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01.
arXiv (quant-ph) 2026-06-11

An Introduction to the Foundations and Interpretations of Quantum Mechanics

arXiv:2603.09818v2 Announce Type: replace Abstract: This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein-Podolsky-Rosen argument, Bell's theorem, and Hardy's paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie-Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.

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

Quantum Dynamics from Lax Pair Theory: A Reconstruction from Spectrum Preservation

arXiv:2606.19664v1 Announce Type: new Abstract: We reconstruct unitary quantum dynamics from a minimal axiomatic foundation built on Hilbert-space observables and isospectral evolution. The only dynamical assumption is that physical time evolution is a continuous one-parameter flow of Hermitian observables that preserves their spectra, i.e. the possible outcomes of measurement. We show that this assumption is already sufficient to force the Lax form of quantum dynamics. The Heisenberg equation, the time-dependent and time-independent Schrödinger equations, conservation laws, and good quantum numbers then follow as theorems rather than postulates. In this formulation, Lax pair theory supplies the missing dynamical bridge between the measurement structure of a Hilbert space and standard quantum evolution: the Hamiltonian is not assumed, but emerges as the generator required for an isospectral observable flow.

03.
arXiv (CS.AI) 2026-06-16

CLoVE: Personalized Federated Learning through Clustering of Loss Vector Embeddings

arXiv:2506.22427v2 Announce Type: replace-cross Abstract: We propose CLoVE (Clustering of Loss Vector Embeddings), a novel algorithm for Clustered Federated Learning (CFL). In CFL, clients are naturally grouped into clusters based on their data distribution. However, identifying these clusters is challenging, as client assignments are unknown. CLoVE utilizes client embeddings derived from model losses on client data, and leverages the insight that clients in the same cluster share similar loss values, while those in different clusters exhibit distinct loss patterns. Based on these embeddings, CLoVE is able to iteratively identify and separate clients from different clusters and optimize cluster-specific models through federated aggregation. Key advantages of CLoVE over existing CFL algorithms are (1) its simplicity, (2) its applicability to both supervised and unsupervised settings, and (3) the fact that it eliminates the need for near-optimal model initialization, which makes it more robust and better suited for real-world applications. We establish theoretical convergence bounds, showing that CLoVE can recover clusters accurately with high probability in a single round and converges exponentially fast to optimal models in a linear setting. Our comprehensive experiments comparing with a variety of both CFL and generic Personalized Federated Learning (PFL) algorithms on different types of datasets and an extensive array of non-IID settings demonstrate that CLoVE achieves highly accurate cluster recovery in just a few rounds of training, along with state-of-the-art model accuracy, across a variety of both supervised and unsupervised PFL tasks.

04.
arXiv (CS.CL) 2026-06-11

TokenRatio: Principled Token-Level Preference Optimization via Ratio Matching

Direct Preference Optimization (DPO) is a widely used RL-free method for aligning language models from pairwise preferences, but it models preferences over full sequences even though generation is driven by per-token decisions. Existing token-level extensions typically decompose a sequence-level Bradley-Terry objective across timesteps, leaving per-prefix (state-wise) optimality implicit. We study how to recover token-level preference optimality using only standard sequence-level pairwise comparisons. We introduce Token-level Bregman Preference Optimization (TBPO), which posits a token-level Bradley-Terry preference model over next-token actions conditioned on the prefix, and derive a Bregman-divergence density-ratio matching objective that generalizes the logistic/DPO loss while preserving the optimal policy induced by the token-level model and maintaining DPO-like simplicity. We introduce two instantiations: TBPO-Q, which explicitly learns a lightweight state baseline, and TBPO-A, which removes the baseline through advantage normalization. Across instruction following, helpfulness/harmlessness, and summarization benchmarks, TBPO improves alignment quality and training stability and increases output diversity relative to strong sequence-level and token-level baselines.

