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01.
arXiv (CS.AI) 2026-06-17

Closing the Feedback Loop: From Experience Extraction to Insight Governance in Verbal Reinforcement Learning

arXiv:2606.17591v1 Announce Type: new Abstract: Training-free verbal reinforcement learning enables LLM agents to learn from world feedback – objective signals such as dynamic task outcomes, market returns, or demand forecasts – by extracting verbal rules from experience and injecting them as context, updating the agent's behavior without parameter changes. However, in non-stationary environments these agents face a retention-forgetting dilemma: retaining stale insights causes negative transfer, while discarding them causes catastrophic forgetting when conditions recur. We identify four requirements for navigating this dilemma – outcome-driven evaluation, persistent structured evidence, non-monotonic knowledge lifecycle, and compositional governance – and show that existing methods invest heavily in experience extraction while underinvesting in insight governance. We propose a three-layer architecture – rules, evidence, and skills – connected by a feedback-driven curation loop that closes the governance gap. Rules capture distilled experience from world outcomes; evidence logs track each rule's reliability across episodes; skills govern which rules to apply, how to resolve conflicts, and when to abstain. On financial forecasting as a case study, where world feedback is naturally abundant, noisy, and non-stationary, we show that the same accumulated experience either degrades performance below the zero-shot baseline or dramatically improves accuracy and risk-adjusted returns, depending on whether the curation loop is present.

02.
arXiv (CS.AI) 2026-06-12

Speculative Rollback Correction for Quality-Diverse Web Agent Imitation

arXiv:2606.12485v1 Announce Type: cross Abstract: Training interactive web agents through imitation learning from expert trajectories has emerged as a highly effective approach. However, determining the optimal timing for expert intervention presents a critical challenge in this context. Delayed intervention often leads to the accumulation of early-stage errors, pushing the page state into an irrecoverable regime. Conversely, premature or excessive intervention causes the agent to become overly reliant on expert policies, trapping the model in local optima characterized by a single, rigid trajectory. We propose Speculative Rollback Correction (SRC), a branch-level imitation framework for resettable agent environments. Instead of requesting teacher labels at every visited state or correcting only after a completed trajectory, SRC uses fixed-horizon branch review: the student executes a short speculative segment before teacher review, and the teacher localizes the first harmful deviation only when local progress breaks. Rollback preserves useful prefixes, while successful rollouts are filtered by a hard verifier and retained in a lightweight quality-diversity archive. The resulting data supports next-action supervised fine-tuning on both localized corrections and verifier-passing trajectories. On WebArena-Infinity, SRC collects 977 verifier-passing trajectories and 9,183 next-action examples; fixed-horizon review improves the recovery-versus-query tradeoff over step-level review while retaining verifier-passing solution variants. Code is available at https://github.com/LongkunHao/SRC_gui_agent.

03.
arXiv (CS.LG) 2026-06-17

MGUP: A Momentum-Gradient Alignment Update Policy for Stochastic Optimization

arXiv:2606.17526v1 Announce Type: new Abstract: Efficient optimization is essential for training large language models. Although intra-layer selective updates have been explored, a general mechanism that enables fine-grained control while ensuring convergence guarantees is still lacking. To bridge this gap, we propose MGUP, a novel mechanism for selective updates. MGUP augments standard momentum-based optimizers by applying larger step-sizes to a selected fixed proportion of parameters in each iteration, while applying smaller, non-zero step-sizes to the rest. As a nearly {plug-and-play} module, MGUP seamlessly integrates with optimizers such as AdamW, Lion, and Muon. This yields powerful variants such as MGUP-AdamW, MGUP-Lion, and MGUP-Muon. Under standard assumptions, we provide theoretical convergence guarantees for MGUP-AdamW (without weight decay) in stochastic optimization. Extensive experiments across diverse tasks, including MAE pretraining, LLM pretraining, and downstream fine-tuning, demonstrate that our MGUP-enhanced optimizers achieve superior or more stable performance compared to their original base optimizers. We offer a principled, versatile, and theoretically grounded strategy for efficient intra-layer selective updates, accelerating and stabilizing the training of large-scale models. The code is publicly available at https://github.com/MaeChd/MGUP.

