arXiv:2208.00859v2 Announce Type: replace Abstract: We propose a novel method enabling autocompletion of chemical flowsheets. This idea is inspired by the autocompletion of text. We represent flowsheets as strings using the text-based SFILES 2.0 notation and learn the grammatical structure of the SFILES 2.0 language and common patterns in flowsheets using a transformer-based language model. We pre-train our model on synthetically generated flowsheet topologies to learn the flowsheet language grammar. Then, we fine-tune our model in a transfer learning step on real flowsheet topologies. Finally, we use the trained model for causal language modeling to autocomplete flowsheets. Eventually, the proposed method can provide chemical engineers with recommendations during interactive flowsheet synthesis. The results demonstrate a high potential of this approach for future AI-assisted process synthesis but also reveal the limitations at the present state and the next steps that need to be taken to deploy this technique in realistic flowsheet synthesis scenarios.
Science Journals
arXiv:2606.09296v1 Announce Type: new Abstract: Constraining the physical properties of Earth's deep interior, particularly the viscosity of the solid inner core and the density structure of large low-velocity provinces (LLVPs), remains a major challenge in geophysics. Here we develop a unified dynamical framework that combines mantle-inner core gravitational coupling (MICG) with torsional oscillations in the fluid outer core and show that their interaction can produce a distinct and testable geodetic signature. Guided by this prediction, we analyze satellite gravity observations together with independent corrections for surface mass variability. We identify a robust approximately 6-year signal in the Stokes coefficient Delta S22, while no corresponding stationary signal is detected in Delta C22. A signal with the same periodicity is independently detected in length-of-day variations (Delta LOD), and the two signals exhibit a near anti-phase relationship. Interpreting this coupled signature within the proposed framework allows us to constrain the inner core viscosity to approximately 4.6 (+/- 1.8) x 10^16 Pa s and the equatorial relief of the inner core boundary to a semi-axis difference of about 200 +/- 70 m. The inversion further indicates mean density anomalies of +5.5 (+/- 0.6) per mil at the base of LLVPs. These results indicate that satellite gravimetry provides a direct observational window into deep-Earth dynamics and the physical properties of Earth's deep interior.
arXiv:2606.09298v1 Announce Type: new Abstract: The Parker transport equation (TPE) has been the equation of choice for the past 60 years in studies of galactic cosmic ray (GCR) modulation. Conversely, the focused TPE describes the same processes on a more fundamental level than the Parker TPE by modelling an anisotropic distribution rather than an isotropic one. It is usually assumed that the Parker TPE is valid for modelling GCRs, but the two TPEs have not been tested against each other in this context. We conduct a first-of-its-kind comparison of these TPEs without particle drifts to test whether they produce the same results under identical diffusion conditions. A new model for protons during solar minimum conditions is developed to numerically solve the TPEs using stochastic differential equations. The TPEs are designed to be as consistent as possible for diffusion by normalising the pitch-angle-dependent diffusion coefficients (DCs) used in the focused TPE to the isotropic DCs used in the Parker TPE. The Parker TPE overestimates the GCR intensity at Earth's orbit for low energies by ~30%, and by ~40% over the poles. This stems from a small first-order anisotropy caused by particle fluxes over the poles. Particles gain easier access to the inner heliosphere by streaming in over the poles, where pitch-angle scattering is generally weaker, and the magnetic field is typically less wound. The focused TPE also yields nearly identical results for different pitch-angle dependencies of the DCs. The description of particle streaming and weak pitch-angle scattering as effective parallel diffusion in the Parker TPE makes it overly diffusive. This suggests that DCs derived from fitting the Parker TPE to observations are likely underestimated. Furthermore, GCR spectral and anisotropy data alone cannot distinguish between scattering theories with similar mean free paths but different pitch-angle dependencies.