05.
arXiv (CS.LG) 2026-06-12

Enhanced Low-Density Region Exploration in Classifier-Guided Diffusion Models Through Modified Reverse Diffusion Sampling

arXiv:2606.13347v1 Announce Type: new Abstract: Diffusion models have emerged as state-of-the-art generative models for high-fidelity image synthesis, particularly in their classifier-free guided and classifier-guided forms. However, standard classifier guidance concentrates probability mass around high-density class mean, leading to poor coverage of rare samples in the tails of the class-conditional distributions. Recent work on diffusion-based tail sampling mitigates this by training an additional low-density-seeking classifier with a synthetic-vs-real discriminator, at the cost of additional networks and training. In parallel, a number of samplers and distillation techniques accelerate or refine diffusion sampling, but do not explicitly address long-tail coverage. We propose a purely sampling-time, density-aware extension of classifier-guided conditional diffusion model that targets low-density regions without any additional training. We have applied guidance at noisy images not on predicted noise like most diffusion models. Starting from a pretrained conditional diffusion model and classifier on ImageNet, we modify the guided reverse dynamics by steering trajectories toward low-confidence regions via the modified classifier gradient, and at each time step, we also guide the sampling process toward the predicted real image. 1st guidance helps explore low-probability samples, and 2nd guidance helps to generate samples to be close to the real data manifold. The proposed sampler consistently improves ADM model recall at 64x64 resolution while maintaining a comparable FID, and with a 256x256 ADM model, we showed the results visually with different combinations of both guidance. We also showed that standard ADM classifier guidance, combined with predicted real image guidance, helps generate high perceptual quality samples with a 256x256 ADM model on ImageNet.

06.
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.

07.
arXiv (math.PR) 2026-06-15

Uniform-in-time error estimates for McKean-Vlasov SDEs with common noise and stochastic algorithms

arXiv:2606.14170v1 Announce Type: new Abstract: In this work, by construct an asymptotic coupling by reflection, we first explore the uniform-in-time estimate on probability distance for two measure-valued processes induced by a McKean-Vlasov SDE with common noise and an interacting particle system, where the drift terms are dissipative merely in the long distance. As direct applications of this estimate, we establish the uniform-in-time error estimates for the numerical solutions derived via backward/tamed/adaptive Euler-Maruyama methods. Moreover, as another direct application, the uniform-in-time conditional propagation of chaos is quantified.

08.
arXiv (CS.AI) 2026-06-17

Querying an astronomical database using large language models: the ALeRCE text-to-SQL system

arXiv:2606.18108v1 Announce Type: cross Abstract: We develop a text-to-SQL (structured query language) system based on large language models (LLMs) using in-context learning and apply it to the Automatic Learning for the Rapid Classification of Events (ALeRCE) astronomical database. ALeRCE is a community broker for the Zwicky Transient Facility and the Vera C. Rubin Observatory. The system enables users to query the database in natural language (NL) and generates executable SQL queries. To develop and evaluate the system, we constructed a dataset of 110 NL/SQL pairs. We propose a step-by-step generation framework comprising four modules: schema linking, query classification, prompt decomposition, and self-correction. The performance of thirteen LLMs is evaluated using in-context learning and prompt engineering techniques. Text-to-SQL performance is assessed using the perfect-match (PM) rate for row identifiers (e.g., object identifiers) and column identifiers (i.e., column names). The proposed step-by-step framework consistently outperforms a direct-inference baseline, while the self-correction module consistently reduces execution errors. For Claude Opus 4.6, PM performance on row (column) identifiers is high for simple queries, reaching 0.97 (0.94), and decreases with query complexity to 0.44 (0.72) for medium queries and 0.59 (0.49) for hard queries. Among the thirteen evaluated models, the best-performing LLMs for the text-to-SQL task are Claude Opus 4.6, Gemini 2.5 Pro, Gemini 3 Flash, and GPT-5.2-Codex.

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

Double-Helix Vision (DH-V2): A Geometry-Based Visual Sampler for Bandwidth-Constrained Perception

作者:

We present Double-Helix Vision (DH), a geometry-based visual sampler that compresses 2D images into compact 1D signals using paired golden-ratio-inspired spiral trajectories. Rather than processing every pixel uniformly, DH employs two phase-shifted helices (Alpha and Beta, offset by 180 degrees) to sample the image with biologically-inspired foveation: high density at the center, sparse coverage at the periphery. At 4K resolution, DH achieves a 1,433x compression ratio (99.93% reduction) while preserving the geometric structure of the scene. The full perception pipeline – including spatial mapping, temporal collision detection, and intra-frame structural disparity estimation – runs in 0.52 ms at 1080p on CPU-only hardware, with no neural network dependencies. On CIFAR-10 at extreme sampling budgets (K=128 points per helix), DH achieves a +6.03% accuracy gain over uniform random sampling. A JSON-serializable Robotics API is provided, delivering sub-millisecond spatial perception reports in 2.7 KB packets. Code and benchmarks are available under the MIT License.