04.
arXiv (CS.AI) 2026-06-15

Listening with Attention: Entropy-Guided Explainability for Transformer-Based Audio Models

arXiv:2606.14647v1 Announce Type: cross Abstract: Transformer-based automatic speech recognition (ASR) models such as Whisper are highly accurate, but their predictions remain difficult to interpret. Existing explainable AI (XAI) methods often lack faithfulness and precise temporal grounding. We propose Listening with Entropy-guided Attention for Faithful explainability (LEAF-X), a model-intrinsic XAI framework for transformer-based ASR. LEAF-X combines entropy-guided attention weighting, multi-layer attention rollout, and optional causal ablations to identify low-entropy, high-impact heads and layers, producing sparse token-to-frame attributions. Unlike perturbation-based explainers or raw attention maps, LEAF-X exploits the internal structure of encoder-decoder and speech-augmented decoder-only models to generate explanations that better reflect model computation. Results show 32% improved faithfulness, 35-39% stronger locality/sparsity, and the most stable attributions, supporting more transparent and auditable ASR.

05.
arXiv (CS.AI) 2026-06-15

Sorries Are Not the Hard Part: An Expert-Review Case Study of a Semi-Autonomous Formalization

arXiv:2606.13925v1 Announce Type: new Abstract: Large language models can often close proof gaps in interactive theorem provers, but a verified theorem is not the same thing as a reusable library contribution. We study this distinction through a detailed case study: a semi-autonomous formalization of Grothendieck's vanishing theorem. The initial version compiles with no sorries, but an expert review found serious problems in definitions, theorem generality, file organization, and the API. We then ran a review-driven refactor and compression process and obtained a second expert review. The before-and-after comparison shows a sharp split: agents adapted well to local, mechanically checkable feedback, but remained weak at choosing definitions and designing APIs. We argue that autoformalization should be evaluated not only by closed sorries, but by whether the resulting formalization survives expert review.

06.
arXiv (CS.CL) 2026-06-18

MemRerank: Preference Memory for Personalized Product Reranking

LLM-based shopping agents increasingly rely on long purchase histories and multi-turn interactions for personalization, yet naively appending raw history to prompts is often ineffective due to noise, length, and relevance mismatch. We propose MemRerank, a preference memory framework that distills user purchase history into concise, query-independent signals for personalized product reranking. To study this problem, we build an end-to-end benchmark and evaluation framework centered on an LLM-based 1-in-5 selection task, which measures both memory quality and downstream reranking utility. We further train the memory extractor with reinforcement learning (RL), using downstream reranking performance as supervision. Experiments with two LLM-based rerankers show that MemRerank consistently outperforms no-memory, raw-history, and off-the-shelf memory baselines, yielding up to +10.61 absolute points in 1-in-5 accuracy. These results suggest that explicit preference memory is a practical and effective building block for personalization in agentic e-commerce systems.

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

ADORE: Iterative Query Expansion with Retrieval-Grounded Relevance Feedback

LLM-based query expansion improves retrieval by enriching the original query with additional context. Yet most methods remain generation-driven, producing plausible pseudo-documents or expansions without checking how the target corpus responds. This can introduce retrieval drift, amplify misleading vocabulary, or miss terms that distinguish relevant from non-relevant documents. We argue that effective expansion requires retrieval-grounded feedback, not just single-pass generation or unverified iteration. We introduce ADORE (ADapt, Observe, Relevance Evaluate), an iterative framework that turns retrieval outcomes into feedback for the next expansion. At each round, an LLM generates pseudo-passages, a retriever exposes the corpus response, and a relevance assessor evaluates retrieved documents against the original query. These judgments identify what to reinforce, what remains undercovered, and what to suppress. Across TREC Deep Learning, BEIR, and BRIGHT, ADORE consistently outperforms strong query expansion baselines with notable improvements across nearly all evaluation settings, improving average nDCG@10 by 24.5% over BM25 and 3.6% over the strongest prior query expansion method on BEIR, and by 122.9% over BM25 and 9.2% over the best query expansion baseline on BRIGHT. Our code and data are publicly available.

