arXiv subjects

Stefano Martiniani

Publications and source records attributed to Stefano Martiniani.

At least 19 recordsLinked to original sources

arXiv2026

Fast generation of spectrally-shaped disorder, on the sphere

The design of disordered point patterns with desirable properties is an exciting and ongoing research endeavor, with applications ranging from materials to computer science. A successful approach in recent years has been the optimization of point patterns through a loss function that enforces properties in their Fourier-space representation. Yet, these methods have so far strictly been limited to flat Euclidean space, precluding their use in the contexts of coatings of curved surfaces for photonics, or of sampling of curved manifolds for instance. We introduce FaSHIoNPOp, an algorithm that relies on fast non-uniform spherical harmonics transforms, to enforce pair correlations in point patterns on the sphere with an $O(N \log N)$ complexity in $N$ the number of points. Having demonstrated its performance, we showcase applications of FaSHIoNPOp, ranging from the generation of hyperuniform structures on the sphere for sampling and physical applications, to the design of gyromorphs (disordered structures with maximal scattering power at a given frequency) on the sphere. We additionally show that FaSHIoNPOp can be combined to both global constraints like centrosymmetry, with applications to the design of more isotropic $3d$ gyromorphs, and local real-space constraints like pair repulsion. Our work paves the way for optimal sampling and coating design on curved manifolds, with many applications across physics, materials and computer science.

cond-mat.stat-mech↗

arXiv2026

A minimal mechanism to generate long timescales without fine tuning

Long timescales in brain dynamics give rise to power law correlations measured in experiments. A simple linear recurrent neural network model can reproduce this power law behavior, but the recurrent interaction strength needs to be fine tuned in order to sit at the edge of stability. We show that by adding a dynamical recurrent feedback gain to the simple linear model removes the need for fine tuning, because the gain self-organizes so that the spectrum of the effective recurrent matrix is always gapless with the top eigenvalue landing on the stability edge for any recurrent strength. As a consequence, long timescales and scale free correlations arise generically, as we demonstrate both analytically and numerically.

cond-mat.dis-nn↗

arXiv2026

AskChem: Claim-Centered Infrastructure for Chemistry Literature Synthesis

Chemistry literature synthesis often requires assembling specific findings scattered across many publications, yet existing literature-search systems primarily return ranked document lists. As a result, scientists and AI agents need to locate relevant information, verify their provenance, and assemble cross-paper answers manually. We present AskChem, a claim-centered infrastructure for cross-paper chemistry search. AskChem changes the unit of retrieval from the paper to the provenance-carrying claim: each paper is converted into atomic, typed claims, each grounded by a source DOI and a verbatim quote or an explicit evidence locator. Over this shared claim store, AskChem exposes complementary structures for search and synthesis: a stabilized faceted taxonomy for hierarchical retrieval and browsing, an evidence graph linking claims through relations, and an exploratory living taxonomy that situates indexed papers under scientific principles. AskChem currently indexes 2.4M claims from 147K papers and provides a web interface, as well as REST, SDK, and MCP access for AI agents. On AskChem-Bench, grounding a GPT-5.5 reader in AskChem yields 100% resolvable DOIs, compared with 88.3% without retrieval, and the highest citation density among five tested systems. AskChem is live at https://askchem.org.

cs.CL↗

arXiv2026

Hyperuniform systems are maximally irreversible

Hyperuniform systems, defined by the anomalous suppression of large-scale density fluctuations, are a paradigm of non-equilibrium self-assembly. While mechanisms underlying the self-assembly of hyperuniform states have been widely studied, the energetics of this process remain unexplored. This raises a fundamental question: what is the energetic cost of self-assembling a hyperuniform system? Here, we address this question across several noisy particle systems drawn from soft matter and machine learning, in which hyperuniformity can be induced by tuning noise correlations. Despite their distinct microscopic dynamics, we uncover a universal behavior across all systems: hyperuniform states are maximally irreversible, as quantified by the entropy production rate. Further, we develop a path integral formulation of the entropy production rate directly from the microscopic dynamics, which explains our observations. Our work establishes a direct link between emergent long-range structure and time irreversibility and opens a new avenue of probing the energetic cost of hyperuniform self-assembly, ubiquitous across physics, biology, and materials science.

