Papers

The performance of large language model (LLM) workflows often depends on selecting a small set of in-context demonstrations to guide model behavior on new tasks. Recent methods improve this process by augmenting prompts with successful reasoning paths. However, their demonstration selection relies on random sampling or metric-based rankings, overlooking the semantic structure of the task. We propose ClusterFewshot, a strategy that combines semantic structuring with utility-aware scoring to construct representative and effective few-shot demonstration sets. Evaluated within DSPy-based pipelines, ClusterFewshot substantially reduces optimization cost across multiple benchmarks, while consistently improving accuracy relative to prior bootstrap-based methods in both standalone prompt tuning and hybrid prompt-weight optimization.

A conformal abstention certificate for text-to-SQL is only as truthful as the correctness labels it is calibrated on. The uncertainty pipelines that read confidence off execution consistency take those labels from the single database a benchmark ships, an oracle known to be lenient. We run a preregistered intervention on Spider-Realistic, swapping that database for the benchmark's distilled multi-instance test suite. Across four SQL-specialist checkpoints and two split schemes, the swap raises the certificate's held-out risk 2.73 to 10.23 points above the risk its own labels report. Neither oracle reports the risk experts assign. Under blinded labels from two SQL experts, a certificate calibrated at a nominal 0.10 carries 20.0 and 17.2 points of risk on two checkpoints. The stricter oracle errs in both directions: most of the answers it rejects are not judged wrong, and some of those it accepts are. An AI-assigned census of what it rejects finds a semantic error in a quarter to a third of them, depending on the population. It attributes most of the rest to underspecified questions, synthetic instances or suspected reference-query defects, a flag supported by a preregistered blinded expert audit. The oracle also decides how a confidence score is judged. Every execution-consistency score looks better under the labels of the oracle that built its clusters, in 16 of 16 combinations. Under expert labels, building such a score on suite clusters instead of shipped-database clusters raises its area under the ROC curve (AUROC) by 6.96 points on one checkpoint and 1.53 on the other. On the second, the expert interval excludes the 8.3 points the suite labels report. A certificate should be reported with both oracles, and an oracle-relative difference read as semantic risk only after the benchmark is audited. A consistency score should be evaluated under an oracle that did not build it.

Frozen visual foundation models provide transferable features for visual place recognition, but fixed aggregation can suppress useful distinctions in new environments. We introduce TFA, a reliability-guided, training-free aggregation method requiring neither place labels nor task-specific weight updates. Our key observation is that reproducible retrieval need not be discriminative: independent codebooks can consistently retrieve a few database hubs. TFA combines cross-codebook agreement, retrieval coverage, and spectral statistics to control residual assignment, spectral shaping, and global-feature fusion. Its spectral kernel exactly recovers original descriptor similarity at zero intervention. Database-only TFA fixes its rules before accessing queries; TFA-C64 uses 64 disjoint unlabeled target images to calibrate retrieval for subsequent queries. Across 20 ground protocols with a fixed DINOv2-B backbone and matched resolution, database-only TFA improves Recall@1 over AnyLoc by 17.39 percentage points on MSLS-val and 9.55 on SPED. C64 mitigates failures of database-only calibration in driving environments. Across eight aerial/cross-view protocols, TFA achieves the highest Recall@1 among compared training-free heads in 14 of 16 DINOv2/DINOv3 backbone-protocol combinations. In a separate native-system comparison, DINOv2-G-based TFA-C64 reaches 91.46% Recall@1 on Pitts30k and 76.29% on VPAIR, outperforming the displayed training-free comparators on all five benchmarks. These results show that reliability-guided aggregation can recover additional retrieval capability from frozen representations, providing a practical baseline for new environments with scarce place supervision.

