arXiv:2607.05776v1 Announce Type: new Abstract: Zero-knowledge proof systems rely on a trusted setup phase to generate a Common Reference String (CRS), yet existing approaches are typically static, one-time ceremonies that are inflexible and vulnerable to long-term compromise. Offloading continuous, recurring trusted setups to a decentralized Layer 2 (L2) network introduces a fundamental coordination challenge arising from the mismatch between high-throughput transaction processing and the multi-round requirements of trusted setup ceremonies. This paper presents an L2-coordinated framework that safely decouples transaction pipelines from ceremony execution to achieve automated, continuous CRS generation without centralized coordination. We design and implement two protocol variants over a decentralized, PBFT-coordinated ZK-rollup architecture: an on-chain smart contract approach and an asynchronous peer-to-peer consensus variant. Both designs utilize non-interactive zero-knowledge proofs of knowledge alongside commit-reveal structures to eliminate adaptive manipulation vectors and isolate ceremony latency. Experimental evaluations under simulated wide-area network constraints and adversarial conditions demonstrate that our architecture successfully isolates ceremony liveness. Continuous setups complete reliably within practical time bounds despite node dropouts or malicious contributions, while preserving stable L2 transaction throughput.
Science Journals
arXiv:2607.05810v1 Announce Type: new Abstract: Code generation with large language models (LLMs) remains unreliable because generated programs can appear correct while still violating key semantic requirements in the natural language specification. Existing feedback-based methods improve over coder-only generation, but they often rely on unstructured critique or execution signals that do not explicitly identify what the code is semantically missing. We present SCOPE, a prover-initialized subgoal critic for code generation. SCOPE adapts a Lean-oriented prover model to produce three parseable feedback fields for downstream code generation: subgoals, gap analysis, and a robustness checklist. Our approach combines supervised fine-tuning, process-aligned reinforcement learning (RL), and feedback-guided inference, with two complementary rewards during RL: a dense reward for structured critique quality and a sparse reward based on whether the critique improves the coder's execution score. Experiments show that SCOPE improves over the compared feedback baselines. On LiveCodeBench V6, SCOPE achieves 39.4% pass@1, compared with 36.6% for Reflexion and 20.6% for the coder-only baseline. On BigCodeBench (Hard), it reaches 42.6%, surpassing Reflexion at 36.5% and coder-only generation at 34.5%. Further analysis shows that SCOPE's gains are concentrated in tasks with concrete semantic constraints and that its code corrections are more localized than Reflexion's.
arXiv:2607.06055v1 Announce Type: new Abstract: We present NEST (Nested Episodic State Topology), a foundational graph-theoretic representational ontology for modeling cognition as structured state formation and transformation rather than as a finished empirical model. Concepts, episodes, percepts, and task contexts are represented as typed, weighted graphs whose nodes may carry internal subgraph payloads; edges are typed under six relation classes -- causal, containment, temporal, associative, evidential, and spatial. Durable belief graphs are separated from capacity-limited working-memory graphs that may host transient non-belief content. WM-belief grounding, conflict catalogs, and belief-update operators specify how transient structure is tested against stored knowledge and how belief is revised. A reusable operator toolkit -- activation, graph-property functionals, working-memory transitions, awareness and trajectory functionals, and belief update -- organizes the formal core. Derived diagnostics such as fragmentation, involvement, signed evaluation, coherence, and active conflict define familiar phenomena in the same ontology; self-related processing is modeled through designated self-image subgraphs within belief. Subsequent sections instantiate this core without new primitives: phenomena signatures, a task-instantiation schema for action selection and failure modes, and compatibility mappings that embed ACT-R, Soar, Sigma, the Common Model of Cognition, Global Workspace Theory, semantic networks, Theory-Theory, and chunking as constrained regions of one language. Mappings constitute the culminating technical section; discussion addresses scope, limitations, and open research directions. The contribution is intentionally foundational: a transparent representational substrate for later empirical, computational, and domain-specific work.
