's few years of hourly prices can supply. Such methods also treat each node as an independent series, discarding the spatial dependencies induced by network topology and congestion. Because price formation across independent system operators (ISOs) is driven by shared physics and largely common market design, we instead treat cross-market history as a pretraining corpus. We present MetaGrid, a topology-aware transformer, meta-trained across markets so that a single zone-count-independent parameter set adapts to an unseen grid. On a leak-free benchmark of five U.S. ISOs, where every model receives the same prices, DA load forecasts and calendar features, MetaGrid attains the lowest average MAE, improving on the best baseline by 3.1% and on the same architecture trained from scratch by 7.7%.
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Numerical Analysis · Cross-listed from math.OC
Beyond periodicity: Fourier methods for optimal control
Fourier-based spectral methods provide compact global approximations, permit simple differentiation and integration, and achieve spectral convergence for smooth periodic functions. Their use in finite-horizon optimal control problems (OCPs) is nevertheless challenged by the generally nonperiodic state and control trajectories: endpoint mismatch induces artificial discontinuities and can destroy spectral convergence. Leveraging Eckhoff-type endpoint-correction techniques, we develop a Fourier-based spectral framework for OCPs with possibly nonlinear dynamics and constraints. The correction improves convergence without enlarging the set of decision variables, yielding an efficient finite-dimensional numerical method. Furthermore, we formulate selected dynamics and obstacle-avoidance constraints through Sobolev residual bounds, which incorporate information about the residuals over the entire time horizon and improve constraint satisfaction. Numerical experiments on benchmark problems demonstrate competitive computational performance, lower residual errors, and improved solution accuracy.
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Systems and Control
Direct Electromechanical Actuation of the Shift Drum in Non-Synchronized Motorcycle Transmissions: From Actuator Sizing and Electronics Design to Closed-Loop Position Control
This thesis presents the direct electromechanical actuation of the shift drum in a non-synchronized motorcycle transmission. A DC motor drives the shift drum through a self-locking worm gear, so the entire foot shift mechanism is eliminated. As a reference, 84 manual gear changes of a large-displacement series-production motorcycle were measured on a chassis dynamometer; the mean shift time is 80 ms for upshifts and 92 ms for downshifts. The system design covers the complete chain from the mechanics to the software. The actuator motor is sized from inertia, friction and gear ratio. A dedicated shift controller is developed with supply filtering, signal conditioning for the position sensor and the incremental encoder, an H-bridge motor driver and a custom circuit board based on a SAMD21 microcontroller. The embedded firmware implements position control of the shift drum with a proportional controller, without inner speed or current loops. On a gearbox test rig, a gear change is completed in less than 80 ms without overshoot in a single measurement, below the mean of the manual reference shifts. The analysis reveals a trade-off in the choice of the worm gear ratio: at a ratio of 30, about 93% of the motor torque is needed to accelerate the motor shaft and the worm. A ratio of about 8 halves the required torque, but the worm gear then loses its self-locking. The measured shift times are published as an open dataset.
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Machine Learning
Measure Neural Mappings
We introduce and define measure neural mappings (MNMs), which combine measure-dependent neural transport with ensemble consistency for learning operators on probability measures. Ensemble consistency requires outputs from growing ensembles sampled from an input law to converge to the specified population output in probability. We establish quantitative continuum limits for attention on noncompact laws under strong sub-Gaussian and tail-integrability assumptions. These laws accommodate unbounded state spaces in scientific machine learning, including Bayesian inference and uncertainty quantification. For fixed self-attention transformers, the expected output Wasserstein error is bounded by the empirical input Wasserstein error plus an additional $N^{-1/2}$ attention term. These self-attention transformers are MNMs under the stated assumptions: pre-norm architectures follow from compact stability after normalization, while post-norm architectures are covered under the stated tail conditions. We prove corresponding cross-attention estimates and extend the results to multihead attention and grouped transformer evaluation, with convergence as the group size grows. For Set Transformers viewed as measure-to-vector mappings, we obtain an $N^{-1/2}$ bound on the expected Euclidean output error under the stated assumptions. Experiments on seven operators in dimensions $d=1,2,3,5,10$ support the predicted particle-count dependence, using one-dimensional Wasserstein computations and Sinkhorn approximations in higher dimensions. The observed Wasserstein and sliced Wasserstein decay rates are close to their respective theoretical sampling benchmarks.