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

Open-World Video Segmentation

While video segmentation has advanced rapidly on short clips and closed-set benchmarks, open-world video segmentation remains largely unexplored. The challenge is twofold: (1) existing methods are not designed to support object discovery and identity maintenance in long videos of dynamic ego-motion, and (2) existing evaluation protocols rely on a rigid 1:1 matching that unfairly penalizes semantically valid predictions with mismatched granularity. To address both gaps, we introduce Savvy, a practical and strong system for zero-shot open-world long-horizon video segmentation. Savvy combines hierarchical mask discovery, deferred admission, and track consolidation to support persistent object discovery, safe track promotion, and stable long-range identity maintenance. We further propose OGA, a granularity-aware evaluation suite for open-world video segmentation. Built on a Granularity-Agnostic (GA) matching protocol, OGA relaxes conventional 1:1 matching to an n:1 mapping, but still enforces temporal rigor by detecting support discontinuities through sever points and scoring each reference object through its dominant coherent fragment. This prevents fragmented or flickering support from being over-rewarded while enabling GA-adapted metrics and structural diagnostics: identity persistence (IP), and identity concentration (IC). On VIPSeg, we show that standard 1:1 evaluation substantially underestimates open-world methods, whereas GA evaluation recovers much of their suppressed performance. On the more realistic long-horizon benchmarks: ScanNet and HM3D, Savvy consistently outperforms strong baselines across both classical and proposed metrics, including STQ, VPQ$_\infty$, IP and IC. Together, these results establish a practical benchmark and a strong baseline for open-world long-horizon video segmentation.

09.
arXiv (CS.LG) 2026-06-16

How Controlling the Variance can Improve Training Stability of Sparsely Activated DNNs and CNNs

arXiv:2602.05779v2 Announce Type: replace Abstract: The Edge-of-Chaos (EoC) theory developed for the random initialization of deep networks allows more efficient training by both preserving information in the initial outputs of the network and minimising exploding or vanishing gradients through characterisation of the intermediate layers as Gaussian processes. This EoC theory provides formulae for the choice of the initialisation distribution variances of the weights and biases. For activations which are approximately linear around the origin, the EoC theory typically encourages the Gaussian process variance to converge towards zero with increasing depth. Here we consider the less studied setting of highly sparsity inducing activations where a large region of values near the origin are set to zero. In this setting we prove a new phenomenon whereby initialisations leading to larger fixed Gaussian processes are beneficial to training stability. This theory informs a new, yet simple, initialisation strategy that allows training DNNs and CNNs with as large as 90\% sparsity in the hidden layers.

10.
arXiv (quant-ph) 2026-06-11

Emergent mirror symmetry in the optimization of the central-spin quantum battery

arXiv:2606.11557v1 Announce Type: new Abstract: Quantum batteries provide a useful setting for exploring nonequilibrium many-body effects in energy storage. Here we investigate the optimization of a quantum battery based on the central-spin model. We identify two complementary structural indicators associated with the effective charging dynamics: one yields an upper bound on the average charging power, while the other characterizes the buildup of stored energy. We show that these two indicators are jointly optimized at a distinguished initial charger excitation number, which selects a particular Dicke sector of the model. At this common optimal point, the effective charging Hamiltonian becomes exactly mirror symmetric, suggesting mirror symmetry as a useful structural indicator for optimizing quantum batteries. We further show that the corresponding optimal dynamics can be closely approximated by product initial states, in particular by spin coherent states whose excitation-number distribution is centered at the symmetry-selected point. Our results establish a direct connection between charging performance, optimal-state structure, and emergent symmetry in the central-spin quantum battery, and suggest symmetry as a useful organizing principle for efficient charging in interacting many-body quantum systems.