cond-mat.soft↗

arXiv2026

Cyclic Denoising Reveals Ultrastable Memories in Diffusion Models

We introduce cyclic denoising -- repeated forward and reverse diffusion at controlled noise amplitudes -- as an extraction attack for image diffusion models. Inspired by random organization in disordered solids, cyclic denoising exposes regions of the learned distribution that are largely inaccessible to standard sampling. The dynamics drive samples toward attractors with a broad stability spectrum. The deepest attractors are ultrastable: they regenerate after near-total corruption and persist through thousands of noising-denoising cycles. Many of these attractors correspond to memorized training images, including stock photographs, brand watermarks, and web-crawl artifacts. The attack requires only sampler-level control, with no gradients, weight inspection, prompts, captions, or prior knowledge of the training data. Unlike generate-and-filter attacks, which rely on large-scale prompted generation and post-hoc similarity or membership-inference filtering, our main protocol is fully unconditioned. We demonstrate the phenomenon in Stable Diffusion v1.4 and in a pixel-space DDPM, showing consistent behavior across latent- and pixel-space diffusion models. Across noise amplitudes, we observe a yielding-like transition: low-amplitude cycling produces trivial absorbing fixed points or limit cycles, while larger amplitudes induce rearrangements, basin hopping, and long-lived trapping in structured memorized attractor basins. We also observe hierarchical partial absorption, prompt-stabilized basins, and cross-initial-condition universality of the recovered attractor set. Our results therefore show that cyclic denoising is both a physics-inspired probe of generative landscapes and a practical tool for memorization auditing, with implications for privacy, copyright compliance, and model fingerprinting.

cs.LG↗

arXiv2026

Exact Variance and Fano Factor for Arbitrary Level Crossings in Stationary Gaussian Processes

Understanding the statistics of level crossings in stochastic processes is crucial across many scientific disciplines. The traditional Kac-Rice formula gives the mean rate of level crossings and has found broad use. However, that mean rate captures only a coarse summary of the crossing process. It depends entirely on local properties of the stochastic process at a given instant and is therefore blind to the correlation structure of the process over time. To understand whether crossing events, such as neuronal spikes, tend to cluster in time, spread apart, or exhibit more complex temporal organization, one must go beyond the mean rate and study higher-order crossing statistics. Here we go beyond the mean by deriving the exact analytical formulae for the variance and Fano factor of arbitrary level crossings in smooth stationary Gaussian processes. Our exact solution reveals how the full temporal correlation structure dictates whether crossings cluster or become regular. In systems with oscillatory correlations, such as a stochastic damped harmonic oscillator, a recent crossing suppresses an immediate subsequent one, producing sub-Poissonian statistics. However, as damping increases and oscillations disappear, a large and slow excursion above the threshold can produce multiple closely spaced crossings, yielding super-Poissonian statistics. In purely relaxational, non-oscillatory systems, such as a mean-reverting process driven by Ornstein-Uhlenbeck noise, the competition between the timescales of the driving noise and system relaxation produces a richer landscape, including reentrant transitions between sub- and super-Poissonian statistics as the threshold level is varied. Taken together, the exact variance and Fano factor derived here complement the Kac-Rice mean rate, enabling more robust parameter estimation and model selection across any setting where Gaussian processes are used.

math.PR↗

arXiv2026

MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching

Molecular crystal structure prediction represents a grand challenge in computational chemistry due to large sizes of constituent molecules and complex intra- and intermolecular interactions. While generative modeling has revolutionized structure discovery for molecules, inorganic solids, and metal-organic frameworks, extending such approaches to fully periodic molecular crystals is still elusive. Here, we present MolCrystalFlow, a flow-based generative model for molecular crystal structure prediction. The framework disentangles intramolecular complexity from intermolecular packing by embedding molecules as rigid bodies and jointly learning the lattice matrix, molecular orientations, and centroid positions. Centroids and orientations are represented on their native Riemannian manifolds, allowing geodesic flow construction and graph neural network operations that respects geometric symmetries. We benchmark our model against a state-of-the-art generative model (MOFFlow) for large-size periodic crystals and a rule-based structure generation method (Genarris) on two open-source molecular crystal datasets. MolCrystalFlow outperforms MOFFlow while achieving competitive performance against Genarris. We also demonstrate an integration of MolCrystalFlow model with universal machine learning potential to accelerate molecular crystal structure prediction, paving the way for data-driven generative discovery of molecular crystals.

cs.LG↗

arXiv2026

Cross-View World Models

World models enable agents to plan by imagining future states, but existing approaches operate from a single viewpoint, typically egocentric, even when other perspectives would make planning easier; navigation, for instance, benefits from a bird's-eye view. We introduce Cross-View World Models (XVWM), trained with a cross-view prediction objective: given a sequence of frames from one viewpoint, predict the future state from the same or a different viewpoint after an action is taken. Enforcing cross-view consistency acts as geometric regularization: because the input and output views may share little or no visual overlap, to predict across viewpoints, the model must learn view-invariant representations of the environment's 3D structure. We train on synchronized multi-view gameplay data from Aimlabs, an aim-training platform providing precisely aligned multi-camera recordings with high-frequency action labels. The resulting model gives agents parallel imagination streams across viewpoints, enabling planning in whichever frame of reference best suits the task while executing from the egocentric view. Our results show that multi-view consistency provides a strong learning signal for spatially grounded representations. Finally, predicting the consequences of one's actions from another viewpoint may offer a foundation for perspective-taking in multi-agent settings.

