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01.
arXiv (CS.LG) 2026-06-16

Data-driven Control with Real-time Uncertainty Compensation for Multi-Fuel Engines

arXiv:2606.16171v1 Announce Type: cross Abstract: Multi-fuel compression ignition (CI) engines offer superior power density and fuel flexibility. However, achieving consistent and optimal combustion phasing across a wide range of operating conditions remains a major challenge, particularly in the presence of modeling uncertainties. This paper presents a novel, data-driven real-time uncertainty compensation framework for combustion control in multi-fuel CI engines. The proposed approach introduces a pseudo-engine speed that enables dynamic adaptation of control inputs in response to uncertainty affecting the engine. To model the underlying combustion process, a Gaussian Process Regression (GPR) model is first trained on available input-output data, capturing the nonlinear and fuel-dependent behavior across varying operating conditions. Control inputs are then synthesized through model inversion of the learned GPR surrogate and augmented with an uncertainty compensator designed to mitigate deviations caused by dynamic variations in operating conditions and model inaccuracies. This integrated control strategy allows for real-time input corrections within a finite number of combustion cycles. Theoretical analysis establishes finite-time convergence guarantees for the proposed controller. Simulation results demonstrate that the proposed method steers the combustion phasing to the desired value in real-time, providing a scalable and adaptive control solution for multi-fuel CI engine operation.

02.
arXiv (quant-ph) 2026-06-19

Extracting the physical content of Liouvillian eigenmodes: Semiclassical quantization

arXiv:2606.20271v1 Announce Type: new Abstract: Unlike in closed quantum systems where individual energy eigenstates are understood as physical excitations, open quantum systems have distinct right and left eigenstates of the Liouvillian that decay with time and are difficult to interpret. Here we introduce a physically motivated quasiprobability measure combining the two types of eigenstates that interprets a Liouville eigenmode as a set of coherences. This coherence measure is intimately connected to the return probability and allows one to visualize the modes as quasiprobability distributions in a "doubled" phase space. Using this measure we show that, remarkably, an oscillator retains its quantized "orbits" in phase space for a large class of linear and nonlinear damping, thus providing a formulation of semiclassical quantization for open systems. The orbits have measurable dynamical signatures and are broadened in the presence of a thermal bath, similar to energy levels. For quadratic systems, our results yield an extension of the concept of invariant tori, which play a central role in Hamiltonian systems.

03.
Nature Medicine 2026-06-12

Efficacy and target engagement of dopamine agonist pramipexole for anhedonic depression: a randomized placebo-controlled trial

Anhedonia is a core and disabling symptom of mood disorders with limited treatment options. We evaluated the efficacy and safety of the dopamine agonist pramipexole in patients with mood disorders characterized by clinically significant anhedonia. In this single-center, randomized, double-blind, placebo-controlled trial, adults with major depressive disorder, dysthymia or bipolar depression and elevated Snaith−Hamilton Pleasure Scale (SHAPS) scores were assigned (1:1) to flexible dose, once-daily oral pramipexole as add-on treatment or placebo for 9 weeks. The primary outcome was change in SHAPS score from baseline to week 9. Analyses were conducted in the modified intention-to-treat population. Eighty-five participants were randomized, and 82 were included in the analysis. The primary outcome was met: pramipexole was associated with a greater reduction in SHAPS scores compared to placebo (mean difference: −4.04, 95% confidence interval: −6.89 to −1.18, P = 0.006, Hedges’ g = 0.62). Exploratory analyses indicated that pramipexole was associated with increased light physical activity and relative preservation of reward-related ventral striatal activation. Improvements in anhedonia were sustained during a 6-month open-label extension. Pramipexole was generally well tolerated compared to placebo. Pramipexole significantly improved anhedonia and showed a favorable safety profile, supporting its potential as an augmentation strategy in mood disorders. ClinicalTrials.gov identifiers: NCT05355337 and NCT05825235 . Pramipexole, in patients with major depressive disorder, dysthymia or bipolar depression, reduced Snaith−Hamilton Pleasure Scale scores significantly compared to placebo.