11.
arXiv (CS.AI) 2026-06-17

Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty

arXiv:2606.17312v1 Announce Type: new Abstract: Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently – a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion – measuring how much sampled answers differ – but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness – consistent with settings where multiple plausible solution paths remain competitive – while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

12.
arXiv (quant-ph) 2026-06-11

Invariants of Sequential Circuits and Generalized Non-Abelian Statistics

arXiv:2606.11527v1 Announce Type: cross Abstract: Non-invertible symmetries in quantum many-body systems generally give rise to sequential unitary circuits that move symmetry defects. In this paper, we investigate invariants defined by sequences of such circuits, which move non-invertible defects and generate a Berry phase evaluated on quantum states with defects. We show that this Berry phase generally defines an invariant under local deformations, provided that the sequential circuits preserve the locality of those deformations. This invariant also rules out a short-range-entangled state that preserves the non-invertible symmetry, thereby signaling the 't Hooft anomaly of a non-invertible symmetry purely in terms of unitary operators acting on a state. We then apply this framework to loop excitations in three spatial dimensions and identify a new loop excitation in the (3+1)D $\mathbb{D}_4$ topological order, which we dub a non-Abelian fermionic loop. Using the invariant of sequential circuits, we characterize the statistics of non-Abelian fermionic loops. In addition, we find a new (3+1)D mixed topological order with a single non-Abelian fermionic loop, whose long-range entanglement is protected by an invariant of sequential circuits.

13.
arXiv (quant-ph) 2026-06-24

Rapid Cavity-Based Mid-Circuit Measurement and Feedforward in a Neutral Atom Array

arXiv:2606.24869v1 Announce Type: new Abstract: Measuring part of a quantum system in the midst of its evolution and acting on the result in real time is essential for numerous quantum information protocols. Neutral-atom arrays are a leading platform for quantum information processing, but their mid-circuit measurement-and-feedforward cycle times have remained slow, typically exceeding 1 ms. Here we demonstrate fast mid-circuit measurement and real-time feedforward in an array of atomic qubits coupled to a high-finesse optical cavity. Local light shifts tune individual data qubits out of resonance with the cavity, shielding their coherence, while a near-resonant probe drives a selected qubit whose emission is collected with Purcell enhancement. Mid-circuit measurements of four qubits with sub percent infidelity reduce the coherence of a fifth unmeasured data qubit by less than 2%. We implement real-time feedforward to correct measurement-induced phase shifts and to realize an adaptive circuit for optimal quantum state discrimination and conditional state preparation. Our approach reduces the measurement-and-feedforward cycle time to below 100 $\mu$s and establishes optical cavities as a route to fast control of neutral-atom quantum systems.

14.
arXiv (CS.AI) 2026-06-24

Bitwise Systolic Array Architecture for Runtime-Reconfigurable Multi-precision Quantized Multiplication on Hardware Accelerators

arXiv:2602.23334v2 Announce Type: replace-cross Abstract: Neural network accelerators have been widely applied to edge devices for complex tasks like object tracking, image recognition, etc. Previous works have explored the quantization technologies in related lightweight accelerator designs to reduce hardware resource consumption. However, low precision leads to high accuracy loss in inference. Therefore, mixed-precision quantization becomes an alternative solution by applying different precision in different layers to trade off resource consumption and accuracy. Because regular designs for multiplication on hardware cannot support the precision reconfiguration for a multi-precision Quantized Neural Network (QNN) model in runtime, we propose a runtime reconfigurable multi-precision multi-channel bitwise systolic array design for QNN accelerators. We have implemented and evaluated our work on the Ultra96 FPGA platform. Results show that our work can achieve 1.3185 to 3.5671 times speedup in inferring mixed-precision models and has less critical path delay, supporting a higher clock frequency (250MHz).

