arXiv:2607.18128v1 Announce Type: cross
Abstract: Entropy regularization smooths equilibrium policies in time-inconsistent stochastic control. At low temperature, the same Gibbs response can strongly amplify errors in learned rewards and dynamics. We show that the derivative of an exploratory equilibrium is governed by a backward Volterra-parabolic resolvent. Along an aligned positive mode, a lower bound has the same exponential order. A block decomposition identifies the source of the amplification: causal paths contribute powers of 1/tau, whereas a positive feedback cycle can produce exponential growth.
At fixed temperature, a local equilibrium branch is twice differentiable with respect to finite-dimensional model parameters, which yields a function-valued delta method. A bounded uniformly elliptic diffusion realizes this path-cycle distinction in every finite dimension. Closing one positive cycle changes the root-n linear-response boundary from a power law to order 1/log n; along the cyclic Perron mode, right-endpoint discretization is relatively consistent exactly when N tau^2 -> infinity. An affine model also gives an exact nonlinear transition at the Lambert-W temperature beta T / W(beta T sqrt(n)). Numerical calculations illustrate these rates.
Science Journals
arXiv:2607.16419v1 Announce Type: cross
Abstract: We demonstrate a novel method for remote open-path Fourier-transform infrared spectroscopy with undetected photons. Similar to previous quantum spectroscopy works, a mid-infrared spectrum is reconstructed by detecting a near-infrared radiation only, thus bypassing important limitations of infrared detectors. Our study however relies on the co-propagation of the photon-pair and the pump-laser over the same optical path, which allows the probing of the open atmosphere over long distances. By sending the photons over unprecedented distances of up-to 43.4m in the outdoor atmosphere, we were able to detect butane released in the open-path, as well as natural atmospheric methane, thus demonstrating the first use of infrared spectroscopy with undetected photons for atmospheric measurements.
arXiv:2406.06629v2 Announce Type: replace
Abstract: This survey examines key advancements in designing features to represent optimization problem instances, algorithm instances, and their interactions within the context of single-objective continuous black-box optimization. These features support machine learning tasks such as algorithm selection, algorithm configuration, and problem classification, and they are also used to evaluate the complementarity of benchmark problem sets. We provide a comprehensive overview of problem landscape features, algorithm features, high-level problem-algorithm interaction features, and trajectory features, including the latest works from the past five years. We also point out limitations of the current state-of-the-art and suggest directions for future research.
arXiv:2503.00163v2 Announce Type: replace
Abstract: The study of collisionless shocks and their role in cosmic ray acceleration has gained importance through observations and simulations, driving interest in reproducing these conditions in laboratory experiments using high-power lasers. In this work, we examine the role of three-dimensional (3D) effects in ion acceleration in quasi-perpendicular shocks under laboratory-relevant conditions. Using hybrid particle-in-cell simulations (kinetic ions and fluid electrons), we explore how the Alfv\'enic and sonic Mach numbers, along with plasma beta, influence ion energization, unlocked only in 3D, and establish scaling criteria for when conducting 3D simulations is necessary. Our results show that efficient ion acceleration requires Alfv\'enic Mach numbers $\geq 25$ and sonic Mach numbers $\geq 13$, with plasma-$\beta \leq 5$. We theoretically found that, while 2D simulations suffice for current laboratory-accessible shock conditions, 3D effects become crucial for shock velocities exceeding 1000 km/s and experiments sustaining the shock for at least 10 ns. We surveyed previous laboratory experiments on collisionless shocks and found that 3D effects are unimportant under those conditions, implying that 1D and 2D simulations should be enough to model the accelerated ion spectra. However, we do find that the same experiments are realistically close to accessing the regime relevant to 3D effects, an exciting prospect for future laboratory efforts. We propose modifications to past experimental configurations to optimize and control 3D effects on ion acceleration. These proposed experiments could be used to benchmark plasma astrophysics kinetic codes and/or employed as controllable sources of energetic particles.