arXiv:2607.06150v1 Announce Type: new Abstract: Reliable seam segmentation is essential for autonomous robotic welding in construction, where harsh illumination, specular reflections, and thin weld geometries often degrade segmentation performance. This study proposes a reflection-robust seam segmentation framework that enhances a BiSeNetV2 backbone through transfer learning and a hybrid Cross-Entropy--Lov\'asz loss. Rather than increasing architectural complexity, the proposed framework improves reflection robustness through learning-stability-oriented optimization. Experimental results show that the proposed method achieves 81.76\% Joint IoU and 90.73\% mIoU, improving Joint IoU by +22.36 percentage points over the OHEM-based baseline while maintaining identical FLOPs, parameter count, and inference speed. The proposed approach also recovers 96.33\% of severe zero-IoU failure cases under reflective conditions. Comparative experiments across BiSeNetV2, DeepLabV3+, UNet, and SegFormer further demonstrate that the proposed optimization strategy is particularly effective for lightweight real-time segmentation architectures. Qualitative analyses additionally show improved seam continuity and reflection robustness in challenging welding environments. These findings suggest that the proposed framework provides a practical and lightweight perception solution for robotic welding applications involving reflective metallic surfaces.
Boundary-preserving hp interpolation and p-robust discrete harmonic extensions on tetrahedral meshes
arXiv:2606.02086v3 Announce Type: replace Abstract: We construct a boundary-preserving hp interpolation operator on three-dimensional tetrahedral meshes with locally variable polynomial degrees. If the trace of an H^1 function on the prescribed Dirichlet boundary is already a piecewise polynomial trace of the finite element space, the interpolant preserves this trace exactly and satisfies the standard local h_K/p_K approximation estimates. The statement follows the scaling form of Melenk's hp quasi-interpolation for nonsmooth functions. As a consequence, a discrete trace is extended by first applying the continuous trace theorem and then applying the boundary-preserving interpolant; the corresponding discrete harmonic extension is bounded by variational comparison. The proof of the interpolation theorem uses local polynomial trace liftings on tetrahedral boundary layers, nonsingular vertex patches, and a variable-degree tetrahedral projection. These auxiliary liftings are also stable in scaled boundary-layer norms.
arXiv:2606.02125v2 Announce Type: replace Abstract: Trace-compatible polynomial extensions are a recurring local ingredient in high-order finite element analysis on conforming hexahedral meshes. They are needed whenever prescribed edge and face traces must be preserved while a polynomial is extended into a neighboring cell or boundary patch. The main contribution of this paper is the construction of p-robust polynomial liftings on nonsingular conforming hexahedral boundary patches, with stable control of both the H^1 norm and the H^1-seminorm estimates needed for energy arguments. These liftings imply H^1-seminorm stable discrete harmonic extensions of polynomial Dirichlet traces. They also serve as boundary corrections for the conforming hp Clement interpolant, yielding trace-preserving interpolation operators for functions with only H^1 regularity. Under the uniform boundary-degree condition the constants are p-uniform; in the non-uniform case the stated logarithmic loss appears. We also treat meshes that may contain conforming singular boundary patches, where the loss remains polylogarithmic in the maximal local degree. Trace-preserving interpolation on reference cells and vertex-supported decompositions are developed as local tools for these patch and mesh-level constructions.