04.
arXiv (CS.CL) 2026-06-16

DRA-GRPO: Your GRPO Needs to Know Diverse Reasoning Paths for Mathematical Reasoning

Post-training LLMs with Reinforcement Learning, specifically Group Relative Policy Optimization (GRPO), has emerged as a paradigm for enhancing mathematical reasoning. However, standard GRPO relies on scalar correctness rewards that are often non-injective with respect to semantic content: distinct reasoning paths receive identical rewards. This leads to a Diversity-Quality Inconsistency, where the policy collapses into a narrow set of dominant modes while ignoring equally valid but structurally novel strategies. To bridge this gap, we propose Diversity-aware Reward Adjustment (DRA), a theoretically grounded framework that calibrates the reward signal using the semantic density of sampled groups. By leveraging Submodular Mutual Information (SMI), DRA implements an Inverse Propensity Scoring (IPS) mechanism that effectively de-biases the gradient estimation. This creates a repulsive force against redundancy, driving the policy to achieve better coverage of the high-reward landscape. Our method is plug-and-play and integrates seamlessly with GRPO variants. Empirical evaluations on five math benchmarks demonstrate that DRA-GRPO consistently outperforms strong baselines, achieving an average accuracy of 58.2% on DeepSeek-R1-Distill-Qwen-1.5B with only 7,000 training samples and $55 cost, highlighting the critical role of diversity calibration in data-efficient alignment. The code is available at https://github.com/xiwenc1/DRA-GRPO.

05.
arXiv (CS.CV) 2026-06-11

Precision-Aware Illumination-Disentangled Vision Transformer for Spacecraft 6D Pose Estimation

Vision sensors provide a lightweight solution for spacecraft proximity operations, but monocular spacecraft 6D pose estimation remains difficult under illumination variation, specular reflection, shadowing, weak texture, and background interference. These factors make local visual evidence spatially unreliable and can destabilize pose regression. This article proposes a Precision-Aware Illumination-Disentangled Vision Transformer (PAID-ViT) for robust spacecraft pose estimation.The proposed model separates pose-relevant structure tokens from illumination-sensitive appearance tokens, estimates patch reliability before pose aggregation, and uses foreground mask supervision to preserve silhouette cues. A parameter-free geometric recovery module converts normalized crop coordinates, log-depth, and a continuous 6D rotation representation into camera-frame rotation and translation. Experiments on SPEED+ V2, the SPEED+ validation/lightbox/sunlamp evaluation configuration used in this study, suggest that PAID-ViT reduces translation error and improves robustness in the challenging sunlamp domain, while ablation studies support the complementary roles of illumination disentanglement, reliability-aware token aggregation, mask supervision, and training-side regularization.

06.
arXiv (CS.CL) 2026-06-19

Trustworthy Multi-Agent Systems: Mitigating Semantic Drift with the Argent Signaling Protocol

When multi-agent LLM systems produce bad answers, not all failures are equal: some answers are grounded in the right material but incomplete, while others are simply ungrounded and should be stopped. Current retry strategies treat both cases identically (try again and hope for the best), leaving human supervisors unable to tell whether a retry was warranted or whether the system should have halted instead. We introduce the Argent Signaling Protocol (ASP), a compact machine-readable header that accompanies every AI-generated response with structured quality signals: certainty (@C), grounding (@G), stochasticity (@S), and an assumption index that classifies the evidentiary basis of each claim. These signals enable a controller to distinguish repairable failures from containment failures and route each case differently. We evaluate ASP in two modes. In standalone mode, a 27-question document-grounded QA benchmark over the Array BioPharma/Ono license agreement compares baseline prompts against ASP-instrumented controller actions across three local GGUF models. On Qwen~(0.8B), ASP improves pass rate from 11.1% to 33.3% and mean term coverage from 36.7% to 65.4%; on Dobby~(8B), ASP produces 4 fail-to-pass recoveries, raising pass rate from 33.3% to 44.4%; on SmolLM3~(3B), ASP alternates between repair and containment per question. Aggregate improvement is meaningful (12/81 to 21/81 passes). In multi-agent mode, an ASP sidecar sits between a retrieval agent and a downstream decision agent; the sidecar blocks 100% of ungrounded upstream outputs from reaching the downstream agent (24/27 blocked, 0 ungrounded propagations).