15.
arXiv (CS.LG) 2026-06-16

ShipNet: A Geometric Deep Learning Surrogate for Real-Time Ship Hydrodynamics

arXiv:2606.15356v1 Announce Type: cross Abstract: Accurate prediction of hydrodynamic performance is central to ship design, yet high-fidelity computational fluid dynamics remains prohibitively expensive for large-scale parametric exploration. This motivates the development of data-driven surrogate models that provide rapid approximations to hydrodynamic predictions at substantially reduced cost. We present ShipNet, a geometric deep-learning surrogate that predicts both hull-surface pressure distributions and far-field free-surface wave patterns directly from hull geometry and speed. The network employs a regularized dynamic graph convolutional backbone on hull point clouds, with a multi-head decoder for simultaneous near-body pressure and free-surface elevation outputs. Training data consist of 420 inviscid free-surface simulations generated using a potential-flow panel method for two parent yacht hulls, each parameterized into 70 variants and evaluated at three speeds. ShipNet predicts per-point pressure coefficient and two-dimensional wave elevation map using a composite loss that combines point-wise regression and image-structure terms. On a geometry-held-out test set, ShipNet achieves R^2=0.98 for hull pressure and R^2=0.91 for wave fields. Inference requires approximately 0.15s per case, yielding over a 550x speedup relative to the potential-flow solver on conventional hardware. Limitations include the restricted geometry and speed ranges and the inviscid training data, while future work will extend the model to high-fidelity viscous simulations with physics-informed regularization.

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

HyDRA: Hybrid Dynamic Routing Architecture for Heterogeneous LLM Pools

Production LLM deployments increasingly maintain heterogeneous model pools spanning order-of-magnitude cost differences. Existing routers make binary strong-vs-weak decisions and couple learned parameters to specific model identities, requiring retraining whenever the catalog changes. We present HyDRA (Hybrid Dynamic Routing Architecture), a framework that predicts fine-grained, multi-dimensional capability requirements per query and matches them against configuration-defined model profiles via shortfall matching. A ModernBERT encoder with K=4 independent sigmoid heads scores each query along reasoning, code generation, debugging, and tool use; a shortfall-matching algorithm then selects the cheapest model whose capabilities meet the predicted requirements. The deployed predictor runs at 86 ms median CPU inference latency in production, and is fully decoupled from the model catalog – adding or removing models requires only a configuration change, with zero retraining. On SWE-Bench Verified (5-model pool: GPT-5.4-mini, Claude Haiku 4.5, GPT-5.3 Codex, Claude Sonnet 4.6, GPT-5.4), HyDRA's tunable shortfall threshold spans three regimes: peak-quality exceeds the always-strong Claude Sonnet 4.6 baseline (75.4% vs. 74.2% resolution) at 12.9% cost savings; iso-quality matches Sonnet at 54.1% cost savings, a 6x improvement over our prior in-house binary router at 9.1%; aggressive pushes savings to 72.5% for a 3.2-point quality trade. Results generalize across LiveCodeBench, BigCodeBench, and tau-bench. HyDRA is deployed to all users in GitHub Copilot's VS Code Chat auto-mode and – to our knowledge for the first time in the LLM routing literature – demonstrates language-invariant routing across CJK, European, and other script families.

17.
arXiv (CS.LG) 2026-06-15

Geometric Domain Adaptation via Optimal Transport for Linear Regression in R^2

arXiv:2606.14023v1 Announce Type: cross Abstract: Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions. We study a supervised domain adaptation problem where source and target domains are related by a rotation or a translation or a homothety in $\mathbb{R}^2$. We prove that the optimal transport map recovers the underlying map when using a $p-$norm cost with $p \geq 2$. Based on this insight, we develop a method combining $K-$means and optimal transport to estimate the underlying map, enabling adaptation of linear regression models when target data is scarce. Simulations demonstrate improved performance over baseline methods. Rather than relying on highly expressive deep learning architectures, we focus on classical machine learning models to emphasize interpretability and theoretical insight. This perspective allows us to explicitly characterize the role of optimal transport in recovering geometric transformations such as rotations, translations, and homotheties. Our contributions include a theoretical result linking optimal transport and rotations, translations and homothecies in $\mathbb{R}^2$, and a practical method for adaptation in linear regression offering both conceptual clarity and applied value in domain adaptation tasks in this space.