arXiv:2606.09617v1 Announce Type: cross Abstract: The rapid expansion of AI globally has led to the proliferation of energy-intensive hyperscale data centres (DCs), making them as a structurally challenging component in power system planning and operation. Using a spatially explicit optimisation model of Europe across 21 AI growth scenarios, we systematically quantify additional demand, capacity requirements, emissions, and operational impacts of DCs. Results indicate that AI could drive 73-723 TWh of extra demand by 2050, risking cumulative emissions overshoots of 67-181 MtCO2 between 2030 and 2050. Our analysis indicates that after 2030, the geography of AI infrastructure will be shaped more by firm power and system flexibility than by the mere abundance of clean energy. In moderate scenarios, AI requires an additional of 200 hours of firm generation, which increases LCOE by 35 EUR/MWh in key hubs. We show that even under the pessimistic scenarios, existing infrastructure would require 70 GW additional capacity, while under managed growth pathways, this expansion could reach 226 GW. We further find DCs workload dynamics strongly shape energy dispatch, system flexibility, and emissions, while improved efficiency significantly reduces capacity needs, and system peaks. While our findings suggest that net-zero targets for 2050 may be achieved, critical emission risks may appear in the intermediate years, and the EU may compromise its carbon-neutral goals unless policies adapt to this accelerating digital transformation.
arXiv:2606.09785v1 Announce Type: cross Abstract: A biclique decomposition of a graph is a partition of its edges into complete bipartite subgraphs. We consider graphs whose vertices can be ordered such that the neighborhood of every vertex is the union of a sublinear number of intervals. We observe that these graphs admit compact representations in the form of biclique decompositions of small size. Here, the size of a decomposition is measured as the sum of the number of vertices of its bicliques. Combining this result with the existence of suitable vertex orderings for graphs of low neighborhood complexity, as proven by Welzl in 1988, we recover and extend several known results up to logarithmic factors. These results include upper bounds on the Zarankiewicz problem, matrix multiplication, quantum circuit complexity, and shortest path algorithms in ``well-structured'' instances.
arXiv:2512.07248v2 Announce Type: replace Abstract: Physics-based motion imitation is central to humanoid control, yet current evaluation metrics (e.g., MPJPE) only quantify imitation outcomes, not their underlying causes. This conflation obscures a critical diagnostic question: when imitation error occurs, does it stem from policy limitations or the intrinsic learning difficulty of the target motion? To resolve this ambiguity, we propose the Torque Variation Score (TVS), a physics-grounded metric that quantifies the inherent learning difficulty of a motion independently of any policy's performance. TVS measures the magnitude of torque variation required to correct small pose perturbations, directly capturing how dynamical properties shape the reinforcement learning landscape. We establish that high-TV motions induce flat reward landscapes and vanishing policy gradients, explaining persistent imitation failures. Extensive experiments with state-of-the-art methods (UHC, PHC+) confirm TVS strongly correlates with imitation error and enables principled error attribution: high error on low-TV motions indicates policy deficiency, while high error on high-TV motions reflects fundamental learning constraints. Beyond error diagnosis, TVS facilitates three practical applications: Maximum Imitable Difficulty (MID) for policy capability assessment, Difficulty-Stratified Joint Error (DSJE) for granular performance profiling, and Flawed Motion Detection for identifying segments with abnormally high learning difficulty to support mocap data curation and quality control. TVS provides a rigorous lens to distinguish policy-induced errors from motion-inherent challenges and enhances motion dataset reliability.
arXiv:2412.06147v2 Announce Type: replace Abstract: For the early identification, diagnosis, and treatment of mental health illnesses, the integration of deep learning (DL) and machine learning (ML) have started playing a significant role. By evaluating complex data from imaging, genetics, and behavioral assessments, these technologies have the potential to improve clinical results significantly. However, they also present unique challenges relating to data integration and ethical issues. The development of ML and DL methods for the early diagnosis and treatment of mental health issues is reviewed in this survey. It examines a range of applications, with a particular emphasis on behavioral assessments, genetic and biomarker analysis, and medical imaging for the diagnosis of diseases like depression, bipolar disorder, and schizophrenia. Predictive modeling for illness development is further discussed in the review, focusing on the function of risk prediction models and longitudinal investigations. Important discoveries show how ML and DL might improve treatment outcomes and diagnostic accuracy while tackling methodological inconsistency, data integration, and ethical concerns. The study emphasizes the significance of building real-time monitoring systems for individualized treatment, improving data fusion techniques, and interdisciplinary collaboration. Upcoming studies should concentrate on surmounting these obstacles to maximize ML and DL's valuable and moral implementation in mental health services.