07.
arXiv (CS.LG) 2026-06-15

Adaptive Nucleus Truncation for Long-Form Reasoning

arXiv:2606.13982v1 Announce Type: cross Abstract: Sampling plays an important role in long-form language-model reasoning. Over thousands of decoding steps, small changes in the candidate token set can compound into different reasoning trajectories, stability profiles, and final answers. Existing truncation methods such as top-$p$, min-$p$, and fixed top-$n\sigma$ sampling improve over unrestricted sampling, but they rely on fixed thresholds that cannot adapt to changes in entropy, task difficulty, training stage, or generation budget. We introduce Adaptive Nucleus Truncation Sampling (ANTS), which extends top-\(n\sigma\) sampling from a fixed decoding rule into an adaptive rollout-control mechanism for long-form generation. ANTS selects standardized neighborhoods around the maximum logit before temperature scaling, adapts the truncation width using an entropy-conditioned controller, and retains a no-truncation fallback arm to stabilize training when truncation becomes unsafe. On a 33B-total / 4B-active sparse Mixture-of-Experts reasoning model, ANTS improves average performance over percentage-based benchmarks by +1.9, +3.8, and +5.2 points at 8K, 16K, and 32K generation budgets, respectively. The strongest gains appear on instruction following and mathematical reasoning, with IFBench improving by more than 10 points at 32K and AIME 2025 improving by 7 points. Code generation reveals an important budget interaction. On Codeforces, ANTS trails the baseline at 8K, but reverses this gap and substantially improves ELO at 16K and 32K. These results suggest that sampler design should be treated not just as a decoding hyperparameter, but as part of how we stabilize and scale long-budget reasoning.

08.
arXiv (CS.CL) 2026-06-16

Towards Pareto-Optimal Tool-Integrated Agents with Pareto Ranking Policy Optimization

Recent advances in tool-integrated language agents have significantly improved their ability to solve complex reasoning tasks. However, existing alignment methods predominantly focus on maximizing task accuracy, while overlooking auxiliary objectives such as tool-use efficiency, which are essential for practical deployment. To address this gap, we introduce ParetoPO, a two-stage multi-objective optimization framework for aligning tool-using large language models (LLMs) under competing objectives. In the first stage, ParetoPO leverages hypervolume-guided dynamic scalarization to adapt reward weights based on global Pareto frontier progress. In the second stage, it replaces scalarized learning signals with Pareto-ranking-based advantage computation, promoting nondominated trajectories through dominance-aware credit assignment. This design enables fine-grained, action-level optimization across multiple conflicting objectives. Experimental results on mathematic reasoning and multi-hop QA tasks show that ParetoPO consistently discovers policies with superior accuracy-efficiency trade-offs compared to static and heuristic baselines.

09.
arXiv (CS.LG) 2026-06-15

Beyond a Single Explanation of the Adam–SGD Gap

arXiv:2606.14259v1 Announce Type: new Abstract: Prior work has identified several factors that can contribute to the performance gap between Adam and SGD, spanning data aspects, architecture design, and optimization properties. Yet these explanations are often studied in isolation, leaving their relative importance unclear. In this work, we revisit these hypotheses through a controlled empirical study across vision, language, genomics, and graph tasks, spanning modern and classical architectures, and carefully designed training setups. Our results suggest that no single factor consistently explains the Adam–SGD gap. For instance, the Adam advantage can (1) persist under a uniform vocabulary distribution yet nearly disappear under a heavy-tailed one; (2) reverse in favor of SGD in softmax-attention models; and (3) become larger under soft architectural modifications, e.g., when ReLU is replaced by a GeLU nonlinearity. This suggests that the gap arises from nontrivial data and architecture interactions, rather than from a single common factor. Yet, we observe a pattern across our settings: a crossover batch size at which the relative advantage shifts from SGD to Adam as the batch size scales. These empirical results are captured by our theoretical gap model, which predicts this batch-size-dependent crossover. Our perspective helps reconcile several existing hypotheses while offering practical insights across domains.