arXiv:2607.17440v1 Announce Type: cross
Abstract: Models of unification predict additional $Z'$ boson, which contributes to parity non-conservation (PNC) in atoms. If $Z'$ boson is light, ratio of $Z'$ boson contribution to the Standard Model $Z$ boson contribution to atomic PNC increases with decreasing nuclear charge $Z$ faster than $1/Z^2$. This motivated our previous study of PNC in hydrogen and deuterium proportional to the weak interaction matrix elements $<s|W|p> $. An enormous additional relative enhancement appears in the matrix elements between higher waves, such as $<p_{1/2,3/2} | W | d_{3/2,5/2}> $, since $p_{3/2}$ and $d_{3/2,5/2}$ wave functions vanish at $r \to 0$, suppressing matrix elements of the contact $Z$ boson mediated contact electron-nucleus interaction. Measurements of $<p_{1/2,3/2} | W | d_{3/2,5/2}> $ will simplify disentanglement of the $Z'$ contribution from the Standard Model background.
arXiv:2607.18215v1 Announce Type: cross
Abstract: Non-Abelian gauge fields play a key role in describing the behavior of particles whose motion is coupled to internal degrees of freedom, such as their spin. Here, we experimentally realize a tuneable non-Abelian gauge field in an active mechanical lattice by using pairs of oscillators to encode a local pseudo-spin for each site, with inter-site spin-dependent couplings engineered via real-time measurement and feedback. We experimentally extract Wilson-loop observables in our set-up and hence demonstrate that we can create a genuinely non-Abelian gauge field. We then exploit the controllability of our mechanical lattice to engineer non-reciprocal hoppings to explore non-Hermitian non-Abelian gauge potentials. For a two-dimensional (2D) lattice, we demonstrate that the non-Hermiticity can manifest in direction-dependent Wilson loops for a single plaquette, while for a one-dimensional (1D) system, we show that a non-Abelian gauge potential can switch the localization of non-Hermitian skin modes between opposite ends of a chain. Our work establishes active mechanical lattices as a flexible and programmable platform for probing non-Abelian gauge fields and exploring their interplay with non-Hermitian dynamics.
arXiv:2607.17647v1 Announce Type: cross
Abstract: Superradiant emission from long-lived excited states of an atomic ensemble confined in an optical cavity constitutes a practical source of light with narrow linewidth. In the pulsed regime, however, superradiance implies rapid emission and a broadening of the spectrum. Recent experiments have demonstrated constructive and destructive interference of superradiant emission by different strontium atomic transitions. In this article, we show that by modulating the atomic transition frequencies with a magnetic field, it is possible to control the release of the atomic excitation energy as a prolonged pulse or a train of superradiant pulses. By simulations, we show that heterodyne detection of the prolonged superradiance shows extremely sharp spectral features, which leads to significantly reduced frequency uncertainty and fluctuation.
arXiv:2103.06611v2 Announce Type: replace
Abstract: With the mass deployment of computing-intensive applications and delay-sensitive applications on end devices, only adequate computing resources can meet differentiated services' delay requirements. By offloading tasks to cloud servers or edge servers, computation offloading can alleviate computing and storage limitations and reduce delay and energy consumption. However, few of the existing offloading schemes take into consideration the cloud-edge collaboration and the constraint of energy consumption and task dependency. This paper builds a collaborative computation offloading model in cloud and edge computing and formulates a multi-objective optimization problem. Constructed by fusing optimal transport and Policy-Based RL, we propose an Optimal-Transport-Based RL approach to resolve the offloading problem and make the optimal offloading decision for minimizing the overall cost of delay and energy consumption. Simulation results show that the proposed approach can effectively reduce the cost and significantly outperforms existing optimization solutions.
arXiv:2503.08245v4 Announce Type: replace
Abstract: In mixed graphs, there are both directed and bidirected edges. An extension of acyclicity to this mixed-graph setting is known as maximally ancestral graphs. This extension is of considerable interest in causal learning in the presence of confounders. There, directed edges represent a clear direction of causality, while bidirected edges represent confounding.