We demonstrate spin–orbit-coupling (SOC) catalysis of magnetization-sector transfer in the half-filled Fermi–Hubbard model. Without SOC, conservation of total magnetization confines the dynamics to the initial sector, preventing an antiferromagnetically correlated state from reaching the polarized ferromagnetic sector under a Zeeman ramp. A transient SOC control lifts this obstruction by coupling otherwise disconnected magnetization sectors and converting symmetry-protected crossings into avoided crossings, thereby opening a finite-gap pathway for magnetic-state conversion. We further accelerate the SOC-enabled dynamics beyond the adiabatic timescale using gradient-ascent pulse engineering (GRAPE) and a variational quantum circuit. Both approaches achieve rapid magnetization transfer in one- and two-dimensional Fermi–Hubbard lattices. Our results establish transient SOC as a controllable catalyst for overcoming symmetry-imposed dynamical constraints, while optimal control sets the timescale for the resulting magnetization-sector transfer.

We present a new semi-implicit structure-preserving (SP) finite volume discretization for a unified first-order hyperbolic model of continuum mechanics. This framework provides a common mathematical description for fluids and solids and incorporates transport, viscous effects, heat conduction, and elastic deformations within a single system of hyperbolic partial differential equations. The coexistence of several physical mechanisms gives rise to multiple characteristic wave speeds, resulting in severe time-step restrictions for fully explicit discretizations. To overcome this difficulty, we develop a four-split scheme in which the governing equations are decomposed into convective, temperature, mechanical, and pressure subsystems. The convective subsystem is the only one that is advanced explicitly in time, while the remaining subsystems are treated implicitly in a sequential manner. As a consequence, the time step restriction of the proposed method depends only on the material velocity and is independent of the acoustic, shear, and thermal wave speeds that characterize the model. The scheme is designed to preserve key structural properties of the underlying equations on unstructured grids. In particular, a compatible vertex-staggered spatial discretization on triangles allows the curl-free involutions associated with the distortion field and thermal impulse to be respected whenever the relaxation source terms in the governing PDE are linear or absent. At the same time, the scheme is asymptotic preserving as it is consistent with the low Mach number limit and with the stiff relaxation limits of the GPR model that recover the classical Navier-Stokes-Fourier equations in fluid mechanics. A series of numerical experiments covering both fluids and solids demonstrates the accuracy, robustness, and multi-scale capabilities of the proposed approach.

We identify a broad class of communication channels that captures common physical constraints in both artificial and natural systems and derive bounds on their thermodynamic cost. We find that the entropy production per channel use is bounded from below by the input-output mutual information, and their ratio -mutual information divided by entropy production- defines the thermodynamic efficiency. Unlike previous studies of energy-constrained communication channels, our analysis shows that thermodynamic costs must be assigned not only to the input symbols themselves, but also to transitions between successive symbols. As a result, maximizing thermodynamic efficiency favors a biased input that switches only rarely, rather than the capacity-achieving input. For the binary symmetric channel, this preference emerges through a pitchfork bifurcation that spontaneously breaks the symmetry of the channel. A minimal model of cellular sensing exhibits the same phenomenon.

Concerns about inauthentic accounts, including foreign actors posing as domestic voices, are central to debates about online discourse. Yet, little is known about accounts with inaccurate location claims and how they behave when discrepancies between their claimed and actual locations become publicly visible. In November 2025, X introduced an "About this account" feature that discloses each account's platform-inferred location of operation. We leverage this intervention in a large-scale quasi-experimental study of 8,200 politically engaged accounts claiming a U.S. location, comparing accounts whose disclosed locations matched versus contradicted their claims across 1.3 million posts and 3.6 million replies over 21 weeks. Before disclosure, location-mismatched accounts posted more misleading, scam-related, and cryptocurrency-related content, but showed no distinctive partisan leaning. Difference-in-differences estimates show that disclosure reduced the posting activity of location-mismatched accounts by 13.1% with the largest declines among accounts revealed to be in Africa (29.2%) and Asia (24.4%), and among accounts with VPN flags, username changes, or scam- and crypto-heavy content. Additionally, the decline in their replies was concentrated in interactions with U.S.-based recipients (10.3%), whereas replies to non-U.S.-based recipients showed no statistically significant change. Conversely, there was no significant change in average audience engagement with their posts. Location transparency thus works primarily by inducing restraint among the disclosed accounts rather than by shifting audience behaviour, and the accounts it constrains look at least as much like cross-border fraud as foreign political influence.

