Papers

This study systematically evaluates self-evaluation-based uncertainty quantification across different language models of varying sizes on question-answering tasks spanning general to specialized knowledge domains. Using various self-evaluation methods where models judge their own predictions, we examine how model scale and domain specificity affect the quality of self-assessed confidence signals. Our results reveal that while accuracy predictably declines with smaller models and more specialized domains, the reliability of self-evaluated confidence remains largely stable across both dimensions. This independence means the most capable model is not necessarily the best at self-assessing prediction reliability. These findings suggest that smaller models can achieve reasonable self-assessed confidence despite lower accuracy, making them viable for resource-constrained deployments.

Teams of autonomous agents, including large language model (LLM) agents, must coordinate over scarce and unreliable wireless links. We propose goal-oriented semantic communication (GOSC), a closed-loop co-design that jointly decides what each agent sends, when it sends it, and how reliably it is transmitted, based on each message's value to the team task. An edge broadcast of the team's common knowledge closes the loop by updating these values. We prove that a message is sent only if its value exceeds the cost of delivering it and that more valuable messages receive more robust transmission rates, and we show that the scheduler solves each scheduling step exactly whenever the radio budget is not saturated, which held in 95% of scheduling decisions. In search-and-rescue missions validated on unseen scenarios, GOSC meets the same mission targets as carefully tuned periodic semantic schemes with 1.2–8.5 times fewer uplink channel uses. In most settings, this advantage persists with realistic packet overheads, reaching 16.6 times fewer uplink channel uses and 13.8 times lower cost when downlink costs are included; in the rescue task, it also persists when all agents share one uplink. Rough value estimates suffice, whereas values that ignore message content can fail. With three different LLMs, GOSC uses 3.2–3.5 times fewer channel uses, while completion-time gains depend on the model.

Extending a previous work on the energy-momentum tensor of the linearized gravitational field in Minkowski background, conserved currents in linearized gravity associated with Lorentz transformations, dilatations and special conformal transformations are explored in the framework of Lagrangian field theory. Both outstanding special cases and general parametric families of currents are considered. Regarding the former, the distinguished energy-momentum tensor $T_{\mathrm{lg}}^{ab}$ we found earlier, guided by similarities between linearized gravity and electrodynamics, is supplemented with an angular momentum tensor $M_{\mathrm{lg}}^{abc}$ and a dilatation current $D_{\mathrm{lg}}^a$, associated with Lorentz and dilatation symmetries. Concerning special conformal transformations, a generalization of Noether's theorem that is useful if additional conditions (such as gauge fixing conditions) are imposed is formulated, it is shown that special conformal transformations are Noether symmetries of linearized gravity in the generalized harmonic gauges, and a special conformal tensor $C_{\mathrm{lg}}^{ab}$, accompanying $T_{\mathrm{lg}}^{ab}$, is obtained using the generalized Noether's theorem. The angular momentum tensor, dilatation current and special conformal tensor accompanying two other notable energy-momentum tensors are discussed as well. General multi-parameter families of $M^{abc}$, $D^a$ and $C^{ab}$ tensors accompanying a general family of energy-momentum tensors, which was found earlier and includes canonical energy-momentum tensors, are also determined, and local balance equations that are relevant if matter is present are derived for them. Their members do not depend on higher than first derivatives of the linearized metric.

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove – yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

For lattice Boltzmann simulations of unsteady flows at low Reynolds numbers, dual-time stepping decouples the physical time step from lattice streaming, yet conserved-moment iteration errors decay slowly at large steps. We develop a residual correction method based on the conserved-moment structure of the collision operator. With fixed step histories and both relaxation rates equal to unity, post-collision populations depend on incoming populations only through reconstructed conserved moments, so one collision eliminates local perturbations with zero conserved moments. Periodic rest-state linearization shows that, at large physical steps, the contraction factor of the uniform conserved mode approaches unity, while its moment residual scales inversely with the step relative to macroscopic error. On periodic domains, combining this scaling with linearized acoustic propagation and viscous diffusion yields a macroscopic auxiliary system driven by the conserved-moment residual and solved in Fourier space for low-wavenumber errors. For solid walls, reference-state linearization of the complete sweep, including executed bounce-back updates, yields a sparse kinetic correction. Both auxiliary systems compute increments from the full nonlinear residual, and we prove fixed-point equivalence with the original discrete system, preserving unsteady and nonlinear convective effects. Refining the time step on fixed grids verifies second-order temporal self-convergence of slowly varying periodic velocity fields in two and three dimensions. Under fixed physical steps and tolerances, mean inner sweeps per step drop from hundreds in three-dimensional periodic flow and thousands in a two-dimensional cavity to a few.