10.
arXiv (CS.CL) 2026-06-11

Fast Speech Foundation Model Distillation Using Interleaved Stacking

Distilling a large speech foundation model (SFM) into an efficient student model has been successfully applied to low-resource environments. Although distillation reduces inference latency, it requires an additional student model training. However, the training efficiency of SFM distillation remains underexplored. In this work, we explore training acceleration of SFM distillation to speed up model deployment. We examine the potential of stacking, in which the model depth is progressively increased through training until the target model depth is reached. While existing stacking methods improve training speed, they suffer from performance degradation. To handle this limitation, we propose interleaved stacking, a novel stacking method that consistently preserves layer position throughout the stacking process. This property is particularly critical in SFMs, in which each layer encodes distinct layer-specific knowledge. We validate the effectiveness of the proposed method on SUPERB.

11.
arXiv (CS.CL) 2026-06-12

Keep Policy Gradient in Charge: Sibling-Guided Credit Distillation for Long-Horizon Tool-Use Agents

Long-horizon tool-use reinforcement learning can learn from outcome verification, but its trajectory-level advantage is broadcast across many reasoning, API, and answer tokens. Self-distillation promises a denser signal by reusing a policy's own rollouts or a privileged teacher. We show, however, that direct token-level self-distillation can silently destroy tool use: it rehearses teacher behavior without knowing which actions the verifier rewards, so useful skills and harmful shortcuts are amplified together. We introduce Sibling-Guided Credit Distillation (SGCD), which uses distillation for credit assignment rather than as a competing actor loss. Dynamic sampling produces mixed successful and failed sibling rollouts; an external LLM summarizes their contrast into a training-only stepwise credit reference; dense teacher/student divergence drives credit reassignment; and bounded detached credit weights reshape GRPO token advantages. The deployed student sees no external LLM, sibling evidence, or oracle. Across AppWorld and $\tau^3$-airline, SGCD improves over matched GRPO comparators: AppWorld TGC $42.9 \to 45.6$ on test_normal and $24.7 \to 27.0$ on test_challenge, and $\tau^3$-airline pass@1 $0.583 \to 0.602$.

12.
arXiv (CS.AI) 2026-06-17

A Machine-Learned Comorbidity Index

arXiv:2606.17450v1 Announce Type: new Abstract: Traditional comorbidity scores (e.g., Charlson and Elixhauser) are widely used for risk adjustment and patient stratification, but they have two key limitations: (i) they are largely mortality-centric and do not align well with other clinical outcomes, and (ii) their linear, rule-based structure cannot capture nonlinear, outcome-specific risk relationships. We propose a Machine-Learned Comorbidity Index (MLCI) that maps diagnosis codes to a single scalar by maximizing the normalized Hilbert-Schmidt Independence Criterion (nHSIC) between the learned score and multiple clinical outcomes. MLCI captures nonlinear risk-outcome dependence and is supported by a theory that characterizes when a unified, informative admission-level ordering can be achieved across outcomes. Empirical results on multiple benchmark electronic health record (EHR) datasets show that MLCI outperforms strong baselines across multiple evaluation metrics.

14.
bioRxiv (Bioinfo) 2026-06-13

Testing the reliability of AI-generated protein structures

Although AlphaFold2 and its competitors have demonstrated remarkable abilities to predict protein structure, more work is needed to explore the limitations of these methods. Here we investigated the reliability of AlphaFold2 and ColabFold by creating a set of realistic but false protein sequences, using ColabFold to predict their structure, and then asking how often the program produces a high-scoring structure for a sequence that does not represent a protein. We determined that AlphaFold2 has a very small but non-zero false positive rate, estimated here at approximately 1 in 435 if one uses a threshold pLDDT score of 70 to define positive predictions. We also discovered, serendipitously, that some high-scoring sequences in the human genome were not false positives, but instead were previously unknown and un-annotated pseudogenes. These latter findings indicate that some well-established human annotations of protein-coding genes may have incorrectly extended the 5-prime untranslated regions too far. They also suggest that the false positive rate of AlphaFold2 is low enough that almost any high-scoring structure, even in a noncoding region, is worthy of further investigation.