2D point cloud registration arises in laser odometry and Simultaneous Localization and Mapping (SLAM) for mobile robots. Iterative Closest Point (ICP) is one of the most widely used approaches. Still, its iterative procedure recomputes correspondences via nearest-neighbor search at every iteration, whereas correspondence-free alternatives focus on scan-to-map alignment. This paper proposes a 2D point cloud registration approach based on unsigned distance maps, precomputing the Euclidean distance to the nearest reference point, along with its spatial derivatives, over a discrete grid, replacing the per-iteration search with O(1) lookups. Moreover, point-to-point and point-to-plane error formulations are derived on the SE(2) manifold and solved via Gauss-Newton optimization. On a synthetic benchmark and the real-world IILABS 3D dataset, the precomputed point-to-point variant outperforms its analytical counterparts, achieving competitive laser-odometry drift compared to point-to-plane formulations, as the precomputed gradient regularizes correspondences in the presence of sensor noise.

We study Lipschitz mappings associated with group actions by similarities, extending the orbit-quotient approach for point-preserving isometric actions. Normalizing by the similarity ratios we obtain isometric representations whose fixed points are character-equivariant Lipschitz mappings. The corresponding quotients by closed spans of orbit differences provide canonical preduals and norm-preserving linearizations, without an amenability assumption. Applications include positively homogeneous, linear, and bilinear mappings. In particular, we prove that the space of positively homogeneous Lipschitz functions form a $1$-complemented subspace of the Lipschitz space (strenghthening the earlier existed result) and interpret existing projections onto linear and bilinear mappings as invariant-mean averages. For amenable groups, the same approach yields isometric realizations of the quotient spaces in the biduals of the original linearization spaces.

Detecting and localizing 3D point-cloud defects is essential for industrial inspection. However, existing methods often suffer from imprecise localization due to the lack of anomaly supervision and reliance on single-granularity representations. To address these limitations, we propose Anomaly Type-Aware 3D Anomaly Detection (AT3D-AD), a unified framework for joint detection, localization, and classification. Specifically, we first design the Physics-Driven Parametric Anomaly Synthesis (PDPAS) module employing multiple parametric functions to generate synthetic anomalies, providing explicit anomaly supervision. Then, we propose the Hierarchical Global-Local Anomaly Alignment (HiGLA) module to align global and local representations within the normal and anomalous groups. Finally, we propose the Semantic-Geometric Anomaly Classification (SGAC) module to jointly learn localization and classification, yielding spatially precise and type-discriminative anomaly representations. Extensive experiments establish new state-of-the-art performance on all four benchmarks. AT3D-AD achieves Object/Point AUROC scores of 98.1%/98.9% on Anomaly-ShapeNet and 95.0%/95.2% on Real3D-AD, while reaching 74.2% Macro-F1 for anomaly-type recognition on Real3D-AD.

We prove that deciding the Berry phase for parameterised 2-local qubit Hamiltonians is BQP-complete when presented with a classical description of a guiding state, promised to overlap with the ground state of the system. Our results extend to systems with weighted Heisenberg interactions and when restricted to a 2D square or triangular lattice geometry. The techniques we develop leverage the Schrieffer–Wolff transformation, typically used in the construction of perturbative gadget reductions for local Hamiltonian problems, extending it to parameterised families of Hamiltonians. We demonstrate that there exists a choice of parameterised simulator Hamiltonians whose Berry phase well-approximates that of a parameterised target family. Using the perturbative gadget reduction framework of Oliveira and Terhal and of Schuch and Verstraete, we adapt the arguments to parameterised interactions and demonstrate the error bounds in the resulting simulation can be controlled. Additionally, we provide an explicit proof that families of 1-local Hamiltonians have a Berry phase that can be efficiently computed to inverse-polynomial precision. This establishes a complexity transition between 1-local and 2-local Hamiltonian families.