arXiv:2606.03141v3 Announce Type: replace Abstract: We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of conforming reaction-diffusion and fitted-interface problems. On conforming simplicial meshes, an owner-selected Falk--Winther bubble transform gives $L^2$- and $H^1$-stable components with constants independent of the mesh size, the local polynomial degrees, and the degree distribution. Minimal-degree owners preserve arbitrary variable-degree spaces with $p_K\ge1$, while coefficient-adapted owners yield weighted estimates under local chain conditions. Combined with a weighted continuous piecewise affine extraction, this gives $hp$-uniform Schwarz preconditioners for conforming reaction-diffusion problems with locally comparable coefficients, and a coefficient-weighted conforming variant in the uniform-degree case. For three-dimensional fitted-interface problems, we use a symmetric Nitsche discretization on a tetrahedral mesh fitted to a piecewise planar interface. Surface jump components are lifted into the side selected by the penalty scaling using patch-level $p$-robust trace liftings. The conforming remainder is decomposed by the low-order extraction and a weighted one-sided bubble transform. Grouping the resulting components by vertices yields a practical vertex-patch Schwarz preconditioner whose condition number is independent of the mesh size, local polynomial degrees, diffusion contrast, and coefficient magnitudes under a common-degree condition on interface-touching tetrahedra. Numerical experiments for pure diffusion problems support the theory and suggest robustness beyond the common-degree assumption.
arXiv:2606.03921v2 Announce Type: replace Abstract: Converting multi-view RGB observations into simulation-ready 3D environments remains challenging because current reconstruction pipelines produce monolithic scene representations without explicit physical structure. They are typically defined up to an arbitrary global rotation and entangle rigid foreground objects with background geometry, which hinders stable physical interaction. Existing solutions often recover interactivity by replacing reconstructed objects with retrieved CAD assets, but this introduces a slow retrieval-and-replacement stage and weakens scene-specific geometric fidelity. We propose GARDEN, an RGB-only framework that reformulates reconstruction as physically-grounded scene factorization and outputs a structured hybrid scene representation. The key idea is to use gravity as a universal physical prior: we first align the reconstruction to a unified Gravity-View frame to resolve gauge ambiguity, then recover object-centric rigid meshes with accurate 6-DoF placement, and finally remove duplicate object geometry from the background through conditional 3D point classification. The resulting representation combines explicit rigid bodies with a decoupled background, enabling direct physics simulation while preserving visual realism. Experiments on both simulated and real multi-view scenes show that GARDEN improves object placement reliability, disentanglement quality, and rendering-simulation efficiency compared with retrieval-based baselines. Project page: https://sunjiahaovo.github.io/garden/
arXiv:2606.03949v2 Announce Type: replace Abstract: Human-in-the-loop reinforcement learning (HIL-RL) improves sample efficiency in real-robot manipulation through online human intervention. However, successful trajectories may include suboptimal actions that deviate from the desired task-execution path and force human intervention. Existing HIL-RL methods typically apply the consistent credit assignment principle to all transitions, uniformly propagating discounted terminal rewards through suboptimal segments, ignoring the actual contribution of each transition to task success. This overestimates Q-values for critic learning and indirectly misguides actor updates toward suboptimal behavior patterns. To this end, we propose PACT, a Preference-calibrated Actor-Critic Training framework that leverages the implicit preference signals induced by intervention to perform credit reassignment on identified suboptimal segments while directly guiding policy training for unbiased critic-actor learning. Specifically, we first design a progress model that learns from human demonstration and identifies suboptimal segments for credit correction. Then, from the human action and resampled policy action at the intervention state, we build preference pairs to define a counterfactual advantage that penalizes Bellman targets of the identified suboptimal segment, enabling directional credit calibration. Moreover, we directly align the policy with human corrective actions in the bounded mean space, providing an additional signal beyond critic-guided updates. Across five real-robot manipulation tasks, PACT improves the average success rate by 24.5% and achieves 1.3 times faster convergence, thereby improving both RL sample efficiency and performance. Code is available at https://anonymous.4open.science/r/HILRL-A1X-BC05.