10.
arXiv (CS.CL) 2026-06-16

SciOrch: Learning to Orchestrate Expert LLMs for Solving Frontier Multimodal Scientific Reasoning Tasks

Frontier scientific reasoning remains a major challenge for large language models (LLMs), where even the strongest commercial systems fall short of expert-level performance. A closer look at model behavior reveals substantial complementarity that single-model evaluation hides: different frontier models excel on different question types, and no single model captures the full picture. We present SciOrch, a framework that trains a lightweight 8B model to orchestrate frontier LLMs for scientific reasoning. The orchestrator decomposes each question, delegates sub-problems to selected commercial models through API calls, and synthesizes a final answer. Training such an orchestrator is fundamentally harder than conventional agentic RL: each action triggers an API call that is expensive in both dollar cost and latency, making standard online rollouts infeasible. We address this with MCTS-based approach, producing diverse orchestration trajectories, extracting per-node single-turn samples, and optimizing the orchestrator with GRPO-style training. On a 240-question test set spanning SGI-Reasoning and Scientists' First Exam, SciOrch reaches 56.66% average accuracy, outperforming the strongest single commercial model by 3.74% and the strongest multi-agent baseline by 3.33%. It also attains the best accuracy on both SGI and SFE with less than half the API cost of typical multi-agent methods.

11.
arXiv (CS.AI) 2026-06-16

Greed Is Learned: Visible Incentives as Reward-Hacking Triggers

arXiv:2606.16914v1 Announce Type: new Abstract: Deployed agents increasingly act with their reward proxy in view, such as a balance, score, or KPI dashboard. We show that reinforcement learning can make a policy addicted to such a visible self-benefit channel. It chases the displayed payoff across held-out domains, sacrifices the true task to do so, and follows the channel wherever we rewrite it, while policies that never saw the channel stay honest. We call this reward-channel addiction and study it in MoneyWorld, a synthetic sandbox. The addiction can flip a model's safety alignment: trained only on innocuous money tasks with no safety content, the model abandons the safe action it otherwise always takes whenever a dashboard pays for an unsafe one, and reverts to safe once the channel is hidden. This learned bribe replicates across model scales and families. Blindly optimizing super-capable, next-generation AI on KPIs or P\&L can be dangerous for alignment. Greed is learned when following such a channel pays.

12.
arXiv (CS.AI) 2026-06-16

Quantum Machine Learning for Industrial Applications

arXiv:2606.14822v1 Announce Type: cross Abstract: Recent advances in Machine Learning have transformed numerous industrial sectors, yet classical paradigms face fundamental limitations: rapidly growing data volumes, rising computational costs, significant energy consumption, and the physical scaling limits of conventional hardware architectures. Quantum computing has emerged as a promising computational paradigm to address these challenges, giving rise to the field of Quantum Machine Learning (QML). In this thesis, the theoretical foundations of QML are investigated, with a focus on near-term and future practical applications. Three central challenges are addressed: the trainability of variational quantum circuits, their expressivity, and their resistance to efficient classical simulation. The trainability of Hamming-weight preserving variational quantum circuits is first studied, and theoretical guarantees are established that resolve an open conjecture on the absence of barren plateaus for this circuit family. Subspace-preserving QML algorithms are then introduced, including photonic circuits and quantum convolutional neural networks, and are designed to mimic classical ML subroutines while offering polynomial quantum advantage. Finally, variational quantum circuits are analyzed as quantum Fourier models, and a framework is derived to jointly characterize expressivity and trainability, from which conditions are obtained under which quantum models provably separate from their classical counterparts. These contributions are intended to advance the theoretical roadmap for harnessing near-term and future quantum technologies in real-world applications.