Unmanned aerial vehicles (UAVs)-based free-space optics (FSO)/quantum key distribution (QKD) systems require high-precision pointing mechanisms. This increases system complexity and limits rapid deployment for lightweight and energy-constrained UAVs. This paper proposes a modulating retroreflector (MRR)-equipped UAV architecture for BB84-QKD systems that enables simplified yet accurate tracking while relaxing pointing requirements. A realistic quantum channel model is developed, for which we newly derive the channel probability distribution of transmittance (PDT). Capitalizing on the derived channel PDT, several QKD performance metrics are analytically obtained. Numerical results verify the feasibility of the proposed MRR-aided UAV for practical QKD deployment, highlight its effectiveness over conventional UAV-ground systems, and validate the accuracy of the developed analytical framework.

Diffusion Large Language Models (dLLMs) have emerged as an efficient alternative to autoregressive models, yet aligning them via Reinforcement Learning (RL) requires likelihood surrogates estimated from masked reconstruction subproblems under a small Monte Carlo budget per rollout. Existing methods construct these subproblems by uniform random masking, leaving open the question of which subproblems to prioritize. We identify a systematic upstream/downstream structure in dLLM rollouts. Some tokens, when revealed, trigger large confidence changes in nearby undecoded positions; we call them upstream. Others induce only small local changes and are therefore downstream. We find masking downstream tokens yields substantially better-posed subproblems than masking upstream tokens, a phenomenon we term subproblem difficulty asymmetry. Based on the observation, we propose Informed Masking (IM), which derives a per-token priority score from the denoising trajectory at zero extra inference cost and biases mask sampling toward downstream tokens. IM is plug-and-play: when plugged into three state-of-the-art dLLM RL methods on LLaDA-8B-Instruct, it delivers up to 2.01%, 8.68%, and 5.77% relative average gains on math and planning benchmarks with improved training stability.

We revisit the modelling of the material decomposition problem in multispectral computed tomography and propose to leverage the known absorption spectra of different materials. With this we both derive new uniqueness conditions for the material decomposition and also offer a three-step reconstruction model. Our uniqueness criterion only requires certain characteristics of the bin sensitivity functions and the material attenuation spectra and hence, can be computed a-priori before measurements are taken.

For arithmetic quotients of Bruhat–Tits trees with finitely many cusps, we establish an explicit unitary correspondence between the spherical Eisenstein transform, with the Eisenstein series normalized by their constant terms, and the scattering transform of an associated Jacobi operator with finite core. Tracking the Haar measure, stabilizer weights, height coordinates, and cusp widths yields the Plancherel measure and shows that the absolutely continuous spectrum has multiplicity equal to the number of cusps. From a discrete Green identity we derive a matrix-valued Maass–Selberg formula for the Hermitian matrix $iS(\theta)^*\partial_\theta S(\theta)$, where $S(\theta)$ is the scattering matrix. Its trace is determined by $\det S(\theta)$, while the full matrix retains additional cusp-to-cusp information. After the corresponding change of normalization, the finite Schur complement obtained by eliminating the cusp rays agrees with the resonance matrix of Arends-Peterson-Weich. Using their resonance computations as input, we distinguish eigenvalues supported entirely in the finite core from poles of the scattering matrix. The Nagao and $\Gamma_0(T)$ quotients, together with a four-cusp quotient arising from an elliptic curve over $\mathbb F_3$, make the normalizations and matrix-valued conclusions explicit.

Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop Counterfactual Tucker Diffusion (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.