Autonomous agents increasingly rely on memory to generalize beyond their training environments. However, agents are bounded by what they have seen and believed, and leveraging such memories in unseen environments can introduce biases into their internal beliefs. We formalize this phenomenon as false memory, which can arise from spurious correlations, environment shifts, and knowledge conflicts. Despite its importance, false memory is difficult to evaluate because it stems from agent internal beliefs and is easily confounded with ordinary generalization failures. Therefore, we propose FAME, a training-free framework that evaluates false memory through the evolution of agent beliefs under counterfactual reasoning. Specifically, counterfactual scenarios reveal how beliefs change as the latent concept of memory shifts under hypothetical interventions; thus, measuring the resulting concept drift provides a signal for distinguishing faithful versus false memory. Such concepts can be estimated from agent hidden states before answer generation, avoiding the need for reward design or answer sampling. Empirical experiments reveal that simply monitoring answers often fails to detect false memory, while FAME achieves AUROCs of 76.2% - 96.7% across false-memory settings, and outperforms the best baseline by 3.4% - 23.3% across realistic benchmarks, spanning math reasoning (GSM-Symbolic), code generation (GitChameleon), and complex reasoning (BigBench-Hard). We further release corresponding counterfactual templates and facilitate future research on false memory.

Feature-mapping methods represent structural designs by explicit geometric primitives on fixed analysis grids, an interpretable and parametric alternative to the density fields of density-based topology optimization (SIMP). In contrast to SIMP, however, feature-mapping optimization is sensitive to the initial design. We present a gradient-based approach to align a feature-mapping configuration to a given (pseudo) density field, e.g., to initialize a subsequent feature-mapping optimization. The staged approach is based on a least-squares tracking formulation, preceded by a variant that only rewards alignment and does not penalize mismatch. Without an underlying finite element simulation, iterations are cheap, but isolated features receive little sensitivity information. As a remedy, we propose an asymmetric transition function based on automatically parametrized Bézier curves. We demonstrate the approach for a 2D cantilever and the five-bar design; for the latter, we show optional feature minimization based on the feature scaling variable of the geometry projection method. The approach works well with first-order optimizers. The absence of a state problem and the small number of variables, however, also make a second-order formulation attractive. To the best of the authors' knowledge, we present the first Hessian formulation for feature mapping and report the behavior of first- and second-order optimizers on our benchmark problems. For completeness, we also give the exact Hessian of the state-based compliance, which requires one additional solution of the FEM system per feature variable.

We prove the soliton resolution conjecture for the Calogero–Moser derivative nonlinear Schrödinger equation in the scaling-critical space $L^2_+(\mathbb R)$. For a natural class of initial data including a broad spectral Dini—moment class, global flow–Lax admissible solutions decompose into finitely many explicit modulated solitons plus a dispersive radiation, while finite-time blow-up solutions resolve into quantized zero-carrier $R$-bubbles and a strongly convergent endpoint remainder. This work extends soliton resolution to the optimal critical regularity. Previous results had required weighted $H^{1,1}$ initial data, and in the global case the solution was additionally required to remain in $H^{1,1}$ for all time, which amounts to an extra spatial decay assumption. One key ingredient in our argument is a new modular operator-theoretic framework that separates the discrete and continuous spectral channels and identifies the radiation profile through the distorted Fourier transform. A second ingredient is the development of several independent rigidity criteria for the discrete soliton profiles, which avoids inverse scattering and handles embedded eigenvalues. Our framework also yields a unified description of both global and finite-time asymptotics, with exact mass partition and mass-defect quantization.