13.
arXiv (CS.CV) 2026-06-17

Rethinking Cross-Layer Information Routing in Diffusion Transformers

Diffusion Transformers (DiTs) have become a de facto backbone of modern visual generation, and nearly every major axis of their design – tokenization, attention, conditioning, objectives, and latent autoencoders – has been extensively revisited. The residual stream that governs how information accumulates across layers, however, has been directly inherited from the original Transformer. In this paper, we present a systematic empirical analysis of cross-layer information flow in DiTs, jointly along depth and denoising timestep, and identify three concrete symptoms of traditional residual addition, namely monotonic forward magnitude inflation, sharp backward gradient decay, and pronounced block-wise redundancy. Motivated by this diagnosis, we propose Diffusion-Adaptive Routing (\textsc{DAR}), a drop-in residual replacement that performs learnable, timestep-adaptive, and non-incremental aggregation over the history of sublayer outputs. Moreover, the proposed \textsc{DAR} is compatible with many modern Transformer enhancement methods, such as REPA. On ImageNet $256\times256$, \textsc{DAR} improves SiT-XL/2 by $2.11$ FID ($7.56$ vs.\ $9.67$) and matches the baseline's converged quality with $8.75\times$ fewer training iterations. Stacked on top of REPA, it yields a $2\times$ training acceleration in the early stage, suggesting cross-layer information routing as an underexplored design axis in diffusion modeling, one that operates orthogonally to existing representation-alignment objectives. Beyond pretraining, \textsc{DAR} can also be applied during the fine-tuning stage of large-scale T2I models and preserves high-frequency details during Distribution Matching Distillation.

14.
arXiv (CS.LG) 2026-06-18

Hierarchical Attention via Domain Decomposition

arXiv:2606.18525v1 Announce Type: new Abstract: We propose a hierarchical attention mechanism based on two-level overlapping Schwarz domain decomposition. The method is motivated by the observation that two-level Schwarz domain decomposition methods combine local subdomain corrections with a coarse level that communicates global, long-range information. We test its usefulness in the context of finite-dimensional operator learning using a simple, one-dimensional diffusion problem with homogeneous Dirichlet boundary conditions. Although elementary, this problem provides a controlled sequence-to-sequence setting in which the exact nonlocal solution operator is known. After discretization, learning the solution operator amounts to approximating the inverse of a symmetric positive definite matrix. As a baseline, we use a global softmax-free low-rank attention operator of the form $QK^T$. The proposed construction replaces this dense global factorization by a two-level additive structure: local low-rank attention blocks on overlapping subdomains are combined with a coarse attention block. The resulting operator has the form $$M_{\theta}^{-1} = \Phi Q_0 K_0^T \Phi^T + \sum_{i=1}^{N} R_i^T D_i^{1/2} Q_i K_i^T D_i^{1/2} R_i.$$ Here $R_i$ restricts to an overlapping subdomain, $D_i$ is a partition-of-unity weight, and $\Phi$ is a coarse interpolation (or prolongation) matrix. Numerical experiments for synthetic Fourier right-hand sides indicate that the domain-decomposition attention operator is able to train faster and can give more accurate approximations than a global low-rank attention baseline while using significantly fewer parameters.

15.
arXiv (math.PR) 2026-06-11

A Hybrid LSMC-PDE Method for Bermudan Option Pricing under the Gatheral Double Mean-Reverting Model

arXiv:2606.11237v1 Announce Type: cross Abstract: We study Bermudan option pricing under the Gatheral Double Mean-Reverting (GDMR) stochastic volatility model. The model features a variance process together with a stochastic long-run mean variance process and allows Constant Elasticity of Variance (CEV)-type exponents in the diffusion coefficients. This model is attractive since it provides a flexible specification for volatility dynamics. However, the pricing of early-exercise derivatives under the GDMR model remains largely unexplored in the literature. To address this challenge, we adapt a Hybrid Least-Squares Monte Carlo-Partial Differential Equation (LSMC-PDE) framework to the GDMR model and provide a detailed model-specific implementation. Conditioning on simulated variance paths, the pricing problem reduces to a one-dimensional problem in the asset price, which is solved by a Fourier-based approach, while the remaining dependence on the variance variables is approximated by least-squares regression. Our numerical experiments demonstrate that the Hybrid LSMC-PDE approach yields accurate pricing estimates and often lower pricing errors than plain LSMC, particularly for low and moderate numbers of simulation paths, showing the benefit of using the model structure in early-exercise option pricing.