Conventional iterative receiver usually begins with channel estimation using sparse pilot observations and follows with data detection based on the channel estimates, and then updates channel estimation using decision feedback, and so on. In Artificial Intelligence (AI)-based receiver design, it is also crucial to make use of such progressively enriched data observations to enhance the generative channel estimation. However, the statistical characteristics and reliability of the data decisions always evolve with the channel estimation processes, which brings great challenges to the design of the overall learning framework and algorithms. In this paper, we propose Diff-Rx, an incrementally conditioned diffusion-based receiver with co-designed data detection and channel estimation, for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Specifically, we develop a condition-adaptive post-training method which enables the generative channel estimator to adapt to the conditioning inputs that are progressively enriched by soft data decisions, and also to implicitly align the pilot- and data-induced channel feature spaces to mitigate potential estimation errors. The threshold-free soft decisions provide smooth condition updates without condition-specific reliability tuning. We further develop a conditional diffusion transformer that is capable of performing robust channel estimation under noisy observations and various pilot patterns while reducing the conventional multi-step diffusion generation to one single step. Simulations on both statistical and site-specific ray-tracing channels show that, Diff-Rx exhibits consistent gains across different noise levels, pilot densities and modulation schemes, and works well at a pilot density as low as 1/32 while achieving significant improvement in channel estimation and data detection performances.

Inspired by recent interests in quantum geometry in electronic bands, we consider a two-dimensional topological Mott insulator, i.e. chiral spin liquid, whose spinon bands develop nontrivial band topological and quantum geometry. The virtual polarization of the gapped charge sector transfers the electromagnetic drive to the charge-neutral spinons through the emergent U(1) gauge field, producing a tensor Ioffe-Larkin response and enabling two complementary optical protocols for measurements. In the off-shell (low-frequency) regime, a self-calibrated ratio of the physical longitudinal and Hall conductivities yields the spinon Chern number without the microscopic knowledge of the charge response. In the on-shell (resonant) regime, combining the inverse Ioffe-Larkin response with the Kramers-Kronig relation enables reconstruction of the quantum-metric and Berry-curvature spectral densities. Our approach directly applies to the triangular lattice Hofstadter-Hubbard model in Moiré systems, can be well adapted to other triangular lattice antiferromagnets such as Nb$_3$Br$_8$ with appropriate modifications. We establish a unified framework for quantitatively probing the quantum geometry of fractionalized quasiparticles in topological Mott regime.

Cybersecurity literature has extensively documented the operational benefits of artificial intelligence (AI) for threat detection, incident response, and prevention, while raising qualitative concerns about over-automation, algorithmic bias, and analyst-skill erosion. What remains largely absent is a formal, falsifiable model connecting three constructs that recur across this literature: Defense-in-Depth Theory, the Artificial Intelligence Theory of Pattern Recognition, and human-AI collaboration in security operations. This paper develops such a model. We formalize layered defense as a Bernoulli detection cascade in which AI augmentation enters multiplicatively across layers; we formalize each layer's pattern-recognition behavior as a Neyman-Pearson/Bayesian detector with a derived closed-form optimal threshold; and we formalize human-AI triage as a capacity-constrained cascade with an explicit, quantifiable trade-off between detection probability and false-alarm ("alert fatigue") rate. A Monte Carlo/analytical simulation evaluated at illustrative but realistic operating points shows that (i) AI augmentation compounds across defense layers, delivering its largest marginal gains exactly where traditional layering saturates, and (ii) full human review of AI-flagged alerts is not optimal: increasing analyst capacity toward 100% coverage cuts false alarms by roughly 20-fold but simultaneously lowers system-level detection probability, because imperfect analyst accuracy is then applied to every alert rather than a filtered subset. These results give the widely repeated qualitative recommendation of "balanced human-AI collaboration" a precise, testable form and suggest an interior-optimum capacity ratio as a concrete design target for security operations centers (SOCs), including those securing IT/OT-converged critical infrastructure.

We study a dissipativity-based model predictive control (MPC) scheme for energy-optimal constrained output stabilization of a discrete-time nonlinear SISO port-Hamiltonian system described by difference and differential representation. For the optimal control problem to be solved in each MPC step, we establish a measure turnpike behavior. The turnpike set in our work is obtained from the underlying port-Hamiltonian structure without assuming existence of steady-states or periodic orbits. In particular, unlike existing results which typically establish the turnpike property w.r.t. a controlled forward invariant set such as optimal steady-states or optimal periodic orbits, we do not require the turnpike set to be forward control invariant. For MPC, we establish recursive feasibility and show practical stability to the turnpike set w.r.t. the MPC closed loop leveraging both dissipativity and the port-Hamiltonian structure. Finally, we demonstrate our results using two numerical examples.