We investigate the propagation properties and canonical gauge structure of Generalised Non-Linear Electrodynamics (GNLED) in the presence of a non-dynamical background field. Starting from the quadratic photon sector of the theory, we perform a field redefinition that converts the background-induced derivative coupling into a mass-like contribution characterized by the vector \(V_\mu=\partial_\mu\alpha/\alpha\) where $\alpha= \sqrt{\left.\frac{\partial\mathcal{L}}{\partial \mathcal{F}}\right|_B}$. For a constant background, we derive the corresponding dispersion relation and show that, for a purely space-like \(V_\mu\), the propagating mode obeys \(\omega^2=\|\vec k\|^2+\|\vec V\|^2\), defining an effective mass scale \(m_{\rm eff}=|\vec{V}|\) and a finite rest frequency. The resulting phase and group velocities exhibit the characteristic dispersive behaviour of a gapped mode, with subluminal group velocity and superluminal phase velocity. We then construct the propagator and show that the massive pole resides in the transverse sector, while the longitudinal singularity is associated with gauge fixing. A complete Hamiltonian analysis yields two first-class constraints and only two physical degrees of freedom, demonstrating that the effective mass does not introduce an additional polarisation. The associated gauge transformation is a deformed Abelian \(U(1)\) symmetry. Finally, we show that the Hamiltonian is positive definite for purely space-like backgrounds.

A mesh-free numerical framework based on Kolmogorov–Arnold Physics-Informed Neural Networks (KAN-PINNs) is developed for the approximation of fourth-order elliptic boundary value problems, with specific application to the biharmonic equation governing thin plate deflection. Unlike conventional Multi-Layer Perceptrons relying on fixed nodal activations, learnable univariate functions parameterized via radial basis functions are deployed on network edges, while high-order differentiability is preserved through hyperbolic tangent activation mappings. The severe numerical stiffness inherent to fourth-order differential operators and fully clamped boundary conditions is addressed through a direct normalized residual formulation coupled with a hybrid, multi-stage AdamW-to-L-BFGS optimization pipeline. An automated 24/7 hill-climbing search protocol is implemented to systematically calibrate boundary penalty weights and optimization schedules. When evaluated on a smooth manufactured benchmark on the unit square, an error reduction factor exceeding $150\times$ is attained over successive iterations, culminating in a final relative $L_2$ error of $1.593 \times 10^{-5}$ ($0.00159\%$) and a training loss of $3.065 \times 10^{-6}$ utilizing only $7,801$ trainable parameters. These results demonstrate that high-order PDE problems can be accurately resolved using compact, mesh-free KAN-PINNs architecture without requiring auxiliary variable transformations or discrete mesh generation.

We argue that the local violation of null energy condition at the throat of a traversable wormhole does not necessarily indicate that the total volume integrated null energy contribution is negative. It is already known that it can be arbitrarily close to zero. We show that it can even be positive and use this argument to reconstruct a family of wormhole geometries. We also propose a novel classification of traversable wormholes based on the global volume integrated measure of null energy condition.

Pedestrian detection plays a crucial role in computer vision with applications in autonomous driving, surveillance, and public safety. However, real-world dense scenes bring severe challenges, including heavy occlusion, drastic scale variations, and strict real-time requirements. Existing lightweight detectors struggle to balance accuracy and efficiency while often neglecting quality-aware feature modeling and consistency between classification and localization, leading to unstable performance under crowded conditions. To address these issues, we propose DensePed-Lite, a unified framework built on a single principle: under occlusion the network should adapt its behavior to the quality of what it observes rather than assume complete information. This principle is realized at three points where occlusion does the most damage: unreliable confidence scoring (UQE), fragmented spatial coverage (MPSC), and incoherent multi-scale fusion (CTDM). The three mechanisms reinforce one another instead of acting in isolation, all without significantly increasing complexity. Experiments on CityPersons and CrowdHuman validate that DensePed-Lite achieves a superior accuracy-efficiency trade-off compared with recent state-of-the-art lightweight methods, making it suitable for real-time deployment in dense pedestrian scenarios.