We propose a branch-and-cut algorithm for learning maximally ancestral graphs using a formulation as a mixed-integer quadratic program. Empirically, our method achieves comparable or improved reconstruction quality while requiring an order of magnitude fewer samples than state-of-the-art approaches.
arXiv:2607.16225v1 Announce Type: cross
Abstract: Brain-Computer Interfaces (BCIs) face a severe calibration bottleneck due to cross-subject spatial covariance shifts and physiological artifacts. To enable zero-calibration BCI, a deep learning pipeline was engineered combining Per-Session Independent Component Analysis, Riemannian Euclidean Alignment, and EEGNet stabilized by Stochastic Weight Averaging (SWA). Evaluated on the strict MOABB BNCI2014-001 benchmark, the proposed architecture successfully isolates true sensorimotor rhythms. For the primary case study (Subject 1), a clinically robust SWA stable accuracy of 90.97% (AUC: 0.976, Cohen's $\kappa$: 0.819) was achieved. Furthermore, expanded 9-fold Leave-One-Subject-Out (LOSO) cross-validation yielded a globally stable mean accuracy of 74.31%, proving hardware-agnostic zero-shot efficacy for binary motor imagery.
arXiv:2607.16875v1 Announce Type: cross
Abstract: We introduce the vehicle routing problem with stochastic demands and outsourcing options (VRP-SDO), in which a logistics service provider partitions customer requests into customers outsourced to a common carrier and customers committed to its fixed fleet. The latter induces a vehicle routing problem with stochastic demands (VRP-SD), solved dynamically. Demands are revealed upon visit; residual demand may be served by other vehicles or after restocking at the depot. Work beyond the regular shift incurs overtime costs, and the unit outsourcing cost decreases with the expected outsourced demand. The objective is to minimize expected travel, overtime, and outsourcing costs. We propose an iterative two-level methodology whose first level partitions customers into committed and outsourced subsets, while the second level estimates the expected VRP-SD routing cost. To avoid solving this problem from scratch at every iteration, we learn an offline routing policy that estimates costs almost instantly for any committed subset. An iterated local search establishes the first-level partitions. We formulate the second level as a Markov decision process and solve it with a deep Q-network whose state is represented by a graph attention network aggregating customer and vehicle information by relevance to the acting vehicle. Trained offline on instances with variable customer cardinality and locations, the policy applies to any daily customer realization; online fine-tuning improves the cost approximation. Experiments show that our policy reduces routing costs by 19.6% relative to a state-of-the-art method and by at least 29.6% over classical heuristics. Our overall algorithm saves 13.7% on average over the version without the attention-based representation and generates high-quality decisions within minutes, whereas benchmarks without an offline-trained estimator require over an hour.
arXiv:2503.01701v2 Announce Type: replace
Abstract: Most microeconomic models of interest involve optimizing a piecewise linear function. These include contract design in hidden-action principal-agent problems, selling an item in posted-price auctions, and bidding in first-price auctions. When the relevant model parameters are unknown and determined by some (unknown) probability distributions, the problem becomes learning how to optimize an unknown and stochastic piecewise linear reward function. Such a problem is usually framed within an online learning framework, where the decision-maker (learner) seeks to minimize the regret of not knowing an optimal decision in hindsight. This paper introduces a general online learning framework that offers a unified approach to tackle regret minimization for piecewise linear rewards, under a suitable monotonicity assumption commonly satisfied by microeconomic models. We design a learning algorithm that attains a regret of $\widetilde{O}(\sqrt{nT})$, where $n$ is the number of ``pieces'' of the reward function and $T$ is the number of rounds. This result is tight when $n$ is \emph{small} relative to $T$, specifically when $n \leq T^{1/3}$. Our algorithm solves two open problems in the literature on learning in microeconomic settings. First, it shows that the $\widetilde{O}(T^{2/3})$ regret bound obtained by Zhu et al. [Zhu+23] for learning optimal linear contracts in hidden-action principal-agent problems is not tight when the number of agent's actions is small relative to $T$. Second, our algorithm demonstrates that, in the problem of learning to set prices in posted-price auctions, it is possible to attain suitable (and desirable) instance-independent regret bounds, addressing an open problem posed by Cesa-Bianchi et al. [CBCP19].