Unconventional magnets combining vanishing net magnetization with spin-split electronic structures and anomalous transport have attracted considerable attention. Using spin-group symmetry analysis, we derive general conditions for odd-parity spin splitting in two- and three-dimensional coplanar noncollinear antiferromagnets. We identify a key spin-group symmetry whose relativistic counterpart forbids time-reversal-odd transport and show that breaking it allows such transport in the presence of spin-orbit coupling. Tight-binding calculations validate these symmetry arguments and demonstrate an anomalous Hall effect in a fully compensated odd-parity magnetic state without an external field. By screening a three-dimensional magnetic materials database and constructing two-dimensional heterostructures, we further identify realistic platforms exhibiting pronounced spin-orientation-dependent anomalous Hall and magneto-optical effects. Our results establish a general symmetry framework for time-reversal-odd responses in odd-parity magnets and highlight fully compensated odd-parity magnets as a promising platform for controlling anomalous transport.

DAG-based consensus protocols can achieve great throughput and the optimal three-message-delay limit for n = 3f+1 consensus. While two-delay protocols exist, they pay with reduced resilience (requiring 5f+1-style committees) or rely on fallbacks that sacrifice the DAG's high throughput. This paper introduces Hydrozoan, the first DAG protocol with a dual commit path under a hybrid fault model of f Byzantine and c crashed validators, on n = 3f+c+2p+1 validators. Leaders commit in two message delays whenever at most p validators are faulty, and in three otherwise, with no extra messages, no view changes, and multiple leaders per round. Both paths are evaluated on the same DAG, using a novel graded indirect rule to reconcile them so that every honest validator reaches the same decision. We show that under geo-distributed conditions, which path is faster is a property of geography rather than the protocol, as rounds reaching a remote region cost far more than those that do not. The (f, c, p) knobs place the fast quorum where the deployment requires it, allowing a commit in two message delays. If misconfigured, Hydrozoan can still commit in three message delays: Hydrozoan commits on whichever path fires first. We also present Optimal-Hydrozoan, a variant that tolerates one more fault on the fast path, the first construction to match the known lower bound. The safety and liveness of both protocols are machine-checked in Lean 4. Our geo-distributed evaluation shows that Hydrozoan matches Mysticeti's throughput, commits ~25% faster when the fast quorum fits fast regions, and falls back to three message delays when it does not or past p faults, where existing two-delay protocols stall.

In this work, we propose a communication-free framework for vision-based formation control of fully actuated underwater robots subject to sensing constraints, collision-avoidance requirements, and input saturations. Recentered barrier Lyapunov functions encode sensing and collision-avoidance constraints, while command-filtered backstepping extends the design to the second-order vehicle dynamics. The resulting control objective is enforced through a quadratic program that explicitly accounts for actuator limits. Conservative sensing domains provide margins from the physical limits and are adaptively relaxed when necessary, allowing temporary violation of the conservative bounds. The proposed approach is validated through realistic Software-in-the-Loop (SITL) simulations in Gazebo.

Mixed-precision weight quantization is commonly formulated as a Multiple-Choice Knapsack Problem (MCKP), yet existing solvers rely on scalar sensitivity proxies that collapse each weight matrix's Hessian into a single number and treat every module independently. We prove that even the optimal scalar proxy incurs multiplicative distortion up to $\sqrt{\kappa(\mathbf{A})\kappa(\mathbf{B})}$ relative to the full activation-aware quadratic, where $\kappa(\mathbf{A})$ and $\kappa(\mathbf{B})$ denote the condition numbers of the input- and output-side Hessian factors. This bound varies from $10^1$ to $10^{13}$ for typical LLM modules, making inter-module sensitivity ranking unreliable. To address these limitations, we propose Cross-layer Activation-aware Sensitivity Allocation (CASA), a two-phase method. In Stage 1, the scalar proxy is replaced by an activation-aware metric derived from the Kronecker-factored Hessian, reducing the MCKP to a form whose continuous relaxation admits a closed-form solution. In Stage 2, a cross-layer-aware local search evaluates bit-width updates using the end-to-end model loss. Experiments on multiple LLMs across different bit budgets show that CASA achieves lower perplexity than the latest scalar-proxy baselines, especially at ultra-low bit-widths ($<3$ bits per weight). Moreover, the performance gain in zero-shot accuracy tracks the per-model average condition-number over modules, confirming the distortion bound as a practical indicator of scalar-proxy failure.