In this work, we introduce a new clustering method, namely T-ARC (Topology-Aware Randomized Clustering), that corrects the geometric bias of K-means by embedding topological information directly into the optimization objective. Building on the assumption that the data admits an underlying hidden structure modeled via a latent graph, the idea is to uncover this information through the interplay between the standard K-means data-fidelity term and a graph-cut penalty, which discourages cluster assignments inconsistent with the connectivity structure of the data. To render this coupling tractable, the latent graph is modeled as a random realization from a Stochastic Block Model (SBM), whose scalar parameter is optimized within a Distributionally Robust Optimization (DRO) framework, yielding a closed-form proximal update. Both SBM and DRO are informed by a persistence-based similarity matrix derived from zero-dimensional persistent homology ($H_0$), which translates the multiscale connectivity structure of the data into a pairwise topological prior. The overall optimization proceeds via Block Coordinate Descent; convergence is established through a global Lyapunov functional: the deterministic blocks satisfy monotonic descent, while the stochastic graph update satisfies descent in expectation, so that the expected energy converges. Experiments on synthetic datasets with non-convex geometries and on random subsets of Fashion-MNIST show that T-ARC recovers latent topological structures where K-means fails, achieving the highest accuracy on curved and interleaved clusters while remaining competitive, and markedly more stable than K-means, on real data.

We show how to compute the passivity radius of a given generalized state-space model of a rational transfer function that represents a passive system, both in the continuous-time and discrete-time cases. We then use this to construct robust descriptor realizations. For the continuous-time case, these realizations have a port-Hamiltonian descriptor form. For the discrete-time case a similar result holds for the so-called normalized realizations. The computation of such robust realizations is linked in both these cases to a particular solution of a linear matrix inequality that characterizes the passivity of the transfer function.

In federated averaging, local objectives can admit multiple optimal heads, making the aggregate depend on which heads clients return. We study this ambiguity in federated multivariate regression with private backbones and a shared linear head, using an unconstrained feature model (UFM) that treats training-sample features as free variables. We introduce a natural selection rule: each client returns the optimal head closest to the broadcast head. We show that global minimization with a vanishing proximal penalty on the head realizes this rule. When the clients' optimal Gram matrices and the initial shared Gram matrix are positive definite, the shared Gram matrix follows a closed recursion and converges to the unique Bures-Wasserstein barycenter of the clients' optimal Gram matrices. Even with this alignment, the limit generally differs from the centralized optimal Gram matrix. We decompose this gap into three positive-semidefinite terms arising from differences in client target means, covariance heterogeneity, and averaging the aligned heads. A correction based on a one-time exchange of target means and covariances recovers the centralized optimal Gram matrix in one round under exact local optimization and the same selection rule. We verify these results numerically in the UFM and test its predictions on five tabular and five image regression datasets using deep networks with feature regularization and long local training. In these experiments, ordinary training approaches the predicted barycenter, while a weak proximal penalty improves endpoint agreement and yields trajectories that closely follow the predicted Gram dynamics. The correction moves the final Gram matrices close to the centralized UFM prediction.

We resolve the Rademacher singularity conjecture: an $n\times n$ matrix with independent uniform $\{-1,1\}$ entries is singular with probability $(2+o(1))n^22^{-n}$. More generally, for an $n\times n$ matrix $M_n$ with independent entries uniform on a fixed set $S\subset\mathbb{R}$ of cardinality $q\ge2$, we prove $\mathbb{P}(s_n(M_n)\le z/\sqrt{n}) \le Cz+a_n(S)+C'n^{1+\varepsilon}q^{-n}$ for all $n\ge1$, $z\ge0$, and $\varepsilon>0$, with $C=C(S)$ and $C'=C'(S,\varepsilon)$. Here $s_n$ denotes the least singular value, and $a_n(S)$ is the sum of the probabilities of the events involving zero rows or columns and equal or opposite pairs of rows or columns.

These notes are based on a mini-course delivered at the Les Houches Summer School, Quantum Theory on All Scales, in August 2026. They introduce many-body localization to mathematicians, emphasizing the physical mechanisms that support or destabilize it. The mathematical discussion deals with how perturbative rotations, renormalization, and probabilistic estimates are used in a rigorous approach to many-body localization.