18.
arXiv (CS.CV) 2026-06-11

What Semantics Survive the Connector? Diagnosing VLM-to-DiT Alignment in Video Editing

Flow matching based video generative models have been increasingly relying on prepended Vision-Language Models (VLMs) to handle complex, instruction-based video editing. The prevailing assumption underlying this paradigm is that a connector module can seamlessly align the VLM's rich multi-modal reasoning with the original text embedding space of DiTs. However, we hypothesize that this alignment acts as a severe semantic bottleneck, degrading fine-grained structural variables. Verifying this is challenging, as end-to-end evaluations conflate alignment failures with generation errors, and natural datasets lack disentangled annotations. To rigorously investigate this, we propose a controlled data processing pipeline based on video composition that results in TRACE-Edit, a diagnostic dataset focusing on relation-based editing. Leveraging this dataset, we propose a comprehensive diagnostic protocol to analyze two important designs of meta-query and connector in the existing video editing models. Systematic evaluation of four representative model cases reveals that fine-grained structural semantics can be severely degraded during alignment. Our findings overturn the assumption of lossless semantic transfer, identifying the VLM-to-DiT alignment as a major bottleneck and providing a new diagnostic foundation for future multi-modal alignment architectures.

19.
bioRxiv (Bioinfo) 2026-06-23

Automated Segmentation of Prostatic Gold Fiducial Markers for MR-Only Radiotherapy Planning Using Multi-Modal Consensus Deep Learning

Purpose: To develop and evaluate a multi-model consensus deep learning approach for automated gold fiducial marker (FM) segmentation in T1-weighted prostate MRI. Materials and Methods: In this retrospective study, T1-weighted MRI and CT-derived reference standard segmentations were collected from 127 prostate cancer patients (all male; mean age, 70 years +/- 7 [standard deviation]; age range, 50-88 years; collected between October 2020 and January 2026) who each had three implanted gold FMs. A 3D U-Net was trained on 93 subjects using four random seeds to produce an ensemble. At inference, marker-class probability maps were averaged across models and the top three connected components selected. Performance was evaluated on 34 temporally held-out subjects (9 tuning, 25 test) using marker-level sensitivity and precision with exact (Clopper-Pearson) 95% confidence intervals (CIs). A model count ablation study was performed. The pipeline was deployed for on-scanner processing on Siemens MRI systems via the OpenRecon framework and as a browser-based application using WebAssembly, executing entirely client-side. Results: The four-model consensus achieved 96% (70 of 73) sensitivity and 95% (70 of 74) precision on 25 test subjects, with 29 of 34 (85%) subjects achieving perfect marker detection. Single models had a mean sensitivity of 84% (SD, 9%), improving to 96% with four-model consensus (SD,

20.
arXiv (CS.LG) 2026-06-16

Reinforcement Learning for LLM-based Event Forecasting

arXiv:2606.15917v1 Announce Type: new Abstract: We use Group Relative Policy Optimization (GRPO), a recently devised sample and memory efficient reinforcement learning method, to finetune pretrained LLMs in the range of 1.5B to 14B parameters equipped with the ability to get current information through the use of a Wikipedia revisions tool, or news summaries, to forecast real events beyond the knowledge cutoff of the LLM, as well as problems made to simulate different aspects of the dynamics of that training. We use the results of these experiments to comment on the scaling capability of LLMs for forecasting, as well as classify how judgmental forecasting fits into the verifiable/unverifiable domain taxonomy, considering the impact of the inherent aleatoric uncertainty when forecasting future events (e.g. the roll of a die). As a result of the GRPO training, we manage to bring a 1.5B parameter transformer (Qwen 2.5 1.5B) to forecasting performance superior to Claude Sonnet 3.5 over the same dataset as measured by cross entropy from the market agreed probabilities. We also discuss various dead ends on the path to this result.