arXiv:2607.18139v1 Announce Type: cross
Abstract: For four agents with nonnegative additive valuations, a complete 1-out-of-5 maximin-share allocation always exists, improving the previous 1-out-of-6 guarantee. Together with known exact-MMS counterexamples, this completely characterizes the four-agent case: the guarantee holds exactly for $d\geq5$. The main technical contribution is a balanced-residual partition lemma: removing rejected bundles with one of the four highest-ranked goods apiece leaves a remainder that still admits the required number of unit-valued balanced bundles. In its central $2+2$ case, three unit bundles repair two pairs of colliding high-valued goods. The theorem is machine-checked in Lean 4.
arXiv:2607.17201v1 Announce Type: cross
Abstract: In this work we study the Best Policy Identification (BPI) problem in online, tabular Reinforcement Learning. This is an active sequential hypothesis testing problem in which the learner's objective is to identify an optimal policy in a Markov Decision Process (MDP) with high confidence, while minimizing the expected sample complexity to do so. We consider an online setting with deterministic rewards, where the agent must strategically navigate through the MDP in order to effectively explore. Previous works in the literature have provided asymptotically optimal methods for BPI, such as the Navigate and Stop (NaS) algorithm and its variants, however existing analysis remains asymptotic. In this work, we fill that gap by providing the first non-asymptotic sample complexity guarantees for NaS, showing that its sample complexity depends not only on the characteristic time, but also on the connectivity of the underlying MDP, the curvature of the optimal characteristic time, and other instance-dependent quantities. We identify these additional attributes and make explicit their contributions to the overall sample complexity.
arXiv:2607.17086v1 Announce Type: cross
Abstract: Any viable interpretation of quantum theory needs to account for the Born rule, from which the theory gets its probabilistic empirical predictions. In this paper, we give an overview of possible approaches to this problem in the context of the Many Worlds interpretation. We argue that, for structural reasons, none of them can possibly succeed. More precisely, we argue that the Many Worlds interpretation must obtain the Born rule by proceeding either axiomatically, deductively, or inductively, and that all three of these approaches run into general, fundamental obstructions.
arXiv:2502.08829v2 Announce Type: replace
Abstract: Federated learning (FL) with non-IID data often degrades client performance below local training baselines. Partial FL addresses this by federating only early layers that learn transferable features, but existing methods rely on ad-hoc, architecture-specific heuristics. We first conduct a systematic analysis of layer-wise generalization dynamics in FL, revealing an early-emerging transition between generalizable (safe-to-federate) and task-specific (should-remain-local) layers. Building on this, we introduce Principled Layer-wise Federated Learning (PLayer-FL), which aims to deliver the benefits of federation more robustly. PLayer-FL computes a novel federation-sensitivity metric efficiently after a single training epoch to choose the optimal split point for a given task. Inspired by model pruning, the metric quantifies each layer's robustness to aggregation and highlights where federation shifts from beneficial to detrimental. We show that this metric correlates strongly with established generalization measures across diverse architectures. Crucially, experiments demonstrate that PLayer-FL achieves consistently competitive performance across a wide range of tasks while distributing gains more equitably and reducing client-side regressions relative to baselines.
arXiv:2607.17343v1 Announce Type: cross
Abstract: For a signing $\sigma$ of a $d$-regular graph, the spectrum of $A_\sigma$ depends only on the signs of cycles. We study the affine $\mathbb F_2$ family of signings making every short even cycle unbalanced, and show that averaging over it converts the sign problem of the Bilu-Linial conjecture into a counting problem: a master identity expresses the family-averaged trace as a parity-weighted sum over wrap classes confined to the span $W$ of the constraint cycles, and the family-averaged Ihara $L$-function diagonalizes so that every prime whose parity escapes $W$ contributes the Ramanujan rate $\sqrt{d-1}$ automatically. Uniform averaging over all signings, by contrast, provably cannot certify a spectral radius below the Kesten profile. We prove matched upper and lower bounds for the confined walk counts, a doubling injection from below, and from above an ear-decomposition encoding in which the number of fresh runs of a non-backtracking walk equals the cycle rank of its support, combined with a window lemma for bicycle-free graphs and a rank bound via the Moore bound for irregular graphs. Consequences include $\varepsilon$-versions of the Bilu-Linial conjecture: every $d$-regular graph that is subcritical at scale $\log n$, and every $d$-regular graph bicycle-free at radius $C\log\log n/\delta$, admits a signing in the parity family with $\rho(A_\sigma)\le2\sqrt{d-1}(1+C\delta\log(1/\delta))(1+o(1))$. We further identify the necessary hypotheses exactly ($K_d$-trapping; tree-burst gadgets), give an exact certificate on the hypercube, and record a decisive obstruction to two-sided interlacing: $\mathbb E_\sigma\det(xI-A_\sigma^2)$ is not real-rooted, already for the quadrilateral, where it equals $(x^2-4x+2)^2+4$.