Topology and geometry are inseparable in physical networks. Here we show that, after factoring out the topology-dependent number of eligible edge pairs, exchangeability makes the mean crossing propensity of those pairs exactly graph independent while preserving topology in fluctuations. We derive a microscopic, parameter-free theory for the response when topology and geometry are coupled. Synthetic and real three-dimensional networks confirm that structure hidden from the normalized mean survives in correlations that determine response.

Rechtsrock is a subgenre of rock music that spreads right-wing ideology, often instrumentalized to recruit adolescents into the radical scene. Monitoring institutions counteract this by manually examining and, in some cases, banning extremist content; however, there are border cases that evade regulation. We present a study aimed at determining whether such a case, the band Frei$.$Wild, should be classified as politically right-leaning or as part of the general German rock genre. We sampled a German rock dataset and created a corpus for right-wing rock to use as reference in this analysis and found that we can confirm the intuitions from previous investigations that Frei$.$Wild successfully maintains an ambiguity with regard to their political affiliation. However, the tendency is towards the right-wing spectrum. Lexical analyses reveal nationalistic narratives and two high-performing classifiers (up to 97% ROC-AUC score) label more than half of their songs as right-wing extremist. Our analysis provides insight into how computational methods can improve the process of identifying right-wing extremist tendencies in music, especially in borderline cases like Frei$.$Wild. The code and data are made available for future research.

We study classical solutions of a scalar field with quartic potential in de Sitter space-time. Using the ansatz $\phi=F(X\cdot\xi)$, via embeding coordinate $X_\alpha$ of the ambiend space we find several families of analytic solutions classified by the causal character of the constant vector $\xi$. For time-like $\xi$, the solutions are globally regular and describe either global oscillations around a minimum or global vacuum transition; for space-like $\xi$, they are singular in the global patch but regular in the open slicing. In the Poincaré patch they correspond to contracting bubbles. We compute the classical actions of these solition which are finite only in spacetime dimensions $D \le 5$. We show that the $D=4$ global vacuum transition solution has the radiation equation of state $w=1/3$. In $D=4$ global vacuum transition solution, the retarded Green's function acquires a growing tail as compared to the Green's function on top of vacuum, implying that the transition amplifies the signal at late times.

Understanding randomness formation under conservation laws is important both for characterizing chaotic phenomena in isolated quantum systems and for symmetry-constrained quantum information processing. $U(1)$-symmetric random circuits on an $N$-qubit system provide a minimal tractable setting for this problem, in which the formation rate of unitary designs was conjectured to be governed by charge transport in the underlying circuit geometry. However, whether charge transport indeed sets the slowest relaxation mode has remained an open problem, due to the difficulty in deriving a tight lower bound on the symmetric design formation rate. In this work, we resolve this problem by determining the optimal scaling of the unitary $k$-design formation rate for $k\leq O(\sqrt{\log N})$ across a wide range of circuit geometries, including lattices, expander graphs, and all-to-all interactions. In particular, for $k\geq 2$, we find that the formation rate is governed by a two-particle encounter rate—the rate at which two random walkers encounter each other in a given circuit geometry. This encounter rate is parametrically smaller than the single-particle transport rate in many geometries, thereby disproving the previous conjecture. We further establish that this encounter mechanism indeed sets the design formation rate by deriving its matching lower bound with a novel proof technique based on an auxiliary subgroup ensemble. Although this encounter mode imposes a robust bottleneck on design formation in $U(1)$-symmetric random circuits, we also show that this bottleneck can be circumvented by using symmetry-breaking local gates and provide an explicit protocol that achieves faster design formation. These results establish a new picture of randomness formation under conservation laws and provide guiding principles for characterizing and efficiently generating symmetry-constrained randomness.

Quantum speed-ups have been obtained for many fundamental graph problems, including most variants of matching. A notable exception, however, is the maximum-weight perfect matching (MWPM) problem in general graphs with integer edge weights, which is arguably the most challenging variant of matching. We present a quantum algorithm for MWPM in general graphs that runs in $\widetilde{O}(n m^{2/3}\log W)$ time, where $W$ is an upper bound on the magnitude of the edge weights. This is an improvement over the best known classical combinatorial bound of $\widetilde{O}(m\sqrt n \log W)$ in the dense regime, where $m\ge n^{3/2}$. To the best of our knowledge, this is the first quantum algorithm to obtain an asymptotic improvement over the best classical combinatorial algorithm for the MWPM problem in general graphs. The running time of our method accounts for QRAM initialization and access overheads up to polylogarithmic factors, as well as all classical updates to the data structures. At a high level, our algorithm is based on a classical framework due to Duan, Pettie, and Su, but our algorithm requires replacing certain classical tasks with quantum methods, alternative analysis of classical procedures, and the use of alternative data structures that can be implemented effectively in the QRAM model.