15.
arXiv (CS.CL) 2026-06-12

SENTINEL: Failure-Driven Reinforcement Learning for Training Tool-Using Language Model Agents

Language model agents are increasingly effective in solving realistic tasks through multi-turn tool use. However, training reliable tool-using agents remains challenging in practice. While reinforcement learning provides an on-policy paradigm for improving agents from their own environment interactions, its effectiveness depends heavily on the training task distribution. When tasks are fixed before training, the task distribution can become increasingly mismatched with the policy's evolving capabilities, causing many rollouts to be spent on uninformative tasks. We propose SENTINEL, a failure-driven reinforcement learning framework that turns the Solver's rollout failures into targeted training tasks. SENTINEL follows a Controller–Proposer–Solver loop: the Controller analyzes failed trajectories and summarizes recurring error patterns, the Proposer generates executable tasks that stress these weaknesses, and the Solver is trained on the targeted tasks. On Tau2-Bench Retail with Qwen3-4B-Thinking-2507, SENTINEL improves Pass\^{}1 from 66.4 to 74.9 and outperforms RL on general synthetic tasks across Pass\^{}k metrics. These results demonstrate that model failures provide an effective and scalable source of targeted training signal for improving tool-using language model agents.

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

Entity Binding Failures in Speech LLM Reasoning: Diagnosis and Chain-of-Thought Intervention

Speech Large Language Models (SLLMs) underperform their text counterparts on complex reasoning. We reveal that this gap is not a uniform cognitive deficit. Evaluating two architecturally diverse SLLMs, we show speech-to-text (S2T) matches or exceeds text-to-text (T2T) on spatial, syntactic, and factual tasks. Yet on logical tasks requiring entity tracking, S2T accuracy collapses to chance. We diagnose this as an entity binding failure: continuous speech features blur precise entity-property associations during implicit reasoning. To validate this diagnosis, we introduce Entity-Aware Chain-of-Thought (EA-CoT), a lightweight inference-time intervention forcing SLLMs to enumerate entities and bind them to claims before reasoning. EA-CoT bridges the gap, even when spoken names are misrecognized, yielding up to a 24.4 percentage-point accuracy gain. Ablations confirm the gains stem from explicit semantic binding, reframing the gap as an elicitation failure rather than a missing capability.

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

Federated Causal Inference from Multi-Site Observational Data via Propensity Score Aggregation

arXiv:2505.17961v4 Announce Type: replace-cross Abstract: Causal inference typically assumes centralized access to individual-level data. Yet, in practice, data are often decentralized across multiple sites, making centralization infeasible due to privacy, logistical, or legal constraints. We address this problem by estimating the Average Treatment Effect (ATE) from decentralized observational data via a Federated Learning (FL) approach, allowing inference through the exchange of aggregate statistics rather than individual-level data. We propose a novel method to estimate propensity scores via a federated weighted average of local scores using Membership Weights (MW), defined as probabilities of site membership conditional on covariates. MW can be flexibly estimated with parametric or non-parametric classification models using standard FL algorithms. The resulting propensity scores are used to construct Federated Inverse Propensity Weighting (Fed-IPW) and Augmented IPW (Fed-AIPW) estimators. In contrast to meta-analysis methods, which fail when any site violates positivity, our approach exploits heterogeneity in treatment assignment across sites to improve overlap. We show that Fed-IPW and Fed-AIPW perform well under site-level heterogeneity in sample sizes, treatment mechanisms, and covariate distributions. Theoretical analysis and experiments on simulated and real-world data demonstrate clear advantages over meta-analysis and related approaches.