We develop a nonlinear thermodynamic formalism for correspondences on compact metric spaces. A continuous energy is evaluated on empirical measures of successive pairs of states. The measure-theoretic pressure of a stationary transition pair is the sum of its kernel entropy and the energy of the joint distribution of two successive states. For forward expansive correspondences satisfying an ergodic-abundance condition, we prove a variational principle and the existence of nonlinear equilibrium pairs. We further prove that limits of the two-coordinate projections of asymptotically maximizing Gibbs ensembles are averages of the two-coordinate distributions of equilibrium pairs. When the energy depends on finitely many potentials on the space of admissible pairs, Legendre regularity assumptions allow us to identify nonlinear equilibrium pairs among linear equilibrium pairs through a self-consistency equation and a global maximization condition. Under these assumptions, real analyticity in one dimension and uniqueness of linear equilibrium pairs imply finiteness of the nonlinear equilibrium set. Finite-state examples exhibit continuous and first-order transitions, metastability, and phases that have identical one-coordinate marginals but distinct two-coordinate distributions. A criterion based on Taylor expansions determines the associated critical exponents

Complex-valued neural networks (CVNNs) are increasingly adopted for complex-valued data; however, they are often trained with first-order optimizers inherited from the real-valued case. The efficiency of these methods depends largely on the step size, and their step-size rules ignore the angular information available in the complex plane. We address step-size adaptation in the complex domain by introducing AURA (Angular Update Rate Adaptation), a per-parameter step-size adaptation that can be added on top of any first-order optimizer, and removed from it, without altering its update direction. AURA measures the agreement between consecutive updates of each complex parameter, in length, alignment, and sense of rotation, and enlarges the step when they are consistent and reduces it when they are not. It requires no additional gradient evaluations and only inexpensive vector operations per step. We combine AURA with Adam and Muon and compare the resulting methods with well-known first-order optimizers on four test cases of increasing complexity, ranging from the approximation of scalar complex functions to physics-informed training. Fully connected neural networks are used throughout this work. All hyperparameters other than the step size are held fixed across test cases; for one case, we also tune the hyperparameters of each optimizer under the same budget. Our empirical tests show that AURA improves the convergence of its base optimizer in most cases with a small per-step overhead, and we identify the conditions under which it fails to do so.

A language agent's execution history can exceed its context window, requiring its memory system to retrieve complete supporting evidence under a hard token budget. Evidence may span multiple execution events, yet conventional retrievers use fixed token windows and fixed-k metrics that reward individual fragments without showing whether the complete evidence set fits in context. Smaller windows reduce irrelevant text but scatter evidence across candidates, while flat-versus-graph comparisons can conflate candidate design with graph propagation. To address these limitations, we formulate agent-memory retrieval as budgeted evidence completion and score exact gold spans in shared source coordinates. We first construct source-aligned provenance units from tool arguments and outputs. We then apply a zero-initialized residual R-GCN to refine frozen dense-retrieval scores over typed provenance edges. We evaluate 2,000 span-grounded memory queries over 1,207 held-out execution-grounded ISETrace trajectories. With matched Dense-FT scoring, provenance units improve Full Support@2048 by 19.07 points over flat 512-token windows and remain 11.96 points above a per-metric oracle over four flat chunk sizes; the pattern also holds with cross-encoder scoring. Holding the candidates and seed scores fixed, graph propagation adds 4.55 points in Full Support@2048 (95% CI [2.98, 6.18]). This gain is concentrated when gold evidence spans multiple events; entity co-occurrence expansion produces no comparable benefit, and relation and topology controls confirm dependence on typed transformations and observed graph structure. Overall, source-aligned candidates address the dominant granularity trade-off, while graph-conditioned propagation adds a smaller, targeted benefit for distributed evidence.