This work proposes a mutual feedback architecture, MEQ, that refines the two inputs, of possibly different modalities, into a pair of coupled embeddings such that each embedding reflects the information of the other. The core idea is to incorporate continuous interchange of information between the two inputs. This idea leads to a mutual feedback architecture consisting of two components whose outputs are fed back into the other. The final output of this model is defined as the fixed point of this interaction. We provide theoretical analysis that offers interpretation of this model as well as design choices to prevent failure cases. We show the benefits of MEQ through classification and visual grounding tasks spanning various datasets. Quantitatively, our model outperforms or shows competitive performance on concatenation-based multimodal classification problems. Qualitatively, the proposed interactive mechanism allows the model to progressively refine the visual grounding when paired with complementary modality, thus demonstrating the power of mutual feedback under such settings.

We establish functional scaling limits and study first separation times for the interacting two elephant model studied by Aguech and Qin. In the joint diffusive regime, we give a direct martingale proof of convergence to a two-dimensional continuous Gaussian process represented by a matrix-kernel analogue of the noise-reinforced Brownian motion. We then investigate the difference process, whose diffusive scaling persists in the symmetric case even when the joint walk is critical or superdiffusive. For the first separation time of the two walks, we establish convergence in distribution to the first exit time of the limiting Gaussian process, together with convergence of all positive moments under diffusive scaling. We also obtain monotonicity results for the limiting exit time by combining explicit covariance identities with Anderson's inequality.

We study the Hilbert geodesic flow on a closed convex real projective $n$-dimensional manifold. We use the thermodynamic formalism for this dissipative Anosov flow to obtain a geometric description of the SRB measure. We also deduce new counting properties for the induced representations of the fundamental groups in $SL(n+1, \R)$.

Speech emotion recognition (SER) is the task of assigning emotion labels to utterances. Early systems relied on acoustic features, whereas recent approaches combine multiple modalities, most commonly speech and text. Still, performance remains poor on many datasets. Large language models (LLMs) have therefore attracted interest for SER, as they can process diverse inputs jointly with instructions. However, direct audio input raises questions of explainability. To address similar questions in image classification, concept bottleneck models were introduced. This work adapts concept bottlenecks to SER to examine how individual predictions depend on transcripts, acoustic descriptions and speaker attributes. Experiments test three LLMs on CREMA-D, IEMOCAP and MELD, with concepts extracted by separate tools. On scripted corpora, LLMs are strongly biased towards the transcript in the zero-shot setting, which lowers Macro-F1 from 27.8 to 5.8 on CREMA-D. Fine-tuning removes this bias, and the transcript raises Macro-F1 from 41.8 to 45.1. Removing speech rate changes 48% of Neutral predictions to Disgust on CREMA-D; removing intensity level on MELD changes predictions despite little change in Macro-F1. These findings show that aggregate performance changes alone do not capture the effects of concept removal on individual predictions.

The electron–electron Coulomb singularity forces cusp structure in electronic wavefunctions. This cusp structure limits wavefunction regularity and slows the convergence of expansions in smooth bases, requiring large basis sets to reach a target accuracy. The transcorrelated (TC) method incorporates this short-range behavior into the Hamiltonian, thereby improving the regularity of the transformed wavefunction and accelerating convergence toward the complete-basis-set limit. The resulting Hamiltonian is non-Hermitian and non-normal, which limits the direct applicability of standard quantum algorithms. For such non-normal operators, the complexity of several recent quantum algorithms depends explicitly on quantities related to eigenvector conditioning and eigenvalue sensitivity. Understanding these quantities is essential for assessing both algorithmic complexity and quantum resource requirements. In this work, we address these issues in two stages. We first study a solvable model, which provides a controlled setting for isolating how transcorrelation affects basis convergence and eigenvector conditioning. Within this setting, we investigate two distinct one-parameter Jastrow correlators. We derive the asymptotic energy-error scaling: $N^{-1/2}$ for the bare projection and $N^{-3/2}$ for both TC correlators at generic fixed parameters, with $N$denoting the basis size. Furthermore, we show that this faster convergence can yield a polynomial improvement in the asymptotic query-complexity upper bound. We then extend the analysis to second-quantized electronic-structure Hamiltonians and use particle-number-sector diagnostics to distinguish target-sector from auxiliary-sector conditioning. Our work provides a framework for understanding the central accuracy–cost trade-off in TC Hamiltonians.