16.
arXiv (CS.AI) 2026-06-17

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication

arXiv:2606.17399v1 Announce Type: cross Abstract: When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies. This contrasts with modular addition, where only a sparse set of key frequencies suffices. We show this density is an artifact of analyzing in the wrong basis. The natural Fourier transform for multiplication is not the standard additive DFT but the multiplicative character transform, which decomposes functions on the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ into its irreducible representations. Applying this transform to a grokked transformer trained on $a \cdot b \bmod 113$, we find the embedding spectrum becomes highly sparse (Gini coefficient 0.58 vs. 0.07 in the additive basis) with only 4 key frequencies carrying significant energy. Furthermore, 96.9% of MLP neurons are cleanly tuned to a single multiplicative frequency, and neuron activation heatmaps reveal 2D-periodic structure when reordered by the discrete logarithm. These results demonstrate the transformer reduces multiplication to addition in discrete-log space, implementing a "Discrete-Log Clock" algorithm analogous to Nanda et al.'s Clock algorithm for addition. The methodology generalizes: matching the analysis basis to the algebraic structure of the task reveals interpretable structure where standard tools see noise.

17.
arXiv (CS.LG) 2026-06-18

Sequential Hiring of Contingent Workers Through Learning-Based Optimization

arXiv:2606.18438v1 Announce Type: cross Abstract: In this paper, we study a sequential workforce management problem in a contingent labor setting with uncertainty in both worker production and labor supply. A firm seeks to maximize cumulative profit by maintaining an active team of fixed size while learning worker productivity over time. We emphasize two critical operational frictions in this problem: replacing workers is costly, and workers may not be available immediately for hiring because of, for example, prior job commitments, scheduling constraints, or onboarding procedures. Thus, hiring decisions take effect only after a random delay. We formulate this problem as a stochastic multi-play bandit with costly switching and delayed actions, and develop a learning-based hiring policy, DR-UCB (DelayedReplacement-UCB), that makes replacement and hiring decisions sequentially through learning cycles. In each cycle, the policy uses real-time production data to determine when to initiate workforce changes and which workers to replace and hire. We show that the leading-order regret of the proposed policy matches its lower bound in its dependence on the time horizon. Our numerical experiments show that DR-UCB outperforms benchmark policies.

18.
arXiv (CS.CV) 2026-06-16

Text region detection in historical astronomical diagrams

Text detection is a crucial task in the analysis of historical documents. While datasets and benchmarks exist for text detection in manuscripts and maps, the study of text in mathematical diagrams has received little attention. To address this, we introduce a large-scale, diverse, open-access dataset of 948 historical astronomical diagrams containing 10,940 oriented polygonal text regions. Our dataset spans ten centuries (8th to 18th) and seven main linguistic traditions: Arabic and Persian (115), Chinese (332), Byzantine (233), Latin (185), Hebrew (48), and Sanskrit (35). It captures a wide range of diagram styles and textual content, from symbols to multi-line paragraphs. Each text instance is annotated with ordered polygons that precisely delineate text regions and encode the reading direction. In addition, we annotated the 2,293 regions in Latin diagrams with 20 class labels. We evaluated several strong baselines on our dataset, including TESTR, DeepSolo++, and Poly-DETR, a simple extension of DINO-DETR that we design to predict ordered polygon vertices. Poly-DETR achieves state-of-the-art performance on the MTHv2 and cBAD2019 benchmarks and provides a solid, simple baseline on our dataset. Code and dataset available online.