arXiv:2606.04935v4 Announce Type: replace Abstract: Active inference casts decision-making as inference, with the Expected Free Energy (EFE) unifying goal-directed and information-seeking behavior. Recent work showed that EFE minimization can be written as Variational Free Energy (VFE) minimization on a generative model augmented with epistemic priors. We prove that the VFE of the augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent. We then show that proper EFE-based planning requires combining these epistemic corrections with a planning correction that turns marginal inference into policy optimization, yielding a full variational characterization of EFE-based planning. This clarifies which corrections are needed for cross-entropy planning and for full EFE-based planning. The same entropy-corrected formulation leads to a detailed message-passing scheme for EFE-based planning together with simpler ablations. Experiments on three grid-world environments show that full EFE-based planning outperforms ablations that omit either the planning correction or the epistemic corrections.
arXiv:2607.05861v1 Announce Type: new Abstract: Large reasoning models (LRMs) improve language model capabilities by generating explicit thinking traces before final answers. In factuality-oriented question answering (QA), such thinking often improves overall performance by helping the model recover relevant knowledge and refine its answers. However, we find that this benefit is not uniform at the instance level: explicit thinking can also overturn correct non-thinking answers and lead to factual drift. We refer to this failure mode as \emph{thinking-induced hallucination}. To explain this phenomenon, we formulate explicit thinking in factuality QA as a thinking residual over the model's direct-answer tendency, which can either recover missing knowledge or introduce unsupported associations. Based on this formulation, we propose MARGO, \underline{\textit{M}}ixed-Mode \underline{\textit{A}}dvantage \underline{\textit{R}}egularization for \underline{\textit{G}}rounded \underline{\textit{O}}ptimization, a reinforcement learning framework that uses non-thinking rollouts as same-model references in advantage estimation. By constructing mixed-mode rollout groups with both thinking and non-thinking trajectories, MARGO evaluates whether explicit thinking adds factual value beyond direct answering, thereby suppressing hallucination-prone thinking while preserving beneficial thinking behaviors. Experiments across multiple factuality-oriented QA benchmarks demonstrate that MARGO improves factual reliability over strong baselines, while evaluations on mathematical benchmarks show that it preserves general reasoning ability.
arXiv:2607.05864v1 Announce Type: new Abstract: In the field of multivariate time series anomaly detection, against the backdrop of increasing data complexity and complex dependencies across multiple temporal scales, traditional methods often struggle to simultaneously capture temporal dynamic features and intricate inter-series correlations. To address this, we propose an innovative framework, MSCENet, which leverages advanced spatio-temporal learning and multi-scale learning techniques to enhance detection accuracy. MSCENet includes a fine-grained temporal convolution module that captures complex temporal dependencies through dilated convolutions, enabling the detection of both short- and long-term patterns. Additionally, the framework models inter-series relationships as a graph structure, using Mixhop graph convolutions to adaptively capture spatial dependencies across varying time scales. To support robust anomaly detection, the multi-scale gated convolution module in MSCENet integrates spatial and temporal attributes through gated mechanisms, facilitating the detection of subtle variations across multiple scales. Experimental evaluations on real-world datasets: SMD, PSM, and SWaT. It provides an adaptable and high-performance solution for anomaly detection in complex time series data environments.
arXiv:2607.06192v1 Announce Type: new Abstract: Virtual admittance (VA) is widely used in cascaded voltage-control and current-control (VC-CC) grid-forming inverters (GFMIs) because it shapes the converter terminal behavior while preserving the current-regulation path required for current shaping and limiting. However, the achievable VC-loop bandwidth remains strongly coupled to the CC-loop bandwidth and to the VA parameters. Voltage-feedback decoupling (VFD) is commonly used to relax this coupling, but in VA-based control its benefit is not unconditional. This paper shows that unity-gain VFD, which represents the full-decoupling condition, removes the low-frequency restoring term associated with the filter capacitor and drives the voltage loop toward a delay-sensitive double-integrator structure. This internal-stability limitation is referred to here as the VFD trap. To address this trap without attenuating VFD, a proportional active-damping (AD) path is proposed, implemented as negative capacitor-voltage feedback in the current-reference path. The proposed path restores the missing low-frequency support while retaining unity VFD and introduces an additional AD-based degree of freedom for VC-loop tuning. A minimum support condition, a delay-aware phase-margin expression, and compact forward/inverse design equations are derived for operating-point selection. Standalone and grid-connected experiments on a 3-kVA prototype verify the analysis, showing that the proposed path recovers stable unity-VFD operation, reduces the voltage-step settling time from approximately 9~ms to 3~ms, and maintains stable power injection.