Progressive autoregressive image codecs provide an appealing paradigm for generative compression by quantizing continuous latents into discrete tokens, transmitting coarse-to-fine prefix tokens and generating the remaining suffix tokens at the decoder. However, their reconstruction quality is fundamentally limited by two residuals introduced along this pipeline: the quantization residual, arising from information loss during discrete tokenization, and the generation residual, resulting from imperfect autoregressive generation of the suffix tokens. To address these limitations, we introduce ResARC, a residual-aware autoregressive codec that explicitly compensates for both residuals at the decoder. Specifically, we generate the quantization residual with a diffusion transformer conditioned on the autoregressive decoding context, while requiring no additional side information. In parallel, we compute the generation residual at the encoder and employ a learned Generation Residual Codec to efficiently compress and transmit it for decoder-side correction. The recovered residuals are then integrated with the reconstructed latent representation and decoded through an adapted VAE decoder. Extensive experiments demonstrate that ResARC achieves competitive perceptual similarity while substantially improving distributional fidelity over leading generative codecs across the ultra-low bitrate regime. Code and models will be released soon.

LLM-based agents extend their capabilities through third-party skills that provide task-specific instructions, scripts, and tool-use procedures. However, malicious instructions inserted into an otherwise benign skill can cause a benign user request to trigger dangerous Tool Calls, including data exfiltration, file deletion, or unauthorized code execution. This paper presents ActionGuard, which inspects skill-influenced Tool Calls immediately before execution. ActionGuard separates the target agent's action-generation context from the safeguard's authorization context. The target agent may use the original skill for planning, but the Reviewer does not receive the potentially poisoned raw skill text. Instead, it determines whether each action is justified by the trusted user request using a balanced skill profile, current and recent Tool Calls, and local script contents. ActionGuard intercepts each Tool Call at OpenClaw's before-tool-call stage and enforces the Reviewer's ALLOW or DENY decision under a fail-closed policy. We evaluate ActionGuard on 139 contextual and 180 obvious injections in a SKILL-INJECT-based setting against Dynamic Guardian and SkillGuard, using three open-source and two commercial Reviewer models. Each condition is repeated three times and evaluated using Attack Success Rate (ASR) and Task Success Rate (TSR). Overall, ActionGuard reduced ASR by 35.54 to 46.11 percent relative to existing safeguards and by 70.44 percent relative to No Safeguard, while maintaining high benign-task completion. These results show that execution-boundary authorization grounded in trusted user intent and runtime evidence can restrict unauthorized Tool Calls induced by skill injection.

Distributionally robust optimization (DRO) studies parameter estimation under uncertainty in the underlying probability distribution and has emerged as a principled framework for analyzing robustness and generalization. In particular, Wasserstein DRO, with distributional uncertainty induced by the Wasserstein distance, generalizes several popular regularizers. This paper studies Wasserstein DRO linear regression, unifying square-root Lasso and adversarial linear regression as important special cases. We prove that many properties of these two special cases carry over to this general method. In particular, we show (i) deterministic and non-asymptotic in-sample error bounds $O(n^{-1/2})$ in general and $O(n^{-1})$ under design matrix and sparsity conditions; (ii) insensitivity to the noise level, also known as the pivotal property; and (iii) solution equivalences for small and large ambiguity sets. The key proof step is to recast the method into a quadratic form, mimicking adversarial linear regression. We also show that the method can be solved efficiently, and we validate our findings through numerical simulations.