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

GRASP: Gradient-Aligned Sequential Parameter Transfer for Memory-Efficient Multi-Source Learning

arXiv:2606.14900v1 Announce Type: new Abstract: Multi-source transfer learning faces a fundamental scalability bottleneck: existing approaches require either loading all K source models into memory simultaneously during parameter fusion, requiring O(K) memory, or deploying all models at inference time, making production deployment infeasible. We propose GRASP (Gradient-Aligned Sequential Parameter Transfer), which achieves superior knowledge integration while maintaining O(1) memory consumption through three key innovations: (1) sequential processing that merges one source at a time into an evolving target model, (2) parameter-wise gradient alignment that selectively transfers only parameters whose optimization directions align with the target domain, avoiding negative transfer, and (3) iterative fine-tuning that adapts transferred knowledge before integrating the next source. Extensive experiments across three continual learning benchmarks (Yearbook, CLEAR-10, CLEAR-100) spanning 10 to 108-year temporal distribution shifts and four architectures (1.3M to 25.6M parameters) demonstrate that GRASP achieves 93.5% mean accuracy over all datasets and architectures compared to ensemble method's 71.7% accuracy while requiring only constant memory versus K models for standard multi-source fusion. Critically, GRASP's sequential previously merged models and scales to arbitrarily many sources without memory growth, making it uniquely suitable for resource-constrained deployment and continually evolving source domains.

19.
arXiv (CS.AI) 2026-06-17

Model Validation of Agentic AI Systems: A POMDP-Based Framework for Belief-State, Forecast, and Policy Validation

arXiv:2606.17383v1 Announce Type: cross Abstract: Agentic artificial intelligence systems introduce a new class of model risk. Unlike traditional predictive models, autonomous agents continuously acquire information, form beliefs regarding latent states of the environment, generate forecasts, select actions, and adapt their behavior over time. Existing validation methodologies focus primarily on predictive accuracy and therefore provide limited insight into the quality of the underlying decision process. This paper proposes a model validation framework for agentic AI based on Partially Observable Markov Decision Processes (POMDPs). The framework decomposes autonomous decision making into information, beliefs, forecasts, actions, and utility, allowing each component to be validated independently. Large language models (LLMs) are formalized as approximate Bayesian filtering operators, and a model-risk taxonomy is developed encompassing state-space, filtering, forecast, policy, utility-specification, and parameter risks. The model risk validation methodology is demonstrated through a portfolio-management case study in which an agent infers latent market regimes from market and macroeconomic information, generates belief-conditioned forecasts, and constructs portfolios using a Black–Litterman framework. Empirical validation combines performance analysis, belief calibration diagnostics, coverage tests, ablation studies, and parameter-sensitivity analysis. The results indicate that latent-state inference contributes independently to decision quality and that the principal conclusions remain robust across a broad range of parameter values. The principal contribution of the paper is a practical framework for extending established model risk management concepts to autonomous AI systems and providing a rigorous foundation for their validation, governance, and monitoring.

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

Task-guided cross-subject latent alignment: a multi-encoder-decoder VAE

arXiv:2606.15989v1 Announce Type: cross Abstract: Aligning neural activity across subjects offers the promise of discovering shared computational principles and generalizable decoders. However, traditional alignment methods require shared stimuli across subjects, a constraint that limits applicability to naturalistic paradigms with limited or non-overlapping data. We introduce a Multi-Encoder-Decoder Variational Autoencoder (MED-VAE) that achieves cross-subject alignment without shared stimuli by anchoring representations to a common scaffold provided by a pretrained ANN. Using the Natural Scenes Dataset, we show that MED-VAE creates common latent spaces with superior semantic organisation, achieving higher cross-subject alignment than common methods while maintaining robust generalisation to held-out stimuli where traditional methods degrade. Reconstructing from these common spaces back to each subject's original neural space, MED-VAE preserves equal stimulus-driven signal in its cross-subject latent space. Finally, we show that this superior alignment directly enables cross-subject neural prediction, as demonstrated via cross-subject image decoding. In summary, we introduce a framework to identify generalisable common subspaces for cross-subject predictions and downstream tasks, demonstrated here for visual cortex responses to static images.

21.
arXiv (CS.LG) 2026-06-16

Bayesian Tensor Decomposition with Diffusion Model Prior

arXiv:2606.03212v2 Announce Type: replace Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.

