This work proposes a novel Coupled Oscillator Network (CON) model that simultaneously tackles all these issues. More specifically, (i) we show analytically that CON is a Lagrangian system - i.e., it possesses well-defined potential and kinetic energy terms.

We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main observation is that the time-varying velocity field of the PDE solution needs to be self-consistent: it must satisfy a fixed-point equation involving the probability flow characterized by the same velocity field.

Moreover, FFA offers bio-plausibility compared to traditional back-propagation (BP) methods in implementation.

Precise and comprehensive situational awareness is a critical capability of modern autonomous systems. Deep neural networks that perceive task-critical details from rich sensory signals have become ubiquitous; however, their black-box behavior and sensitivity to environmental uncertainty and distribution shifts make them challenging to verify formally. Abstraction-based verification techniques for vision-based autonomy produce safety guarantees contingent on rigid assumptions, such as bounded errors or known unique distributions. Such overly restrictive and inflexible assumptions limit the validity of the guarantees, especially in diverse and uncertain test-time environments. We propose a methodology that unifies the verification models of perception with their offline validation. Our methodology leverages interval MDPs and provides a flexible end-to-end guarantee that adapts directly to the out-of-distribution test-time conditions. We evaluate our methodology on a synthetic perception Markov chain with well-defined state estimation distributions and a mountain car benchmark. Our findings reveal that we can guarantee tight yet rigorous bounds on overall system safety.

Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike common score-based generative models (SGMs), which are governed by a single stochastic differential equation (SDE), SGGMs involve a system of coupled SDEs. In SGGMs, the graph structure and node features are governed by separate but interdependent SDEs. This distinction makes existing convergence analyses from SGMs inapplicable for SGGMs. In this work, we present the first non-asymptotic convergence analysis for SGGMs, focusing on the convergence bound (the risk of generative error) across three key graph generation paradigms: (1) feature generation with a fixed graph structure, (2) graph structure generation with fixed node features, and (3) joint generation of both graph structure and node features. Our analysis reveals several unique factors specific to SGGMs (e.g., the topological properties of the graph structure) which affect the convergence bound. Additionally, we offer theoretical insights into the selection of hyperparameters (e.g., sampling steps and diffusion length) and advocate for techniques like normalization to improve convergence. To validate our theoretical findings, we conduct a controlled empirical study using synthetic graph models, and the results align with our theoretical predictions. This work deepens the theoretical understanding of SGGMs, demonstrates their applicability in critical domains, and provides practical guidance for designing effective models.

Fine-tuning large language models (LLMs) with low-rank adaptaion (LoRA) is a cost-effective way to incorporate information from a specific dataset. However, it is often unclear how well the fine-tuned LLM will generalize, i.e., how well it will perform on unseen datasets. Methods have been proposed to improve generalization by optimizing with in-context prompts, or by using meta-learning to fine-tune LLMs. However, these methods are expensive in memory and computation, requiring either long-context prompts or saving copies of parameters and using second-order gradient updates. To address these challenges, we propose Amortized Bayesian Meta-Learning for LoRA (ABMLL). This method builds on amortized Bayesian meta-learning for smaller models, adapting this approach to LLMs while maintaining its computational efficiency. We reframe task-specific and global parameters in the context of LoRA and use a set of new hyperparameters to balance reconstruction accuracy and the fidelity of task-specific parameters to the global ones. ABMLL provides effective generalization and scales to large models such as Llama3-8B. Furthermore, as a result of using a Bayesian framework, ABMLL provides improved uncertainty quantification. We test ABMLL on Unified-QA and CrossFit datasets and find that it outperforms existing methods on these benchmarks in terms of both accuracy and expected calibration error.

Quantifying out-of-sample discrimination performance for time-to-event outcomes is a fundamental step for model evaluation and selection in the context of predictive modelling. The concordance index, or C-index, is a widely used metric for this purpose, particularly with the growing development of machine learning methods. Beyond differences between proposed C-index estimators (e.g. Harrell's, Uno's and Antolini's), we demonstrate the existence of a C-index multiverse among available R and python software, where seemingly equal implementations can yield different results. This can undermine reproducibility and complicate fair comparisons across models and studies. Key variation sources include tie handling and adjustment to censoring. Additionally, the absence of a standardised approach to summarise risk from survival distributions, result in another source of variation dependent on input types. We demonstrate the consequences of the C-index multiverse when quantifying predictive performance for several survival models (from Cox proportional hazards to recent deep learning approaches) on publicly available breast cancer data, and semi-synthetic examples. Our work emphasises the need for better reporting to improve transparency and reproducibility. This article aims to be a useful guideline, helping analysts when navigating the multiverse, providing unified documentation and highlighting potential pitfalls of existing software. All code is publicly available at: www.github.com/BBolosSierra/CindexMultiverse.

The Model Context Protocol has emerged as a transformative standard for connecting large language models to external data sources and tools, rapidly gaining adoption across major AI providers and development platforms. However, existing benchmarks are overly simplistic and fail to capture real application challenges such as long-horizon reasoning and large, unfamiliar tool spaces. To address this critical gap, we introduce MCP-Universe, the first comprehensive benchmark specifically designed to evaluate LLMs in realistic and hard tasks through interaction with real-world MCP servers. Our benchmark encompasses 6 core domains spanning 11 different MCP servers: Location Navigation, Repository Management, Financial Analysis, 3D Design, Browser Automation, and Web Searching. To ensure rigorous evaluation, we implement execution-based evaluators, including format evaluators for agent format compliance, static evaluators for time-invariant content matching, and dynamic evaluators that automatically retrieve real-time ground truth for temporally sensitive tasks. Through extensive evaluation of leading LLMs, we find that even SOTA models such as GPT-5 (43.72%), Grok-4 (33.33%) and Claude-4.0-Sonnet (29.44%) exhibit significant performance limitations. In addition, our benchmark poses a significant long-context challenge for LLM agents, as the number of input tokens increases rapidly with the number of interaction steps. Moreover, it introduces an unknown-tools challenge, as LLM agents often lack familiarity with the precise usage of the MCP servers. Notably, enterprise-level agents like Cursor cannot achieve better performance than standard ReAct frameworks. Beyond evaluation, we open-source our extensible evaluation framework with UI support, enabling researchers and practitioners to seamlessly integrate new agents and MCP servers while fostering innovation in the rapidly evolving MCP ecosystem.