arXiv:2412.07550v4 Announce Type: replace Abstract: Traditional science maps visualize topics by clustering documents within a network, but they are inherently biased toward clustering certain topics over others. If these topics could be chosen, then the science maps could be tailored for different needs. In this paper, we explore the extent to which the topic bias of a science map can be changed by choosing different data sources to build the document network. We analyze this by evaluating the clustering effectiveness of several topic categories over two sources that are traditionally used for the creation of science maps (citations and text similarity) and six non-traditional data sources, which we found favor different kinds of topics: Health issues for Facebook users, biotechnology topics for patent families, government and social issues for policy documents, food topics for Twitter conversations, nursing topics for Twitter users, and geographical entities for document authors (the favoring in this latter source was particularly strong). Our results show that diverse data sources can be used to control topic bias, which opens up the possibility of creating science maps tailored for different needs.
arXiv:2601.02880v3 Announce Type: replace Abstract: Every existing inference-time reasoning framework discards all failure context at problem boundaries, leaving a model solving problem 500 no wiser than it was on problem 1. We present ReTreVal (Reasoning Tree with Validation), a training-free framework that closes this gap through adaptive tree exploration with tool-augmented node refinement, typed-failure backtracking that injects categorized error context into the recovered branch, and a self-rewriting memory that accumulates and revises strategy entries across problems, enabling inference-time cross-problem learning on any fixed, unmodified LLM without fine-tuning. ReTreVal achieves 85.8% pass@1 on MATH-500 (+8.6 pp over Zero-Shot CoT, +8.6 pp over the strongest baseline Self-Refine) and 54.4% on MMLU-Pro (+15.3 pp over Self-Refine), with a 3.4:1 win-to-regression ratio confirming genuine error recovery rather than noise. These capabilities, previously requiring gradient updates, allow a 32B model to compete with much larger single-pass systems.
arXiv:2601.15423v2 Announce Type: replace Abstract: We introduce Lattice, a hybrid sequential prediction system that conditionally activates learned behavioral structure using binary confidence gating. The system summarizes behavior windows as behavioral archetypes and activates archetype-based scoring only when an in-support confidence signal exceeds a validation-calibrated threshold, falling back to backbone predictions when uncertain. Our primary estimand is the controlled effect of adding Lattice to a fixed backbone on identical test rows. On MovieLens (30 paired seeds, full-catalog ranking), LSTM+Lattice improves HR@10 by +31.7% (gated) versus the LSTM backbone alone (p much less than 10^-20); ungated fusion reaches +58.7% on the same protocol. We do not claim gating maximizes pooled accuracy. With backbone-native archetypes (fit in each backbone's embedding space), gated lifts of +13.3% (transformer) and +17.0% (SASRec) hold under the same evaluation design. A prior approximately 0% transformer row in version 1 reflected an invalid cross-backbone transfer, not evidence that composition cannot help stronger encoders. Amazon Electronics provides supporting cross-domain evidence (+124.0% gated, 15 seeds, high variance). Controlled shift checks (appendix) illustrate gate refusal under distribution shift. Standalone SASRec and BERT4Rec scores are contextual references, not the target estimand. We report what composition achieves and when it activates; production calibration and implementation details remain proprietary pending patent prosecution.
arXiv:2401.07986v3 Announce Type: replace Abstract: Let $n$ be a prime power, $r$ be a prime with $r\mid n-1$, and $\varepsilon\in (0,1/2)$. Using the theory of multiplicative character sums and superelliptic curves, we construct new codes over $\mathbb F_r$ having length $n$, relative distance $(r-1)/r+O(n^{-\varepsilon})$ and rate $n^{-1/2-\varepsilon}$. When $r=2$, our binary codes have exponential size when compared to all previously known families of linear and non-linear codes with relative distance asymptotic to $1/2$, such as Delsarte--Goethals codes. Moreover, concatenating with a Reed-Solomon code we get a family of codes of length $n$ and rate $n^{-1/(2n+2)-2\varepsilon/(n+1)}+O(n^{-1/(n+1)})$ and relative distance $1/2+O(n^{-\varepsilon})$. This shows that, for a fixed length, the rate of the concatenation suggested by Kschischang and Tasbihi (2024) of a Reed-Solomon and a Reed-Muller code can be made an order of magnitude smaller than a concatenation of a Reed-Solomon with a large dimensional Shadow code, while still keeping the regime of relative distance $1/2$. Finally, we show that the square of a Shadow code behaves like a random code and the Shadow code itself has a decoding algorithm, which suggest that such class of codes has the potential to be interesting for cryptographic applications.