21.
arXiv (quant-ph) 2026-06-12

Approximability limits for bounded-degree max-LINSAT and implications for decoded quantum interferometry

arXiv:2606.13570v1 Announce Type: new Abstract: For general max-k-XORSAT with $k \geq 3$, no polynomial-time algorithm can do substantially better than random guessing on worst-case instances unless $\mathsf{P} = \mathsf{NP}$: approximating beyond the random-assignment value of $1/2$ is $\mathsf{NP}$-hard. The picture changes when each variable appears in at most $D$ constraints. In that bounded-degree setting, polynomial-time algorithms can provably beat the random baseline by an additive amount of order $1/\sqrt{D}$. For Boolean instances, this scaling is known to be optimal: the matching hardness result is due to Trevisan, while the corresponding algorithmic guarantee was established by Barak et al. Whether the same holds over general finite fields, and what it implies for quantum algorithms, has not been established. We make this connection explicit and extend the hardness to max-E$k$-LINSAT$(q,r)$ with bounded degree $D$ and over arbitrary finite fields $\mathbb{F}_q$, proving that it is $\mathsf{NP}$-hard to exceed $r/q + \mathcal{O}_{q,r}(1/\sqrt{D})$. These results provide the complexity-theoretic benchmark for the bounded-degree instances targeted by decoded quantum interferometry (DQI), QAOA, and classical heuristics. Any quantum advantage on bounded-degree instances is therefore confined to the constant prefactor. We further show that in the context of DQI and on $(k,D)$-regular instances, this prefactor is sensitive to the nature of the decoder: DQI with classical decoders faces an information-theoretic $1/\sqrt{D \log D}$ barrier that prevents it from matching the hardness scaling, while DQI with quantum decoders is compatible with the $1/\sqrt{D}$ scaling – identifying quantum decoding as the key ingredient for matching the complexity-theoretic scaling with DQI.

22.
arXiv (CS.LG) 2026-06-18

Generalised Eigenvalue Geometry of Semantic Adversarial Attacks

arXiv:2606.19212v1 Announce Type: cross Abstract: Recent empirical work shows that semantically equivalent paraphrases can fool financial sentiment classifiers: although a paraphrase remains close to the original under a strong reference embedding, it may shift the target model's representation enough to change the predicted class. Existing robustness theory either assumes a single-model threat model or focuses mainly on empirical attack algorithms. We develop a continuous local model of semantic paraphrase perturbations that captures this two-model structure. We show that the worst-case local displacement of the target representation, subject to a proxy-model budget, is governed by the largest generalised eigenvalue of a matrix pencil $(A,B)$ constructed from the Jacobians of the two embedding maps. The resulting attackability index $\lambda^*(x)$ is intrinsic to the local paraphrase geometry and the chosen embedders, yields a closed-form prediction-flip condition for affine readouts, and supports conservative population and finite-sample attackability certificates. For uniform control over classes of affine readouts, we derive a distribution-free VC bound for binary attackability indicators and a scale-sensitive margin bound based on an attackability-adjusted margin that subtracts a local geometric penalty from the standard classifier margin. We also connect the continuous theory to discrete paraphrase search, identify an asymmetry between successful and unsuccessful finite searches, and give a covering condition under which the discrete and continuous settings agree. Finally, we propose an empirical verification framework using soft-token relaxations and generated paraphrase sets to assess the local eigenvalue geometry, prediction-flip condition, and finite-search approximation on a deployed financial-text classifier.