22.
arXiv (quant-ph) 2026-06-12

Representation-Induced Symmetry Trapping in Adaptive Variational Quantum Simulations of Multi-Reference Topologies

arXiv:2606.13387v1 Announce Type: new Abstract: Evaluating the trainability of adaptive quantum chemistry algorithms under multi-reference static correlation requires understanding how representation topologies intertwine with molecular geometry. We systematically expose a deep physical dependence on point-group symmetry by evaluating a spin-conserved SUSD operator pool across highly stretched configurations (2 x Re) of asymmetric LiH, symmetric BeH2, and asymmetric H2O. Under asymmetric distortions, the non-local mapping constraints of the Bravyi-Kitaev transformation create an optimization trapping effect–an encodement-locked manifestation of the broader barren plateau crisis. Crucially, by comparing these to the symmetrical stretching baseline of BeH2, we demonstrate that the preservation of point-group symmetry structurally protects the optimization landscape, proving that ansatz symmetry restrictions are necessary but insufficient without accounting for the underlying fermion-to-qubit representation. While current methods rely on numerical pruning to throttle pool sizes, our structural approach establishes that the mapping representation remains a critical factor in maintaining landscape trainability. Furthermore, exploiting structural overlap within our pool, we introduce a covariance-driven, adaptive shot-allocation filter. Diverging from static energy-variance minimization frameworks, our allocation engine operates as a dynamic runtime diagnostic tool. By continuously monitoring the gradient precision threshold epsilon, it aggressively prunes dead symmetry channels and triggers an automated circuit-termination sequence upon detecting representation-induced flat-lined states (dE/dtheta approx 0). This integration of algebraic measurement reuse with topology-aware statistical filtering provides a promising, resource-efficient strategy for executing deep variational algorithms on early fault-tolerant architectures.

23.
arXiv (quant-ph) 2026-06-11

Enhancing Many-Body Chaos via Entropy Injection from Environment

arXiv:2606.11784v1 Announce Type: new Abstract: In closed quantum systems, local information spreads throughout the entire system and becomes highly complex under unitary evolution. In contrast, when the system is embedded in an environment, system-environment coupling can transfer information from the system into the environment, thereby reducing the rate of complexity growth within the system. This leads to the environment-induced scrambling transition established in previous works. In this work, we identify entropy injection from the environment as a different physical process that instead enhances many-body chaos. Our setup consists of coupling a system that is already in equilibrium with one environment to another environment, which serves as an entropy reservoir and drives the system into a non-equilibrium state. When entropy flows into the system through either heat transfer or particle transfer, the effective Hilbert space explored by the system enlarges, a mechanism that can enhance many-body chaos. We explicitly demonstrate this idea by constructing a solvable complex Brownian SYK model, in which both the relaxation toward the steady state and the steady-state quantum Lyapunov exponent can be computed analytically. Our results provide a controllable mechanism for tuning quantum scrambling through entropy flow in quantum many-body systems coupled to environments.

24.
arXiv (CS.LG) 2026-06-18

On the Residual Scaling of Looped Transformers: Stability and Transferability

arXiv:2606.18524v1 Announce Type: new Abstract: Looped (weight-tied) Transformers apply a shared residual block $N$ times ($h \leftarrow h + \varepsilon\,f(h)$, same $f$ at each step), increasing effective depth without adding parameters. Prior depth-scaling analyses prescribe $\varepsilon = 1/\!\sqrt{L}$ for depth-$L$ residual networks. We show that this is insufficient for looped architectures: weight sharing makes residual updates correlated across iterations, requiring the stronger scaling $\varepsilon = 1/N$. For multi-layer blocks ($L$ unique layers looped $N$ times), we derive a factored parameterization $\varepsilon = \lambda/(N\!\sqrt{L})$ that separates the two sources of growth: $1/N$ controls the within-layer loop correlation, and $1/\!\sqrt{L}$ controls the across-layer variance. A key consequence is that the optimal learning rate depends only on the number of unique layers $L$, not on the loop count $N$, enabling direct hyperparameter transfer from small to large $N$ without retuning. Experiments on looped Transformers confirm that $1/N$ scaling improves trainability and yields better loss than $1/\!\sqrt{N}$ scaling across loop counts.