arXiv:2402.08922v3 Announce Type: replace Abstract: Large-scale black-box models have become ubiquitous across numerous applications. Understanding the influence of individual training data sources on predictions made by these models is crucial for improving their trustworthiness. Current influence estimation techniques involve computing gradients for every training point or repeated training on different subsets. These approaches face obvious computational challenges when scaled up to large datasets and models. In this paper, we introduce and explore the Mirrored Influence Hypothesis, highlighting a reciprocal nature of influence between training and test data. Specifically, it suggests that evaluating the influence of training data on test predictions can be reformulated as an equivalent, yet inverse problem: assessing how the predictions for training samples would be altered if the model were trained on specific test samples. Through both empirical and theoretical validations, we demonstrate the wide applicability of our hypothesis. Inspired by this, we introduce a new method for estimating the influence of training data, which requires calculating gradients for specific test samples, paired with a forward pass for each training point. This approach can capitalize on the common asymmetry in scenarios where the number of test samples under concurrent examination is much smaller than the scale of the training dataset, thus gaining a significant improvement in efficiency compared to existing approaches. We demonstrate the applicability of our method across a range of scenarios, including data attribution in diffusion models, data leakage detection, analysis of memorization, mislabeled data detection, and tracing behavior in language models. Our code will be made available at https://github.com/ruoxi-jia-group/Forward-INF.
arXiv:2601.03256v2 Announce Type: replace Abstract: We present Muses, the first training-free method for fantastic 3D creature generation in a feed-forward paradigm. Previous methods, which rely on part-aware optimization, manual assembly, or 2D image generation, often produce unrealistic or incoherent 3D assets due to the challenges of intricate part-level manipulation and limited out-of-domain generation. In contrast, Muses leverages the 3D skeleton, a fundamental representation of biological forms, to explicitly and rationally compose diverse elements. This skeletal foundation formalizes 3D content creation as a structure-aware pipeline of design, composition, and generation. Muses begins by constructing a creatively composed 3D skeleton with coherent layout and scale through graph-constrained reasoning. This skeleton then guides a voxel-based assembly process within a structured latent space, integrating regions from different objects. Finally, image-guided appearance modeling under skeletal conditions is applied to generate a style-consistent and harmonious texture for the assembled shape. Extensive experiments establish Muses' state-of-the-art performance in terms of visual fidelity and alignment with textual descriptions, and potential on flexible 3D object editing. Project page: https://luhexiao.github.io/Muses.github.io/.
arXiv:2601.04094v3 Announce Type: replace Abstract: Effective regulation of AI is a defining policy challenge, driven by their integration into all aspects of society. To remain responsive to their rapid development and emergent properties, policymakers across the globe rely on high-level principles and abstract legal requirements. Yet, while this flexibility supports future-proofing human-centred regulations and aligning them with socio-ethical values, it also causes legal uncertainty downstream as developers, companies, and auditors struggle with translating these abstract requirements into verifiable technical requirements. Using the AI Act as an example, this paper draws on Coleman's bathtub to analyse the regulatory learning space in AI governance. It argues that legal uncertainty cannot be fully reduced ex ante and that, within reasonable bounds, it is also necessary for regulatory learning because it creates the space in which boundary negotiation over socio-technical meaning can occur. Building on this analysis, the paper shows how boundary objects and boundary negotiating artifacts help explain the translation of legal requirements into operational practice. By examining technical sandbox frameworks, it further identifies concrete properties that technical infrastructures must possess to function effectively as boundary negotiation artifacts in AI assessment. The paper concludes that legal certainty remains the long-term aim, but that premature closure of regulatory instruments risks undermining the learning processes needed for adaptive governance.
arXiv:2606.09304v1 Announce Type: new Abstract: On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.
arXiv:2606.09448v1 Announce Type: new Abstract: Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since. Linearized Algebraic Geometry codes, the analogue of AG codes in the sum-rank metric, were instead introduced more recently [9], using quotients of the ring of Ore polynomials with coefficients in an algebraic function field. In this paper, we further investigate the results in [9], providing explicit, optimal and asymptotic constructions.
