arXiv:2504.03485v2 Announce Type: replace 
Abstract: We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base multivariate normal distribution with an exponentiated GP refinement, and so we refer to it as a GP-tilted nonparametric density. By representing the GP part of the score as a linear function using the random Fourier feature (RFF) approximation, we show that optimization can be solved in closed form for the three FD-based objectives considered. This includes the basic and noise conditional versions of the Fisher divergence, as well as an alternative to noise conditional FD models based on variational inference (VI) that we propose in this paper. For this novel learning approach, we propose an ELBO-like optimization to approximate the posterior distribution, with which we then derive a Fisher variational predictive distribution. The RFF representation of the GP, which is functionally equivalent to a single layer neural network score model with cosine activation, provides a useful linear representation of the GP for which all expectations can be solved. The Gaussian base distribution also helps with tractability of the VI approximation and ensures that our proposed density is well-defined. We demonstrate our three learning algorithms, as well as a MAP baseline algorithm, on several low dimensional density estimation problems. The closed form nature of the learning problem removes the reliance on iterative learning algorithms, making this technique particularly well-suited to big data sets, since only sufficient statistics collected from a single pass through the data is needed.

تم اقتراح مقدر كثافة غير معلمي جديد يعتمد على العمليات الغاوسية (GP) ويتميز بثلاثة خوارزميات تعلم جديدة مغلقة الشكل مستمدة من مطابقة درجات تباين فيشر (FD). يجمع هذا المقدّر بين توزيع طبيعي متعدد المتغيرات الأساسي مع تحسين GP مرفوع الأس، ويشار إليه بكثافة غير معلم مائل GP. يمكن حل الأمثلية لهذه الخوارزميات في شكل مغلق، بما في ذلك النسخ الأساسية والشرطية للضوضاء من تباين فيشر، بالإضافة إلى بديل يعتمد على الاستدلال التبايني.

Se ha propuesto un nuevo estimador de densidad no paramétrica basado en procesos gaussianos (GP), que presenta tres nuevos algoritmos de aprendizaje en forma cerrada derivados del emparejamiento de puntuaciones de divergencia de Fisher (FD). Este estimador combina una distribución normal multivariada base con un refinamiento GP exponencial, denominado densidad no paramétrica inclinada GP. La optimización para estos algoritmos se puede resolver en forma cerrada, incluyendo versiones básicas y condicionales al ruido de la divergencia de Fisher, así como una alternativa basada en inferencia variacional.

Un nouvel estimateur de densité non paramétrique basé sur des processus gaussiens (GP) a été proposé, avec trois nouveaux algorithmes d'apprentissage en forme fermée dérivés de l'appariement de score de divergence de Fisher (FD). Cet estimateur combine une distribution normale multivariée de base avec un raffinement GP exponentié, appelé densité non paramétrique inclinée GP. L'optimisation pour ces algorithmes peut être résolue sous forme fermée, y compris les versions de divergence de Fisher conditionnelles au bruit et une alternative basée sur l'inférence variationnelle.

A new nonparametric density estimator based on Gaussian processes (GP) has been proposed, featuring three novel closed-form learning algorithms derived from Fisher divergence (FD) score matching. This estimator combines a base multivariate normal distribution with an exponentiated GP refinement, referred to as GP-tilted nonparametric density. The optimization for these algorithms can be solved in closed form, including basic and noise conditional versions of Fisher divergence, along with a variational inference-based alternative.

Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching

arXiv:1906.07172v5 Announce Type: replace-cross 
Abstract: Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as equivarification. We further show that group convolutional neural networks (G-CNNs) arise as a special case of our framework.

Equivariant neural networks and equivarification

arXiv:2311.13745v4 Announce Type: replace-cross 
Abstract: Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration complexity of sampling, assuming access to an accurate diffusion model. In this work, we focus on understanding the sample complexity of training such a model; how many samples are needed to learn an accurate diffusion model using a sufficiently expressive neural network? Prior work showed bounds polynomial in the dimension, desired Total Variation error, and Wasserstein error. We show an exponential improvement in the dependence on Wasserstein error and depth, along with improved dependencies on other relevant parameters.