arXiv:2607.05868v1 Announce Type: new Abstract: Designing cost functions of adaptive steganography traditionally requires extensive manual tuning, while deep learning methods lack interpretability. Although large language models (LLMs) offer an automated alternative via evolutionary generation, they often violate domain specific mathematical constraints due to a lack of explicit domain knowledge. To address this problem, we propose a novel evolutionary system focused on exploiting Retrieval-Augmented Generation (RAG) enhanced LLMs for the automatic code-level generation of spatial steganography cost functions. This system incorporates a core Self Evolving RAG (SE-RAG) module, wherein a Code Semantic Signature (CSS) translates procedural code into aligned queries, retrieving explicit guidance from static literature and dynamic experience knowledge bases to steer the LLM generation process. A dedicated feedback mechanism then continuously refines the dynamic knowledge base with successful optimization strategies. Extensive experiments on the BOSSBase and BOWS2 datasets demonstrate that the proposed framework consistently achieves higher steganographic security than existing automatically designed methods, and increases the average code execution rate by 46.3% while reducing the search cost by 26.1%, thereby highlighting the effectiveness, efficiency, and potential of combining LLMs with domain-specific knowledge in the field of automatic steganographic algorithm generation.
arXiv:2606.05615v2 Announce Type: replace Abstract: We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces, with arbitrary fixed Sobolev order k >= 1, on fitted interface meshes. The cells are coordinate-compatible cuboids, the local spaces are Q_{p_K}(K) with arbitrary elementwise degrees satisfying p_K >= 2k-1, and the coefficient may have arbitrarily large jumps across material interfaces. Under local coefficient oscillation bounds and a local high-side connectivity condition, both the conforming H^k space and the nonconforming spaces V_h^{(s)}, 0 <= s <= k, admit stable decompositions with constants which may depend on the fixed parameters d and k, but are independent of the mesh size, all polynomial degrees, neighboring degree ratios, and the global coefficient contrast. The argument combines a Hermite endpoint transform for endpoint jets of order 0,...,k-1, its tensor-product extension, weighted broken patch Poincare inequalities, and a successive correction of normal derivative jumps. Numerical experiments for a three-dimensional DG problem with large coefficient jumps and strongly varying local polynomial degrees support the predicted robustness. For k = 1 the same conclusions hold on uniformly regular mapped cubical meshes whose neighboring element maps agree on each common face.
arXiv:2606.06576v2 Announce Type: replace Abstract: In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples. Multi-output Gaussian processes excel in low-data regimes but typically struggle with high-dimensional outputs. Compress-then-predict pipelines such as PCA-GP (principal component analysis plus Gaussian process regression) handle high dimensionality, but rely on bases optimized for reconstruction rather than prediction. To address this gap, we propose a model that represents each output as a linear-Gaussian decoding of a low-dimensional latent state drawn from a Gaussian process prior. By analytically marginalizing the decoder weights, we couple compression and prediction in a single objective that scales to high-dimensional outputs. We refer to this model as Gaussian process latent factor regression (GPLFR). We demonstrate GPLFR by building the first spatially resolved emulator of global climate models for rocky exoplanets.