We propose a thresholding scheme for the half-harmonic map heat flow from the flat torus $\mathbb{T}^d$ into the unit sphere $\mathbb{S}^m$ in $\mathbb{R}^{m+1}$, whose iterates are given by convolution with the Poisson kernel, replacing the Gaussian kernel of the classical Merriman-Bence-Osher algorithm, and pointwise normalization. We prove that the piecewise constant interpolants subconverge to a weak solution of the half-harmonic maps heat flow that attains the initial map strongly in the energy space and satisfies the energy-dissipation inequality. For a spectrally truncated variant, convergence holds under a condition on the step size. A key ingredient is the derivation of the precise energy-dissipation identity directly from a refined within-step estimate, without resorting to De Giorgi interpolation typically used in the minimizing movement framework. This provides a direct way to recover the appropriate energy-dissipation property in the limit and, in turn, enables weak-strong uniqueness: every energy-dissipating weak solution coincides with the strong solution whenever the latter exists.

Dependency-update pull requests are frequent and mostly routine, but a small subset requires non-trivial compatibility repair. Recent repository-level coding agents make such repair increasingly plausible, yet invoking them on every dependency update wastes model calls, CI time, repository context, and review attention. We frame this as a pre-agent routing problem: deciding which dependency-update pull requests should be escalated before downstream diagnosis or repair attempts. We introduce DepFixRouter, a lightweight router that ranks dependency updates by historical compatibility-repair likelihood using creation-time textual and metadata signals. On 497 labeled GitHub dependency-update candidates, only 72 require substantive repair. A creation-time-safe LinearSVC using only PR titles and bot/dependency flags reaches 0.488 repair F1 and captures 51.4% of repairs within the top 20% routed pull requests, improving calls per captured repair from 6.90 under route-all or random policies to 2.68. Retrospective full-history signals improve top-20% recall to 65.3%, revealing substantial hindsight leakage in pull-request histories rather than deployment-time routing utility. In a 60-case diagnosis-agent pilot, router-gated diagnosis reduces actual LLM calls by 66.7% and tokens by 66.1%, suggesting budgetaware escalation while measuring diagnosis rather than patch generation. DepFixRouter can serve as a lightweight escalation layer between routine dependency-update automation and expensive repository-level agents, enabling budget-aware maintenance without relying on retrospective repair evidence for deployment-time routing.

We investigate, for the first time, the non-radial $f$-mode oscillations of neutron stars (NSs) with a dark energy (DE) core utilising a fully general relativistic treatment. We construct the stellar profile by considering a relativistic mean field model for nuclear matter and a modified Chaplygin fluid like prescription for DE. We compute the stellar structure, $f$-mode oscillations, tidal deformability, and gravitational wave (GW) energy and strain of the NS with DE core by varying the DE equation of state (EoS) parameters. Our study reveals that the inclusion of DE softens EoS and reduces the maximum mass compared to the pure neutron star. The obtained mass-radius values are consistent with observational constraints from massive pulsars such as PSR J0030+0451 and PSR J0740+6620. We find that the extent of the DE core, determined by the transition density, plays a crucial role in modifying the stellar structure and oscillation properties, with lower transition densities producing appreciable changes over a wider mass range. The $f$-mode frequencies and damping times exhibit systematic modifications, for higher mass configurations, while the correlation between the $f$-mode frequency and tidal deformability remains consistent with observational constraints from GW170817 and GW190814. Further, the normalised oscillation energy distribution remains nearly universal, with only minimal deviations for the higher mass configurations. Finally, we estimate the characteristic GW strain associated with the $f$-mode oscillations and find that the predicted signals lie within the sensitivity band of future third generation GW detectors.