arXiv:2606.09750v1 Announce Type: new Abstract: Many works have attempted to estimate the correlation and integral timescales associated with turbulent fluctuations in the solar wind, which are interpreted as length scales based on Taylor's~Hypothesis. However, accurate estimates of these timescales from spacecraft observations heavily rely on the accurate estimation of autocorrelation functions (ACF), which have been recently shown to depend strongly on the interval length used to estimate them. In this Letter, we show that this dependence on interval length may be artificial because common ACF estimators do not correctly capture the long-lag behavior of the true ACF of the underlying turbulence. We introduce a new ergodicity-based methodology to unambiguously estimate the integral timescale, and a new ACF estimator with better ergodic convergence than current ones. Due to its ergodic properties, the new ACF estimator properly captures the long-lag behavior, and is independent of the interval length. We use this approach to estimate the integral and correlation scales of magnetic fluctuations in the solar wind near $1~{\rm au}$.
arXiv:2601.09085v2 Announce Type: replace Abstract: Group Relative Policy Optimization (GRPO) has become a standard approach for training mathematical reasoning models; however, its reliance on multiple completions per prompt makes training computationally expensive. Although recent work has reduced the number of training steps required to reach peak performance, the overall wall-clock training time often remains unchanged or even increases due to higher per-step cost. We propose MMR-GRPO, which integrates Maximal Marginal Relevance to reweigh rewards based on completion diversity. Our key insight is that semantically redundant completions contribute limited marginal learning signal; prioritizing diverse solutions yields more informative updates and accelerates convergence. Extensive evaluations across three model sizes (1.5B, 7B, 8B), three GRPO variants, and five mathematical reasoning benchmarks show that MMR-GRPO achieves comparable peak performance while requiring on average 47.9% fewer training steps and 70.2% less wall-clock time. These gains are consistent across models, methods, and benchmarks. Our code is released at: https://github.com/WeiKangda/MMR-GRPO.
arXiv:2601.09900v4 Announce Type: replace Abstract: This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical schemes for solving initial value problems for first-order ordinary differential equations. Based on numerical simulations, we select one scheme and prove its second-order consistency and convergence. By modifying this scheme, we also obtain a numerical scheme with zero local truncation error for ODEs whose solution trajectories are ellipses.
arXiv:2412.06288v4 Announce Type: replace Abstract: The surging demand for artificial intelligence (AI) has led to a rapid expansion of energy-intensive data centers, contributing to criteria air pollutant emissions and raising public health concerns that have received comparatively limited attention in sustainability assessments. This paper introduces a principled methodology to model air pollutant emissions for data centers and estimate the public health impacts. Our findings reveal that the growing demand for AI and computing technologies is projected to push the total annual public health burden of U.S. data centers up to more than $20 billion in 2028. Although national-level impacts remain modest, data center health costs are unevenly distributed: in the most affected counties, the estimated per-household health burden can reach about seven times the national average. Next, we propose a health-informed computing framework that explicitly incorporates public health impacts into data center resource management across space and time, mitigating public health costs while supporting environmental sustainability. More broadly, we recommend extended energy reporting to include public health impact of data centers and paying attention to all impacted communities.
arXiv:2508.16564v2 Announce Type: replace Abstract: A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a rank-adaptive decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This approach establishes a foundation for extending modern rank-adaptive techniques to solve the Boltzmann equation in realistic settings, particularly where structured representations, such as conformal geometries, may not be feasible in practical engineering applications. A nodal discontinuous Galerkin method is employed for spatial discretization, coupled with a rank-adaptive decomposition over the velocity grid, as well as implicit-explicit Runge-Kutta methods for time integration. To handle the limit of vanishing collision time, a multiscale implicit integrator based on an auxiliary moment equation is utilized. The algorithm's order of accuracy, reduced computational complexity, and robustness are demonstrated on a suite of canonical gas kinetics problems with increasing complexity.
arXiv:2606.09262v1 Announce Type: new Abstract: Two-view correspondence learning aims to distinguish true correspondences (inliers) from false ones (outliers) in image pairs by leveraging their underlying differences. Existing methods mainly rely on coordinate-based geometric consistency. However, they often struggle with pseudo-consistent outliers in scenes containing repetitive structures, textureless regions, or locally similar geometric patterns. To address this limitation, we propose TriMatch, a multi-source feature fusion framework for two-view correspondence learning, which consists of two parts: feature extraction and feature refinement. In feature extraction, TriMatch jointly extracts geometric, texture semantic, and structural semantic features to provide complementary evidence for correspondence discrimination. To bridge the gap between semantic and geometric features, texture and structural semantic features are aligned with geometric features through dedicated Texture-Geometric Alignment and Structural-Geometric Alignment modules, respectively. We further introduce a Semantic-Guided Correspondence Modulation module, which modulates geometric features using semantic information to suppress geometrically plausible but semantically inconsistent correspondences. In feature refinement, a Hierarchical Semantic-Enhanced Correspondence Refinement strategy progressively models correspondence dependencies and recalibrates multi-context feature responses, enabling more reliable inlier-outlier discrimination. Extensive experiments demonstrate the effectiveness, robustness, and generalization capability of TriMatch.