cs.CV↗

arXiv2026

Open Materials Generation with Inference-Time Reinforcement Learning

Continuous-time generative models for crystalline materials enable inverse materials design by learning to predict stable crystal structures, but incorporating explicit target properties into the generative process remains challenging. Policy-gradient reinforcement learning (RL) provides a principled mechanism for aligning generative models with downstream objectives but typically requires access to the score, which has prevented its application to flow-based models that learn only velocity fields. We introduce Open Materials Generation with Inference-time Reinforcement Learning (OMatG-IRL), a policy-gradient RL framework that operates directly on the learned velocity fields and eliminates the need for the explicit computation of the score. OMatG-IRL leverages stochastic perturbations of the underlying generation dynamics preserving the baseline performance of the pretrained generative model while enabling exploration and policy-gradient estimation at inference time. Using OMatG-IRL, we present the first application of RL to crystal structure prediction (CSP). Our method enables effective reinforcement of an energy-based objective while preserving diversity through composition conditioning, and it achieves performance competitive with score-based RL approaches. Finally, we show that OMatG-IRL can learn time-dependent velocity-annealing schedules, enabling accurate CSP with order-of-magnitude improvements in sampling efficiency and, correspondingly, reduction in generation time. The OMatG-IRL code is included in a new release of the Open Materials Generation (OMatG) framework available at https://github.com/FERMat-ML/OMatG.

cs.LG↗

arXiv2026

Spatial self-organization driven by temporal noise

The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by local spatial noise is well studied, whether temporal noise can also drive such organization remains an open question. Here, by studying interacting particle systems, we show that temporally correlated noise can lead to a self-organized state with suppressed long-range density fluctuations, or hyperuniformity. Further, we develop a fluctuating hydrodynamic theory that quantitatively explains the origin of this phenomenon. Finally, by casting the dynamics as a stochastic optimization problem, we show that temporal correlations lead to better solutions, akin to perturbed gradient descent in neural networks -- where noise is injected during training to escape poor minima. This reveals a striking correspondence between perturbed gradient descent dynamics on the energy landscapes of particle systems and the loss landscapes of neural networks. Our study establishes temporal correlations as a novel mechanism for noise-driven self-organization, with broad implications for self-assembling materials, biological systems, and optimization algorithms that leverage temporal noise for applications like differentially private learning.

cond-mat.soft↗

arXiv2026

Contrastive Self-Supervised Learning As Neural Manifold Packing

Contrastive self-supervised learning based on point-wise comparisons has been widely studied for vision tasks. In the visual cortex of the brain, neuronal responses to distinct stimulus classes are organized into geometric structures known as neural manifolds. Accurate classification of stimuli can be achieved by effectively separating these manifolds, akin to solving a packing problem. We introduce Contrastive Learning As Manifold Packing (CLAMP), a self-supervised framework that recasts representation learning as a manifold packing problem. CLAMP introduces a loss function inspired by the potential energy of short-range repulsive particle systems, such as those encountered in the physics of simple liquids and jammed packings. In this framework, each class consists of sub-manifolds embedding multiple augmented views of a single image. The sizes and positions of the sub-manifolds are dynamically optimized by following the gradient of a packing loss. This approach yields interpretable dynamics in the embedding space that parallel jamming physics, and introduces geometrically meaningful hyperparameters within the loss function. Under the standard linear evaluation protocol, which freezes the backbone and trains only a linear classifier, CLAMP achieves competitive performance with state-of-the-art self-supervised models. Furthermore, our analysis reveals that neural manifolds corresponding to different categories emerge naturally and are effectively separated in the learned representation space, highlighting the potential of CLAMP to bridge insights from physics, neural science, and machine learning.

cs.LG↗

arXiv2025

PropMolFlow: Property-Guided Molecule Generation with Geometry-Complete Flow Matching

Molecule generation is advancing rapidly in chemical discovery and drug design. Flow matching methods have recently set the state of the art (SOTA) in unconditional molecule generation, surpassing score-based diffusion models. However, diffusion models still lead in property-guided generation. In this work, we introduce PropMolFlow, an approach for property-guided molecule generation based on geometry-complete SE(3)-equivariant flow matching. Integrating five different property embedding methods with a Gaussian expansion of scalar properties, PropMolFlow achieves competitive performance against previous SOTA diffusion models in conditional molecule generation while maintaining high structural stability and validity. Additionally, it enables faster sampling speed with fewer time steps compared to baseline models. We highlight the importance of validating the properties of generated molecules through DFT calculations. Furthermore, we introduce a task to assess the model's ability to propose molecules with underrepresented property values, assessing its capacity for out-of-distribution generalization.