23.
arXiv (CS.CL) 2026-06-11

ClawEnvKit: Automatic Environment Generation for Claw-Like Agents

Constructing environments for training and evaluating claw-like agents remains a manual, human-intensive process that does not scale. We argue that what is needed is not just a dataset, but an automated pipeline capable of generating diverse, verified environments on demand. To this end, we introduce ClawEnvKit, an autonomous generation pipeline that instantiates this formalism from natural language descriptions. The pipeline comprises three modules: (1) a parser that extracts structured generation parameters from natural language input; (2) a generator that produces the task specification, tool interface, and scoring configuration; and (3) a validator that enforces feasibility, diversity, structural validity, and internal consistency across the generated environments. Using ClawEnvKit, we construct Auto-ClawEval, the first large-scale benchmark for claw-like agents, comprising 1,040 environments across 24 categories. Empirically, Auto-ClawEval matches or exceeds human-curated environments on coherence and clarity at 13,800x lower cost. Evaluated across 4 model families and 8 agent harness frameworks, we find that harness engineering boosts performance by up to 15.7 percentage points over a bare ReAct baseline, completion remains the primary axis of variation with no model saturating the benchmark, and automated generation enables evaluation at a scale previously infeasible. Beyond static benchmarking, ClawEnvKit enables live evaluation: users describe a desired capability in natural language and obtain a verified environment on demand, turning evaluation into a continuous, user-driven process. The same mechanism serves as an on-demand training environment generator, producing task distributions that adapt to an agent's current weaknesses rather than being bounded by existing user logs.

24.
arXiv (quant-ph) 2026-06-24

Exact log-depth preparation of highly entangled matrix product states

arXiv:2606.24475v1 Announce Type: new Abstract: Preparing matrix product states (MPS) on a quantum device is a key subroutine in many quantum algorithms. The most competitive methods, based on the renormalisation group, prepare translationally invariant MPS of size $L$ and bond dimension $\chi$, up to an error $\varepsilon$, in circuit depth $\tilde O(\chi^{4}\log(L/\varepsilon))$ or $\tilde O(\chi^{6}\log\log(L/\varepsilon))$. We improve multiple aspects of these methods. First, using block-encoded correction maps, whose post-selection succeeds with constant probability, we render the preparation exact without sacrificing the scaling in $L$. Second, through a generalisation of oblivious amplitude amplification to isometries, we reduce the bond-dimension dependence, improving the depth to $\tilde O(\chi^{2}\log L + \chi^{4})$ or $\tilde O(\chi^{2}\log\log L + \chi^{4})$, and even to $\tilde O(\chi^{3}\log L)$ for incoherent preparations. Finally, we extend the framework to non-translationally invariant MPS and prove logarithmic-depth exact preparation for independent and identically distributed random tensor sequences. Confirmed by numerical studies, these results constitute, to the best of our knowledge, the most efficient exact MPS preparation protocols in the relevant parameter regimes.

25.
arXiv (CS.CV) 2026-06-17

HLS-GPT: A Generative Pretrained Transformer (GPT) for Continental-Scale NASA Harmonized Landsat and Sentinel-2 (HLS) Reflectance Reconstruction Across All Bands on Arbitrary Dates

Recent deep learning methods for Landsat and Sentinel-2 reflectance time series reconstruction remain limited by restricted spectral coverage, limited geographic scalability, or patch-based designs with short temporal contexts. We present HLS-GPT, a large-scale generative pretrained Transformer model for reconstructing NASA Harmonized Landsat Sentinel-2 30 m surface reflectance for all bands, any date, and any pixel location. HLS-GPT uses a hierarchical Transformer architecture to handle the different spectral band configurations of Landsat and Sentinel-2 and operates on single-pixel 12-month time series. To capture geographic and seasonal variability, the model was trained with nine years of HLS time series from more than 0.25 million training pixels across the conterminous United States. A random cropping and masking strategy extracts 12-month periods with varying start dates across epochs, masks 50% of valid observations, and trains the model to reconstruct the masked reflectance values from the remaining observations. Evaluation using more than 62,000 independent test pixels shows robust reconstruction under diverse land surface conditions, including complex crop phenology and sparse, irregular observations. Leave-one-observation-out evaluation achieved reconstruction RMSE below 0.026 for all HLS spectral bands, with relative RMSE below 35% for visible bands and below 13% for other bands. Red-edge band errors were comparable to red and near-infrared errors despite the absence of red-edge bands on Landsat. Sensitivity analyses that randomly masked 10% to 90% of test observations showed only modest degradation when 10% to 50% of observations were masked, with all-band RMSE below 0.028. Image reconstruction over nine independent 109 by 109 km CONUS HLS tiles further demonstrates that HLS-GPT outperforms two conventional methods and the NASA-IBM Prithvi model.