Improved Sample Complexity Bounds for Diffusion Model Training

arXiv:2410.22995v2 Announce Type: replace-cross 
Abstract: A hallmark of advanced artificial intelligence is the capacity to progress from passive visual perception to the strategic modification of visual information to facilitate complex reasoning. This advanced capability, however, remains critically underdeveloped in current Large Multi-modal Models (LMMs). The deficiency is often masked by evaluation metrics that prioritize final-answer accuracy, creating an illusion of competence where genuine reasoning is absent. Using the domain of geometric problem-solving as a precise instrument, we probe this issue through tasks that require constructing visual aids. To this end, we introduce \textbf{VisAidMath}, a challenging benchmark, and our novel Three-Layered Funnel Evaluation Framework. This framework moves beyond simple accuracy (ACCU) to scrutinize the generation of valid visual aids (PVA) and the soundness of subsequent reasoning steps (SPRS). Our extensive experiments on state-of-the-art models, including Doubao-Seed-1.6 and o4, reveal a profound ``Reasoning Illusion''. We observe that high surface-level accuracy conceals a catastrophic failure in the models' ability to produce valid visual aids or to reason from them. Our findings expose a fundamental schism between visual perception and logical deduction in modern LMMs. We host an evaluation platform at CodaBench for testing publicly. Homepage: https://nlp2ct.github.io/VisAidMathHomepage/ Evaluation: https://www.codabench.org/competitions/7634/

VisAidMath: Benchmarking Visual-Aided Mathematical Reasoning

arXiv:2508.01249v3 Announce Type: replace-cross 
Abstract: Large Language Model (LLM) agents offer a powerful new paradigm for solving various problems by combining natural language reasoning with the execution of external tools. However, their dynamic and non-transparent behavior introduces critical security risks, particularly in the presence of prompt injection attacks. In this work, we propose a novel insight that treats the agent runtime traces as structured programs with analyzable semantics. Thus, we present AgentArmor, a program analysis framework that converts agent traces into graph intermediate representation-based structured program dependency representations (e.g., CFG, DFG, and PDG) and enforces security policies via a type system. AgentArmor consists of three key components: (1) a graph constructor that reconstructs the agent's runtime traces as graph-based intermediate representations with control and data flow described within; (2) a property registry that attaches security-relevant metadata of interacted tools \& data, and (3) a type system that performs static inference and checking over the intermediate representation. By representing agent behavior as structured programs, AgentArmor enables program analysis for sensitive data flow, trust boundaries, and policy violations. We evaluate AgentArmor on the AgentDojo benchmark, the results show that AgentArmor can reduce the ASR to 3\%, with the utility drop only 1\%.

AgentArmor: Enforcing Program Analysis on Agent Runtime Trace to Defend Against Prompt Injection

arXiv:2511.14691v1 Announce Type: cross 
Abstract: Attention is the brain's ability to selectively focus on a few specific aspects while ignoring irrelevant ones. This biological principle inspired the attention mechanism in modern Transformers. Transformers now underpin large language models (LLMs) such as GPT, but at the cost of massive training and inference energy, leading to a large carbon footprint. While brain attention emerges from neural circuits, Transformer attention relies on dot-product similarity to weight elements in the input sequence. Neuromorphic computing, especially spiking neural networks (SNNs), offers a brain-inspired path to energy-efficient intelligence. Despite recent work on attention-based spiking Transformers, the core attention layer remains non-neuromorphic. Current spiking attention (i) relies on dot-product or element-wise similarity suited to floating-point operations, not event-driven spikes; (ii) keeps attention matrices that suffer from the von Neumann bottleneck, limiting in-memory computing; and (iii) still diverges from brain-like computation. To address these issues, we propose the Spiking STDP Transformer (S$^{2}$TDPT), a neuromorphic Transformer that implements self-attention through spike-timing-dependent plasticity (STDP), embedding query--key correlations in synaptic weights. STDP, a core mechanism of memory and learning in the brain and widely studied in neuromorphic devices, naturally enables in-memory computing and supports non-von Neumann hardware. On CIFAR-10 and CIFAR-100, our model achieves 94.35\% and 78.08\% accuracy with only four timesteps and 0.49 mJ on CIFAR-100, an 88.47\% energy reduction compared to a standard ANN Transformer. Grad-CAM shows that the model attends to semantically relevant regions, enhancing interpretability. Overall, S$^{2}$TDPT illustrates how biologically inspired attention can yield energy-efficient, hardware-friendly, and explainable neuromorphic models.