physics.chem-ph↗

arXiv2025

MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matching

Key objectives in conditional molecular generation include ensuring chemical validity, aligning generated molecules with target properties, promoting structural diversity, and enabling efficient sampling for discovery. Recent advances in computer vision introduced a range of new guidance strategies for generative models, many of which can be adapted to support these goals. In this work, we integrate state-of-the-art guidance methods -- including classifier-free guidance, autoguidance, and model guidance -- in a leading molecule generation framework built on an SE(3)-equivariant flow matching process. We propose a hybrid guidance strategy that separately guides continuous and discrete molecular modalities -- operating on velocity fields and predicted logits, respectively -- while jointly optimizing their guidance scales via Bayesian optimization. Our implementation, benchmarked on the QM9 and QMe14S datasets, achieves new state-of-the-art performance in property alignment for de novo molecular generation. The generated molecules also exhibit high structural validity. Furthermore, we systematically compare the strengths and limitations of various guidance methods, offering insights into their broader applicability.

cs.LG↗

arXiv2025

Spatial and Temporal Cluster Tomography of Active Matter

Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on two-point correlation functions. In this Letter, we show that cluster tomography -- the study of one-dimensional cross-sections of the clusters that emerge near a phase transition -- is an alternative higher-order tool that efficiently locates and characterizes phase transitions in active systems. First, using motility-induced phase separation as a paradigmatic example, we show how complex geometric features of clusters, captured by spatial cluster tomography, can be used to measure critical exponents in active systems without explicitly introducing system-specific order parameters. Second, we introduce temporal cluster tomography, an analogous cluster-based measurement that characterizes the dynamical behavior of active systems. We show that cluster dynamics can be captured by a generalization of burstiness analysis in complex temporal networks. Both spatial and temporal cluster tomography are easy to implement yet powerful approaches to study non-equilibrium systems, making them useful additions to the standard toolbox of statistical physics.

cond-mat.stat-mech↗

arXiv2025

All that structure matches does not glitter

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task$\unicode{x2014}$generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains $\approx$40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms $N$, one with enantiomorphs, and two containing only identical structures but with different unit cells. We also propose new splits for datasets with polymorphs, ensuring that polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

cs.LG↗

arXiv2025

Gyromorphs: a new class of functional disordered materials

We introduce a new class of functional correlated disordered materials, termed Gyromorphs, which uniquely combine liquid-like translational disorder with quasi-long-range rotational order, induced by a ring of $G$ delta peaks in their structure factor. We generate gyromorphs in $2d$ and $3d$ by spectral optimization methods, verifying that they display strong discrete rotational order but no long-range translational order, while maintaining rotational isotropy at short range for sufficiently large $G$. Using a coupled dipoles approximation, we numerically show that these structures outperform quasicrystals, stealthy hyperuniformity, and Vogel spirals in the formation of low-index-contrast isotropic bandgaps in $2d$, for both scalar and vector waves, and open complete isotropic bandgaps in $3d$. This claim is further supported by analytical effective-medium theory and by numerical estimates of scattering mean-free paths. Finally, we introduce ``polygyromorphs'' with several rotational symmetries at different length scales (i.e., multiple rings of delta peaks), enabling the formation of multiple bandgaps in a single structure, thereby paving the way for fine control over optical properties.

cond-mat.stat-mech↗

arXiv2025

Guided Diffusion for the Discovery of New Superconductors

The inverse design of materials with specific desired properties, such as high-temperature superconductivity, represents a formidable challenge in materials science due to the vastness of chemical and structural space. We present a guided diffusion framework to accelerate the discovery of novel superconductors. A DiffCSP foundation model is pretrained on the Alexandria Database and fine-tuned on 7,183 superconductors with first principles derived labels. Employing classifier-free guidance, we sample 200,000 structures, which lead to 34,027 unique candidates. A multistage screening process that combines machine learning and density functional theory (DFT) calculations to assess stability and electronic properties, identifies 773 candidates with DFT-calculated $T_\mathrm{c}>5$ K. Notably, our generative model demonstrates effective property-driven design. Our computational findings were validated against experimental synthesis and characterization performed as part of this work, which highlighted challenges in sparsely charted chemistries. This end-to-end workflow accelerates superconductor discovery while underscoring the challenge of predicting and synthesizing experimentally realizable materials.

cond-mat.supr-con↗

arXiv2025

A geometric condition for robot-swarm cohesion and cluster-flock transition

We present a geometric design rule for size-controlled clustering of self-propelled particles. We show that active particles that tend to rotate under an external force have an intrinsic, signed parameter with units of curvature which we call curvity, that can be derived from first principles. Experiments with robots and numerical simulations show that properties of individual robots (radius and curvity) control pair cohesion in a binary system, and the stability of flocking and self-limiting clustering in a swarm, with applications in meta-materials and in embodied decentralized control.

cond-mat.soft↗