arXiv:2606.08343v3 Announce Type: replace Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space. Existing structure-preserving neural operators enforce at most a single conservation law or reversible (Hamiltonian) structure, while thermodynamically consistent learning has been confined to finite-dimensional, graph, or particle systems. GENERIC-FNO closes this gap: it learns the energy and entropy functionals as neural operators and parameterizes the Poisson and friction operators as diagonal Fourier multipliers sandwiched between rank-one projections that enforce the degeneracy conditions exactly, by construction, with no penalty term, update projection, or residual. The degeneracy identities hold to machine precision (residuals ~10^-13) for any initialization, dimension, or resolution, so the continuous-time dynamics conserve the learned energy and produce entropy exactly; the explicit time stepping adds only a small O(dt^2) drift (per-step residual ~10^-6). We further note that the (E,S,L,M) decomposition of a given flow is not unique, and introduce a gauge-invariant dissipation diagnostic separating reversible from dissipative dynamics independently of the learned functionals. Across three operator backbones (1D/2D FNOs and DeepONet) and four PDEs spanning reversible, dissipative, and mixed regimes, GENERIC-FNO preserves its exact structural guarantees zero-shot across a 4x super-resolution range (64 to 256), recovers the ground-truth ordering of physical dissipation, and is competitive with strong unconstrained and energy-penalized baselines, outperforming them on several dissipative and mixed problems at comparable or fewer parameters.
arXiv:2606.08516v2 Announce Type: replace Abstract: The main ingredient of this paper is an edge-local variable-degree projection on a triangle that is uniformly stable in both L2 and H1. We use this two-dimensional operator in two tetrahedral constructions. First, on a reference tetrahedron, we build an H1-stable projection from a high order polynomial space onto a variable-degree space whose degrees are prescribed independently on edges, faces, and in the volume. Since the tetrahedral projection is local and trace-compatible, it also gives an h- and p-uniform stable decomposition, in the weighted energy norm, for conforming hp spaces, and hence a uniform additive Schwarz preconditioner for the conforming Laplace operator. Second, on a uniformly regular mapped tetrahedral mesh with elementwise variable polynomial degrees, the same triangular projection gives the finite-layer edge truncation needed in a p-uniform stable DG-to-CG decomposition for the symmetric IPDG norm. The DG-to-CG decomposition, combined with the conforming splitting, gives the IPDG preconditioner. The constants depend only on reference shapes, the local degree-spread bound within each tetrahedron, the neighbor-degree bound across mesh faces, uniform map-regularity, patch cardinalities, and the coefficient path constants; they are independent of h, of the local polynomial degrees, and of the coefficient contrast.
arXiv:2606.08671v3 Announce Type: replace Abstract: Agent skills extend language-model agents with task-specific procedures, scripts, and references, but the tasks and environments they target continually change. Existing methods improve skills in bounded runs and retain only the final artifact, discarding the decision history that later agents need to interpret prior revisions, evaluations, and rejected alternatives. We introduce SkillHone, a harness for continual agent skill evolution grounded in persistent decision history. SkillHone pairs skill revisions with evaluation-side evidence that supplies practice feedback, recording structured histories of diagnoses, revisions, evidence, and outcomes. Role-separated subagents run candidate skills on practice probes with redacted reporting and propose revisions informed by prior decisions, enabling cross-session refinement without rediscovering past rationale. On deep-research benchmarks, SkillHone runs without a pre-integrated search stack and outperforms the commercially backed deep-research agent by 15.8 points on GAIA and 3.2 points on WebWalkerQA-EN, while also exceeding prior skill-evolution methods. We further deploy SkillHone on internal tool-mediated analysis scenarios, where it improves accuracy by an average of 18.8 points across seven settings.