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Machine Learning
Variable Input Masked Autoencoders for Wrist-Worn Accelerometry
Large-scale repositories of wearable sensor data have enabled the development of foundation models for human activities and behavior. However, existing models are pretrained using fixed input durations and sampling rates, despite substantial heterogeneity in recording conditions, downstream tasks, and deployment constraints. We introduce VarMAE, a variable input masked autoencoder that learns a single representation across sampling rates and temporal contexts. During pretraining we construct two views of the same signal: a long duration high frequency view, and a short duration lower frequency view, obtained via random cropping and downsampling. We perform masked reconstruction within each view and introduce a cross-resolution masked reconstruction objective that uses visible tokens from the long view to predict masked tokens from the short view. Cropping and downsampling impose complementary information bottlenecks, encouraging the model to learn representations that remain effective across input durations and sampling rate changes. We pretrain VarMAE on the large-scale NHANES dataset, producing a single pretrained encoder matching or outperforming controlled foundation model baselines on eight benchmark datasets. With only 3.82M parameters, VarMAE is parameter efficient and shows that a single foundation model can achieve broad transfer capabilities across sensing configurations.
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Machine Learning
Mitigating Black-Box Score-Based Query Attacks via Gradient Confusion
Score-based black-box adversarial attacks pose a serious threat to deployed machine learning systems by exploiting repeated model queries to craft adversarial examples, requiring neither access to model parameters nor architecture. Existing defenses predominantly rely on stochastic output perturbations, which fail to prevent determined attackers from recovering stable gradient estimates by increasing query budgets or averaging over randomness. In this work, we propose the Gradient Confusion Defense (GCD), a retraining-free, deterministic test-time wrapper that actively shapes the probability vector returned to querying adversaries. By solving a constrained optimization problem grounded in the model's Jacobian, GCD aligns the exposed logit-gradient with a target confusion direction that is maximally misaligned with the true adversarial loss gradient—increasing the query complexity of attacks without sacrificing predictive utility or top-1 accuracy. We provide rigorous theoretical analysis demonstrating that GCD provably slows gradient-estimation-based attacks and induces systematic accept/reject errors in random search-based attacks, with the confusion effect amplifying as the fraction of defended queries increases. Extensive experiments on CIFAR-10 and ImageNet across multiple architectures (ResNet-18, ResNet-50, ViT-B/16) and four state-of-the-art attacks confirm these predictions: GCD achieves state-of-the-art robustness, while incurring zero clean accuracy degradation. %Crucially, unlike randomization-based defenses, GCD's deterministic structure provides resilience against adaptive attacks that exploit stochasticity, making it well-suited for security-critical deployment settings.
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Machine Learning
Robustly Reliable Learning for Regression
We introduce the problem of robustly reliable learning for the regression setting in adversarial environments. Given a test point $x_{test}$, a training dataset $S$ of $n$ data points, a corruption budget $b \ll n$, and a real-valued hypothesis class $\mathcal H$, our goal is to output the optimal prediction range $I^*_{x_{test}}(S, b)$, such that any $L$-Lipschitz predictor consistent with all but at most $b$ points in $S$ must predict a value $h(x_{test}) \in I$. We then instantiate the analysis for $L$-Lipschitz hypothesis classes, a natural and widely studied class in the regression setting, focusing on two key scenarios. First, for the restricted case where the corrupted dataset is guaranteed to be $L$-Lipschitz consistent, we propose a simple and efficient $b^{th}$-best heuristic algorithm and prove its correctness in computing the tightest possible range $I^*_{x_{test}}(S, b)$. We then establish its computational complexity of $O(n)$ and show that it is computationally optimal in this scenario. Building on this foundation, we address the general scenario where the dataset $S$ is no longer $L$-Lipschitz consistent. We demonstrate that computing the optimal range in this setting reduces to analyzing a violation graph, which models the pairwise $L$-Lipschitz violations among data points. By leveraging the structural properties of this graph's kernel, we propose a Fixed-Parameter Tractable (FPT) algorithm that computes the exact optimal range in $O(n^2 + b^4)$ time. Furthermore, under the Strong Exponential Time Hypothesis (SETH), we establish a computational lower bound of $\Omega(n^{2 - o(1)})$, proving that our algorithm is computationally optimal. Finally, we discuss open directions for the problem of robustly reliable learning for regression.
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Networking
What Is the Cost of a Handover Interruption? Rethinking 5G Mobility for Aerial Vehicles
Low-altitude aviation is moving toward large-scale operations increasingly dependent on 5G cellular connectivity. However, 5G mobility remains blind to the operational risk of its decisions: the same interruption may be harmless in cruise over an empty field but critical near obstacles, crowds or other aircraft. Although 5G already provides mechanisms to obtain location, population density, and radio conditions, mobility decisions do not translate this information into an operational risk metric. We propose Risk-Aware Mobility (RAM), which maps predicted communication disruptions to an operational-risk proxy using information staleness, position uncertainty, and operational context, and exposes this risk to existing mobility mechanisms. In a dense São Paulo deployment with 188 licensed 5G sectors, risk-aware handover timing reduces the mean operational-risk proxy by 45% relative to conventional A3 without degrading serving-link quality. These results motivate shifting 5G mobility from optimizing handover performance to managing the operational risk of mobility decisions. Beyond handover timing, this perspective raises a broader question: which cells should serve aerial operations when connectivity is evaluated by operational risk rather than radio performance alone?