arXiv:2607.17350v1 Announce Type: cross
Abstract: We present a black box algorithm that constructs standard generators for the Suzuki groups $Sz(q)$, where $q = 2^{2m+1}$ for some $m > 0$. The algorithm is one-sided Monte Carlo, with no false positives. We also present a black box algorithm that performs constructive membership testing in $Sz(q)$, and writes an element as a straight line program in the standard generators. Finally, we give a presentation for $Sz(q)$ that is efficient to verify. The algorithms have been implemented in the computer algebra system Magma.
arXiv:2407.04900v2 Announce Type: replace
Abstract: Numerous existing studies have examined the performance of Sample Average Approximation (SAA) in the fundamental newsvendor problem. Despite these advances, critical gaps remain in two aspects. First, existing works focus on the linear-cost newsvendor problem and heavily rely on the quantile expression of the optimal solution. As a result, their analytical methods limit generalizability to more general inventory problems, where the optimal solution is not a quantile of the demand distribution. Second, even within the linear-cost setting, notable gaps exist between the state-of-the-art regret lower bound and upper bound for SAA under various conditions.
In this paper, we generalize the structure of the newsvendor problem to generic convexity conditions and provide a unified regret analysis of SAA for general sequential stochastic optimization problems. Our approach provides further insights to a broader range of data-driven inventory problems, improves both the upper and lower regret bounds, and establishes the regret rate optimality of SAA. Our lower bound identifies the performance limit achievable by any policy for sequential stochastic optimization and inventory management problems, offering important guidance for future policy design in this area. Moreover, in empirical studies, SAA's performance is frequently used as a benchmark for evaluating new algorithms. The regret rate optimality result provides strong support for its role in assessing other data-driven methods, benefiting both practitioners and researchers. Our new analysis techniques enrich the analysis tools for regret upper and lower bounds for data-driven decision-making problems and other general stochastic optimization problems.
arXiv:2509.02522v3 Announce Type: replace
Abstract: Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming, however existing RLVR methods often suffer from sparse reward signals and unstable policy gradient updates inherent to RL-based approaches. To address the challenges, we propose PACS, a novel RLVR framework that achieves imPlicit Actor Critic coupling via a Supervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while providing more stable and efficient training. Extensive experiments demonstrate that PACS significantly outperforms strong open-source models and RLVR baselines, yielding substantial average gains of +8.26% (4B) and +9.57% (8B) over base models offering a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.
arXiv:2607.16778v1 Announce Type: cross
Abstract: Treewidth is the standard measure for how ``tree-like'' a graph is. This paper studies how the treewidth of a product graph depends on the treewidth of its factors. Kozawa, Otachi, and Yamazaki [2014] and Hickingbotham and Wood [2025] independently showed that $\text{tw}(G\boxtimes H)\geq (\text{tw}(G)+1)\text{had}(H)-1$ for all graphs $G$ and $H$, where $\text{had}(H)$ is the Hadwiger number of $H$. We improve this bound to $\text{tw}(G\boxtimes H)\geq (\text{tw}(G)+1)(\text{tw}(H)+1)-1$, thereby solving an open problem of Hickingbotham and Wood. We also prove analogous product inequalities for pathwidth, Cartesian products, and strict bramble number, which is a parameter that is tied to treewidth. As an application of our results, we show that products of expanders have large subgraphs that are expanders.