arXiv:2607.06120v1 Announce Type: new Abstract: Text-to-image diffusion models have achieved high visual fidelity and broad adoption, but remain vulnerable to safety violations when adversaries exploit them to synthesize illicit content. Existing alignment paradigms, from input sanitization to structural feature pruning, are largely organized around unsafe concepts explicitly exposed during filtering, editing, or localization. This leaves a blind spot for visual synonym attacks (VSA), a jailbreak where benign-looking prompts elicit prohibited imagery through implicit visual associations. As a result, current defenses face a safety-utility dilemma: they may either under-mitigate VSA threats or over-suppress visually similar benign concepts. The core challenge is that VSA hides the unsafe target at the textual surface while revealing it through generation-time visual-semantic convergence. In this work, we therefore shift from static suppression of pre-specified unsafe concepts to dynamic tracing of how unsafe semantics emerge during generation. Our mechanistic analysis shows that VSA and explicit unsafe prompts converge through sparse semantic-injecting attention heads, which serve as inference-time bottlenecks for prohibited visual semantics. Based on this insight, we propose AEGIS (Adaptive Evasion Guard via Identification and Steering), an inference-time defense that applies similarity-aware repulsion only at the identified vulnerable heads. Evaluated against 16 baselines, AEGIS improves both safety and utility. On SD 1.4, it reduces ASR to $\mathbf{0.00}/\mathbf{0.03}$ for in-domain violence/nudity VSA and achieves ASRs $\le \mathbf{0.09}$ on out-of-domain explicit and adversarial attacks. It preserves benign fidelity, avoids suppressing hard-negative concepts, and transfers to SD 2.1 and FLUX.1 after re-identifying the critical heads for each backbone.
arXiv:2607.05559v1 Announce Type: new Abstract: Foundation machine learning force fields (MLFFs) such as MACE-MP-0 and UMA cover broad chemical space at near density functional theory (DFT) accuracy. However, they assume equilibrium ground-state physics and do not natively handle externally induced changes to the electronic state, such as charging, applied fields, or electronic excitation, which limits their use for driven processes such as photoexcitation and charge injection. We propose EquiFiLM, a lightweight extension that adds continuous external conditioning to any equivariant foundation MLFF via a per-layer Feature-wise Linear Modulation (FiLM) block, learning externally driven changes to the potential energy surface from minimal training data. The block modulates only scalar channels and preserves E(3)-equivariance exactly. We demonstrate the recipe on charged liquid water with the foundation model MACE-MatPES as the backbone, yielding E-MACE. On the four training charges, E-MACE delivers a $3.1\times$ reduction in force RMSE ($21.3$ to $6.96$ meV/$\mathring{A}$) and a $61\times$ reduction in per-atom energy RMSE ($6.1$ to $0.1$ meV/atom) over a baseline without EquiFiLM trained on the same data, at indistinguishable inference cost. Across seven held-out interpolation and extrapolation charges, force RMSE stays within $18-61$ meV/$\mathring{A}$ and energy RMSE within $0.7-5.4$ meV/atom. The model runs stable molecular dynamics across the full range tested and predicts the charge-dependent first-shell response of the reduced pair distribution function probed by ultrafast electron diffraction. Adding this conditioning axis to the foundation requires only a few thousand DFT-labeled frames, against the $\approx 10^8$ structures of a charge-aware foundation trained from scratch. The recipe is backbone- and conditioning-agnostic: it applies without architectural change to any equivariant MLFF with scalar interaction-layer channels.
arXiv:2607.06392v1 Announce Type: new Abstract: Self-supervised learning (SSL) models, such as Wav2Vec2, HuBERT, and WavLM, have become foundational across a wide range of speech and audio tasks. Despite their success, understanding their internal layer-wise dynamics remains an ongoing challenge. To address this, we propose a two-part model-centric framework called InsideSSL. First, we establish a task-agnostic analysis from three intrinsic per-layer perspectives: compression (entropy), geometry (curvature), and robustness to perturbations. We show that varying training objectives induce distinct regimes of acoustic compression and manifold unfolding. Second, we introduce the cross-layer Generative Compatibility Matrix (GCM) to evaluate functional transferability, exposing stable phonetic cores, identity volatility, and deep-layer semantic pruning. In addition to these evaluations, linear probing connects the model-centric perspective to downstream tasks, demonstrating how layer topology dictates phoneme, pitch, and speaker encoding.