Attention via Synaptic Plasticity is All You Need: A Biologically Inspired Spiking Neuromorphic Transformer

arXiv:2511.08955v2 Announce Type: replace-cross 
Abstract: Simulating microstructure evolution (MicroEvo) is vital for materials design but demands high numerical accuracy, efficiency, and physical fidelity. Although recent studies on deep learning (DL) offer a promising alternative to traditional solvers, the field lacks standardized benchmarks. Existing studies are flawed due to a lack of comparing specialized MicroEvo DL models with state-of-the-art spatio-temporal architectures, an overemphasis on numerical accuracy over physical fidelity, and a failure to analyze error propagation over time. To address these gaps, we introduce MicroEvoEval, the first comprehensive benchmark for image-based microstructure evolution prediction. We evaluate 14 models, encompassing both domain-specific and general-purpose architectures, across four representative MicroEvo tasks with datasets specifically structured for both short- and long-term assessment. Our multi-faceted evaluation framework goes beyond numerical accuracy and computational cost, incorporating a curated set of structure-preserving metrics to assess physical fidelity. Our extensive evaluations yield several key insights. Notably, we find that modern architectures (e.g., VMamba), not only achieve superior long-term stability and physical fidelity but also operate with an order-of-magnitude greater computational efficiency. The results highlight the necessity of holistic evaluation and identify these modern architectures as a highly promising direction for developing efficient and reliable surrogate models in data-driven materials science.

MicroEvoEval: A Systematic Evaluation Framework for Image-Based Microstructure Evolution Prediction

arXiv:2508.20067v2 Announce Type: replace-cross 
Abstract: A key objective in spatial statistics is to simulate from the distribution of a spatial process at a selection of unobserved locations conditional on observations (i.e., a predictive distribution) to enable spatial prediction and uncertainty quantification. However, exact conditional simulation from this predictive distribution is intractable or inefficient for many spatial process models. In this paper, we propose neural conditional simulation (NCS), a general method for spatial conditional simulation that is based on neural diffusion models. Specifically, using spatial masks, we implement a conditional score-based diffusion model that evolves Gaussian noise into samples from a predictive distribution when given a partially observed spatial field and spatial process parameters as inputs. The diffusion model relies on a neural network that only requires unconditional samples from the spatial process for training. Once trained, the diffusion model is amortized with respect to the observations in the partially observed field, the number and locations of those observations, and the spatial process parameters, and can therefore be used to conditionally simulate from a broad class of predictive distributions without retraining the neural network. We assess the NCS-generated simulations against simulations from the true conditional distribution of a Gaussian process model, and against Markov chain Monte Carlo (MCMC) simulations from a Brown--Resnick process model for spatial extremes. In the latter case, we show that it is more efficient and accurate to conditionally simulate using NCS than classical MCMC techniques implemented in standard software. We conclude that NCS enables efficient and accurate conditional simulation from spatial predictive distributions that are challenging to sample from using traditional methods.

تقدم الورقة المعنونة 'المحاكاة الشرطية العصبية للعمليات المكانية المعقدة' طريقة جديدة تُعرف باسم المحاكاة الشرطية العصبية (NCS) تهدف إلى تحسين الإحصاءات المكانية. تستخدم NCS نماذج الانتشار العصبي لمحاكاة التوزيعات التنبؤية من حقول مكانية جزئية الملاحظة، مما يعالج عدم الكفاءة في الطرق التقليدية. تتطلب هذه الطريقة عينات غير شرطية فقط من العملية المكانية للتدريب، مما يمثل تقدمًا كبيرًا في التنبؤ المكاني وقياس عدم اليقين.

El artículo titulado 'Simulación Condicional Neuronal para Procesos Espaciales Complejos' presenta un nuevo método llamado simulación condicional neuronal (NCS) que busca mejorar la estadística espacial. La NCS utiliza modelos de difusión neuronal para simular distribuciones predictivas a partir de campos espaciales parcialmente observados, abordando las ineficiencias de los métodos tradicionales. Este enfoque solo requiere muestras incondicionales del proceso espacial para su entrenamiento, lo que representa un avance significativo en la predicción espacial y la cuantificación de la incertidu…

L'article intitulé 'Simulation conditionnelle neuronale pour des processus spatiaux complexes' présente une méthode novatrice appelée simulation conditionnelle neuronale (NCS) visant à améliorer les statistiques spatiales. La NCS utilise des modèles de diffusion neuronale pour simuler des distributions prédictives à partir de champs spatiaux partiellement observés, répondant ainsi aux inefficacités des méthodes traditionnelles. Cette approche nécessite uniquement des échantillons inconditionnels du processus spatial pour l'entraînement, ce qui représente une avancée significative dans la prédi…

The paper titled 'Neural Conditional Simulation for Complex Spatial Processes' introduces a novel method called neural conditional simulation (NCS) aimed at enhancing spatial statistics. NCS utilizes neural diffusion models to simulate predictive distributions from partially observed spatial fields, addressing the inefficiencies of traditional methods. This approach requires only unconditional samples from the spatial process for training, making it a significant advancement in spatial prediction and uncertainty quantification.

Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching

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