arXiv:2607.16869v1 Announce Type: cross
Abstract: Algebra and RANGE global optimization play complementary, explicitly separated roles in identifying measurement structure beyond orbital rotations. In the fixed (1,1)-particle sector of two spatial orbitals per spin, algebra proves that one particle-number-preserving orbital-rotation context contributes a rank-one two-body correlation block $T$: an observable needs at least $\mathrm{rank}\,T$ such contexts, and its best $K$-context correlation-block approximation is exactly the Eckart-Young singular-value tail, attained by the truncated SVD. A continuous RANGE search over the physical rotation angles independently corroborates this exact trade-off. A Bell-diagonal, Heisenberg-type witness has correlation rank three: it needs at least three orbital-rotation contexts, while one explicit physical Clifford circuit measures its commuting Pauli representatives. For spin-conserving Jordan-Wigner molecular Hamiltonians we also prove the parity ceiling $r_X \le 2(N-1)$ for any Pauli subset, tight even within commuting subsets; $X$-rank is a routing diagnostic, and the strict separation is carried by the correlation-rank theorem. The discrete mode of RANGE locates high-$X$-rank commuting families across molecular and production f-element Hamiltonians, finding ceiling-saturating witnesses for CH4 and NdO; values are best found unless a proved ceiling is attained. Applying the companion certificate framework, enlarging product settings by fully commuting, Clifford-accessible settings reduces the certified leading shot cost by 31-70% on four 29-35-qubit f-element Hamiltonians, a QWC-versus-QWC+FC result rather than a Gaussian-versus-Clifford pricing. Controlled-Pauli insertions in Hadamard tests are Clifford; these zero-$T$ statements concern measurement circuitry only, while shot counts and state preparation retain their full costs.
arXiv:2503.10677v3 Announce Type: replace
Abstract: Retrieval-Augmented Generation (RAG) has gained significant attention in recent years for its potential to enhance natural language understanding and generation by combining large-scale retrieval systems with generative models. RAG leverages external knowledge sources, such as documents, databases, or structured data, to improve model performance and generate more accurate and contextually relevant outputs. This survey aims to provide a comprehensive overview of RAG by examining its fundamental components, including retrieval mechanisms, generation processes, and the integration between the two. We discuss the key characteristics of RAG, such as its ability to augment generative models with dynamic external knowledge, and the challenges associated with aligning retrieved information with generative objectives. We also present a taxonomy that categorizes RAG methods, ranging from basic retrieval-augmented approaches to more advanced models incorporating multimodal data and reasoning capabilities. Additionally, we review the evaluation benchmarks and datasets commonly used to assess RAG systems, along with a detailed exploration of its applications in fields such as question answering, summarization, and information retrieval. Finally, we highlight emerging research directions and opportunities for improving RAG systems, such as enhanced retrieval efficiency, model interpretability, and domain-specific adaptations. This paper concludes by outlining the prospects for RAG in addressing real-world challenges and its potential to drive further advancements in natural language processing.
arXiv:2607.17388v1 Announce Type: cross
Abstract: We investigate the capacity of current language models to contribute to mathematical research. In Banach space theory, AI systems generated key ideas and proofs for five new results, which were then verified and refined by humans. We also developed an automated system that searches the literature for open problems and attempts solutions at scale. Our results show both the potential of language models for mathematical discovery and the continuing importance of expert verification.
arXiv:2409.10067v2 Announce Type: replace
Abstract: Fluid dynamics, and flight in particular, is a domain where organisms challenge our understanding of its physics. Integrating the current knowledge of animal flight, we propose to revisit the use of live animals to study physical phenomena. After a short description of the physics of flight, we examine the broad literature on animal flight focusing on studies of living animals. We start out reviewing the diverse animal species studied so far and then focus on the experimental techniques used to study them quantitatively. Our network analysis reveals how the three clades of animals performing powered flight - insects, birds and bats - are studied using substantially different combinations of measurement techniques. We then combine these insights with a new paradigm for increasing our physical understanding of flight. This paradigm relies on the concept of Animal Learning, where animals are used as probes to study fluid phenomena and variables involved in flight, harnessing their natural adaptability.