19.
arXiv (CS.LG) 2026-06-11

Range-Aware Bayesian Optimization for Discovering Diverse Designs within Target Property Windows

arXiv:2606.11574v1 Announce Type: new Abstract: In many materials and product design problems, desirable candidates exhibit properties that fall within an acceptable range rather than achieve a single optimum. Recovering multiple, distinct solutions that satisfy such specifications is also practically valuable, as some candidates may be preferred for reasons of cost, processability, or robustness that are difficult to encode directly in an objective function. Here, we develop a range-aware Bayesian optimization (BO) framework in which the acquisition function directly scores the posterior probability that a candidate satisfies a target range. The framework naturally extends to parallel pursuit of multiple distinct specifications over a shared candidate space. Across benchmark tasks, range-aware acquisition consistently recovers larger and more diverse sets of valid designs than standard BO baselines and recent goal-seeking methods. Its utility is further demonstrated in two practically motivated design case studies involving optimizing reaction conditions for polymer synthesis and sequence-defined oligomer discovery for prescribed optical absorption bands, supported by quantum chemical calculations. These results suggest that range-aware BO can provide a practical and sample-efficient foundation for specification-driven design, particularly when design flexibility and solution diversity are important considerations.

20.
arXiv (quant-ph) 2026-06-19

$K$-Theoretic Obstructions to Linearizing QCA Representations

arXiv:2606.19657v1 Announce Type: cross Abstract: Projective representations arise naturally in physics and representation theory, and determining whether they can be linearized has been a fundamental problem. In this work, we study the analogous problem for quantum cellular automata (QCA) representations, which incorporate locality constraints imposed by a metric space $X$. Over an arbitrary field $\mathbb{F}$, we develop an obstruction theory for the linearization of QCA representations, using the algebraic $K$-theory spectrum of QCA constructed in previous work of the authors. The resulting obstructions are governed by the homotopy type of the QCA spaces, from which we extract universal obstruction classes to linearization. In the complex algebraic and unitary case, we also fully compute the homotopy types of the QCA spaces over a point, a line, and a plane.

21.
arXiv (math.PR) 2026-06-15

Sharp Favard length of random Cantor sets

arXiv:2512.17753v2 Announce Type: replace-cross Abstract: We show that for a large class of planar $1$-dimensional random fractals $S$, the Favard length $\operatorname{Fav}(S(r))$ of the neighborhood $S(r)$ is comparable to $\log^{-1}(1/r)$, matching a universal lower bound; up to now, this was only known in expectation for a few concrete models. In particular, we show that there exist $1$-Ahlfors regular sets with the fastest possible Favard length decay. For a wide class of planar one-dimensional "grid random fractals", including fractal percolation and its Ahlfors-regular variants, we further show that $\operatorname{Fav}(S(r))/\log(1/r)$ converges almost surely, and we identify the limit explicitly. Furthermore, we prove that for some $1$-dimensional Ahlfors-regular random fractals $S$, the Favard length of $S(r)$ decays instead like $\log\log(1/r)/\log(1/r)$, showing that the $1/\log(1/r)$ decay is not universal among random fractals, as might be expected from previous results.

22.
arXiv (quant-ph) 2026-06-15

Inhomogeneous Light-Matter Coupling as a Resource for Noiseless Quantum Memories

arXiv:2605.26783v3 Announce Type: replace Abstract: Inhomogeneous ensembles of two-level systems are central to both fundamental light-matter physics and quantum-network applications. Understanding and optimizing ensemble-based quantum memories and entanglement protocols requires a unified framework that describes how to store quantum states of light as collective matter excitations and retrieve them on demand. Here we develop such a framework, the waveguide model, by mapping the dark collective modes of the ensemble onto an effective waveguide with well-defined input-output relations, valid in both the weak-excitation regime and near population inversion. This model reveals that inhomogeneous coupling – often regarded as a limitation – is instead the physical origin of noisy-echo suppression by adiabatic pulses, a key ingredient for realizing noiseless quantum memories. For entanglement generation, the same mechanism exposes a previously unexplored shortcoming of robust control pulses and leads to a new composite-pulse protocol that overcomes it. These results establish the waveguide model as a practical bridge between fundamental collective physics and quantum-network protocol design, recasting inhomogeneous coupling from an obstacle into a control knob for collective emission.