arXiv:2607.05450v1 Announce Type: new Abstract: This paper explores the "Granularity Paradox" in time-series forecasting, wherein finer temporal disaggregation (e.g., Monthly to Weekly/Daily) improves in-sample diagnostics and dataset size (N), but degrades out-of-sample accuracy due to recursive error compounding over longer horizons (H). Conversely, coarse aggregation (Annual) eliminates recursive error propagation but reduces data available to estimators. We formalize this trade-off and benchmark 10 models - spanning na\"ive, statistical, machine learning, and deep learning architectures - across six granularities using a 13-year public procurement dataset. The empirical results reveal a non-monotonic threshold structure: recursive autoregressive and seasonal models degrade substantially under high-frequency forecasting (e.g., Holt-Winters reaches a Test R-squared of -151 and TPFE of 425.85% at the Daily grain), while the LSTM traces a U-shaped error curve, worsening from Monthly (19.66%) through Bi-Weekly (35.94%) before overcoming the error propagation penalty at Daily (TPFE of 4.35%, R-squared of 0.66). Linear Regression remains stable across all granularities (16.3-17.0% TPFE), confirming that the paradox is driven by recursive feedback topology, not model complexity. The results demonstrate that standard pointwise metrics (RMSE, MAE) systematically mask cumulative error propagation, and that evaluating forecasts without goal-dependent cumulative metrics produces misleading assessments of model adequacy. We introduce a consensus-dissensus diagnostic comparing the directional behaviour of pointwise metrics against cumulative TPFE across granularities, enabling the identification of models whose standard diagnostics mask systematic error propagation.
arXiv:2607.06453v1 Announce Type: new Abstract: Low-rank tensor methods are an important tool in the numerical treatment of equations with a high-dimensional state space. Nearest neighbor interaction systems like the Ising model or more general Markov jump processes, as well as 1D finite-state quantum systems are examples of such problems. While low-rank tensor train/matrix product state models have been shown to be highly efficient for the simulation of such systems, providing theoretical justification for this remains a challenging task. One approach for obtaining estimates on required ranks for certain accuracies is to investigate the rank increase in Krylov subspace methods for solving the problem at hand. In the context of area laws for ground states of 1D spin systems, nontrivial results on rank-increasing properties of nearest neighbor operator polynomials have been obtained in work of Arad et al. [arXiv:1301.1162] by studying the partial commutativity of local operators. In the present work, this technique is applied to polynomial methods for definite linear equations and dissipative linear ODEs with nearest neighbor structure. This allows to derive corresponding low-rank approximability statements for solutions of such problems which are independent of the system size. Numerical simulations of high-dimensional nearest neighbor systems illustrate the theoretical findings.
arXiv:2607.06458v1 Announce Type: new Abstract: The analytical modeling of a plasma wakefield driven by a relativistic proton beam is an element in optimizing advanced plasma-based acceleration schemes. In this work, we present a 1D nonlinear fluid framework under the quasi-static approximation to describe the wake potential excited by a positively charged proton driver. We examine our model using a two-bunch pump-probe configuration, demonstrating close agreement between the analytical invariants and adaptive numerical integrations. The distinct geometric curvature changes observed at the micro-bunch boundaries are shown to be physical consequences of step-discontinuities in the second derivative of the wake potential across the beam interfaces. Furthermore, by scaling this numerical framework to a train of $N=100$ micro-bunches undergoing seeded self-modulation (SSM), we model the physical parameters of the CERN AWAKE facility ($n_0 = 7.0 \times 10^{14}\text{ cm}^{-3}$). Our model replicates the characteristic linear growth envelope and matches the calibrated field envelope boundaries of approximately $\pm 0.75\text{ GV/m}$ inferred from the experiment. This piece-wise framework provides a computationally efficient foundation for investigating customized, asymmetric micro-bunch profiles designed to optimize the transformer ratio beyond the fundamental symmetric limit of 2.