arXiv:2606.09271v1 Announce Type: new Abstract: Parkinson's disease (PD) is a progressive neurodegenerative disorder that frequently causes speech impairments associated with hypokinetic dysarthria. As speech production relies on the precise coordination of complex neuromuscular mechanisms, speech analysis has emerged as a promising non-invasive and cost-effective biomarker for early PD detection. Recent deep learning approaches have shown encouraging results; however, most existing methods rely on a single speech representation, potentially overlooking complementary pathological information encoded across different feature spaces. In this work, we propose a multi-branch deep learning framework for automatic PD detection from speech. Each recording is segmented into 5-second chunks and represented using three complementary modalities: Log-Mel spectrograms, MFCCs, and HuBERT embeddings extracted from raw waveforms. The spectrograms are processed using a pre-trained ResNet-18 encoder, MFCC sequences are modeled through a BiLSTM network, and raw speech is encoded using a pre-trained HuBERT model. To effectively integrate these heterogeneous representations, we introduce a context-guided cross-modal attention mechanism that dynamically weights temporal HuBERT embeddings according to the global acoustic context derived from the spectrogram and MFCC branches. Experiments conducted on the publicly available Spanish PC-GITA corpus under strict speaker-independent 5-fold cross-validation demonstrate the effectiveness of the proposed approach. The proposed architecture achieves an accuracy of 91.51%, an F1-score of 91.24%, and an AUC of 95.97%. Furthermore, ablation studies confirm the contribution of both the proposed context-guided cross-modal attention mechanism and the integration of complementary speech representations. These findings highlight the potential of heterogeneous speech modeling for robust and clinically reliable PD detection.
arXiv:2602.05175v2 Announce Type: replace Abstract: Deep neural networks demonstrate impressive performance in visual recognition but remain highly vulnerable to imperceptible adversarial attacks. Existing defense strategies such as adversarial training and diffusion-based purification have achieved significant progress but are frequently constrained by high computational cost, information loss, and inference latency. To address these challenges, we propose a Geometric and Texture balancing Purification (GeoTexPuri) framework that enhances adversarial robustness by harmonizing invariant geometric structures with textural features. Specifically, the framework integrates dense geometric guidance into the training phase by transforming discrete image masks into continuous spatial fields via Signed Distance Fields (SDF). This process establishes stable structural anchors that shield the model from local pixel noise. Through a multi-stream training objective, the model learns to internalize purified representations that effectively align semantic textural cues with these underlying geometric invariants. Extensive experiments on ImageNet demonstrate the efficacy of our approach. GeoTexPuri achieves 84.79\% clean accuracy and 83.52\% robust accuracy under the AutoAttack. Crucially, GeoTexPuri functions as a deterministic classifier during inference, requiring only the input image without any auxiliary geometric modules or additional computational costs, thereby ensuring a scalable and efficient solution for real-time applications.
arXiv:2606.09275v1 Announce Type: new Abstract: The Material Point Method provides an effective approach for modelling the large deformations that often arise from contact interactions between rigid structures and surrounding continua. However, solving these problems requires accurate representation of the continuum-structure interface, which necessitates high resolution background mesh and material point discretisations. This requirement, combined with evolving continuum-structure interfaces and the fact that most Material Point Method implementations are dependent on structured meshes, can result in large numerical systems and long run times especially when modelling problems in three-dimensions. Motivated by this issue, this paper provides the first octree-based implicit Material Point Method for efficient solution of large deformation continuum-structure interaction problems. The octree background mesh provides a natural way to automatically adapt both the computational mesh and the material point discretisation based on the position of the interaction between the structure and continuum. The new approach is demonstrated on a number of large deformation benchmark and continuum-structure interaction problems, where up to a 5.5-times speed up and a consequent 21-times CO2 saving is achieved when running on a HPC compared to results obtained using a conforming mesh.