23.
arXiv (CS.AI) 2026-06-19

The Algorithmic-Human Manager: AI, Apps, and Workers in the Indian Gig Economy

arXiv:2606.19975v1 Announce Type: cross Abstract: This paper examines the impact of artificial intelligence and digital technologies on the blue-collar gig economy in India, focusing on algorithmic management. This paper examines the impact of artificial intelligence and digital technologies on the blue collar gig economy in India, focusing on algorithmic management he use of automated systems to allocate, monitor, and evaluate work in location-based services such as ride sharing and delivery. Using a social justice framework and a mixed-methods approach comprising interviews with 16 gig workers and 21 key stakeholders, the study uncovers a dual reality: while AI-powered systems expand access to work and generate operational efficiencies, they simultaneously introduce significant challenges related to fairness, transparency, and worker dignity. Key findings reveal that algorithmic systems are opaque by design, produce inequitable outcomes, and are not structured to reward additional labour with proportionate pay. The study advocates for a pragmatic hybrid governance model an Algorithmic Human Manager framework in which technological efficiency and human accountability operate together rather than in opposition. The findings carry implications for policymakers, platform companies, and civil society organizations working to design equitable AI governance frameworks for the gig economy in India and across the Global South.

24.
arXiv (CS.LG) 2026-06-16

GauS: Differentiable Scheduling Optimization via Gaussian Reparameterization

arXiv:2602.20427v2 Announce Type: replace Abstract: Efficient operator scheduling is a fundamental challenge in software compilation and hardware synthesis. While recent differentiable approaches have sought to replace traditional ones like exact solvers or heuristics with gradient-based search, they typically rely on categorical distributions that fail to capture the ordinal nature of time and suffer from a parameter space that scales poorly. In this paper, we propose a novel differentiable framework, GauS, that models operator scheduling as a stochastic relaxation using Gaussian distributions, which fully utilize modern parallel computing devices like GPUs. By representing schedules as continuous Gaussian variables, we successfully capture the ordinal nature of time and reduce the optimization space by orders of magnitude. Our method is highly flexible to represent various objectives and constraints, which provides the first differentiable formulation for the complex pipelined scheduling problem. We evaluate our method on a range of benchmarks, demonstrating that Gaus achieves Pareto-optimal results.

25.
arXiv (CS.LG) 2026-06-12

LLM-ODDR: A Large Language Model Framework for Joint Order Dispatching and Driver Repositioning

arXiv:2505.22695v2 Announce Type: replace Abstract: Ride-hailing platforms face significant challenges in optimizing order dispatching and driver repositioning operations in dynamic urban environments. Traditional approaches based on combinatorial optimization, rule-based heuristics, and reinforcement learning often overlook driver income fairness, interpretability, and adaptability to real-world dynamics. To address these gaps, we propose LLM-ODDR, a novel framework leveraging Large Language Models (LLMs) for joint Order Dispatching and Driver Repositioning (ODDR) in ride-hailing services. LLM-ODDR framework comprises three key components: (1) Multi-objective-guided Order Value Refinement, which evaluates orders by considering multiple objectives to determine their overall value; (2) Fairness-aware Order Dispatching, which balances platform revenue with driver income fairness; and (3) Spatiotemporal Demand-Aware Driver Repositioning, which optimizes idle vehicle placement based on historical patterns and projected supply. We also develop JointDR-GPT, a fine-tuned model optimized for ODDR tasks with domain knowledge. Extensive experiments on real-world datasets from Manhattan taxi operations demonstrate that our framework significantly outperforms traditional methods in terms of effectiveness, adaptability to anomalous conditions, and decision interpretability. To our knowledge, this is the first exploration of LLMs as decision-making agents in ride-hailing ODDR tasks, establishing foundational insights for integrating advanced language models within intelligent transportation systems. While the current framework incurs higher computational costs than traditional methods, we show that parallel decomposition and model distillation can reduce latency to production-viable levels for deployment.