arXiv:2609.08981v2 Announce Type: replace-cross Abstract: A growing body of work establishes that large language models are not mere statistical memorizers, but are capable of in-context learning: performing inference at test time using only examples provided in the prompt, without any parameter updates. Prior theoretical work has shown that this capability extends to supervised learning tasks such as linear regression. We prove that in-context learning extends further to \emph{data generation}: frozen transformers can simulate iterative generative samplers from in-context samples. We first show that transformers can realize closed-form and smoothed closed-form diffusion samplers. The construction identifies a concrete generative role for softmax attention: it computes responsibility weights and weighted empirical averages, while feedforward layers implement Euler updates. To empirically relate these constructions to pretrained language models, we study \emph{semantic-topic sampling}: prompts consisting of words drawn from a common semantic category, such as animals, foods, or cities. Across transformer layers, the normalized hidden states exhibit a two-stage geometry: they move toward a uniform spherical reference in intermediate layers and then return to structured, topic-dependent representations near the output. We further measure an interacting-particle energy on these hidden-state clouds and observe the same U-shape pattern. We then prove that transformers can approximate an energy-based sampler, constructing the same U-shape energy across the layers.

arXiv:2605.25234v1 Announce Type: cross Abstract: Epistemic uncertainty is often viewed as a reducible uncertainty that vanishes with increasing data. This perspective implicitly assumes parameter identifiability and equates epistemic uncertainty with predictive variability. In overparametrized neural networks, however, model parameters are typically non-identifiable due to symmetries and redundant representations. As a consequence, substantial parameter uncertainty can persist even when the underlying function is fully identified. In this work, we analyze epistemic uncertainty through the lens of non-identifiability and characterize both discrete and continuous sources of residual uncertainty. Focusing on one-hidden-layer ReLU networks, we thoroughly analyze the resulting posterior structure and validate our theoretical insights through empirical studies.

arXiv:2604.03898v1 Announce Type: new Abstract: This paper introduces discourse_simulator, an open-source framework that combines LLMs with agent-based modelling. It offers a new way to simulate how public attitudes toward immigration change over time in response to salient events like protests, controversies, or policy debates. Large language models (LLMs) are used to generate social media posts, interpret opinions, and model how ideas spread through social networks. Unlike traditional agent-based models that rely on fixed, rule-based opinion updates and cannot generate natural language or consider current events, this approach integrates multidimensional sociological belief structures and real-world event timelines. This framework is wrapped into an open-source Python package that integrates generative agents into a small-world network topology and a live news retrieval system. discourse_sim is purpose-built as a social science research instrument specifically for studying attitude dynamics, polarisation, and belief evolution following real-world critical events. Unlike other LLM Agent Swarm frameworks, which treat the simulations as a prediction black box, discourse_sim treats it as a theory-testing instrument, which is fundamentally a different epistemological stance for studying social science problems. The paper further demonstrates the framework by modelling the Dublin anti-immigration march on April 26, 2025, with N=100 agents over a 15-day simulation. Package link: https://pypi.org/project/discourse-sim/

arXiv:2409.09787v5 Announce Type: replace-cross Abstract: Developing an efficient sampler capable of generating independent and identically distributed (IID) samples from a Boltzmann distribution is a crucial challenge in scientific research, e.g. molecular dynamics. In this work, we intend to learn neural samplers given energy functions instead of data sampled from the Boltzmann distribution. By learning the energies of the noised data, we propose a diffusion-based sampler, Noised Energy Matching, which theoretically has lower variance and more complexity compared to related works. Furthermore, a novel bootstrapping technique is applied to NEM to balance between bias and variance. We evaluate NEM and BNEM on a 2-dimensional 40 Gaussian Mixture Model (GMM) and a 4-particle double-well potential (DW-4). The experimental results demonstrate that BNEM can achieve state-of-the-art performance while being more robust.

arXiv:2410.19412v3 Announce Type: replace-cross Abstract: Agent-Based Model (ABM) validation is crucial as it helps ensuring the reliability of simulations, and causal discovery has become a powerful tool in this context. However, current causal discovery methods often face accuracy and robustness challenges when applied to complex and noisy time series data, which is typical in ABM scenarios. This study addresses these issues by proposing a Robust Cross-Validation (RCV) approach to enhance causal structure learning for ABM validation. We develop RCV-VarLiNGAM and RCV-PCMCI, novel extensions of two prominent causal discovery algorithms. These aim to reduce the impact of noise better and give more reliable causal relation results, even with high-dimensional, time-dependent data. The proposed approach is then integrated into an enhanced ABM validation framework, which is designed to handle diverse data and model structures. The approach is evaluated using synthetic datasets and a complex simulated fMRI dataset. The results demonstrate greater reliability in causal structure identification. The study examines how various characteristics of datasets affect the performance of established causal discovery methods. These characteristics include linearity, noise distribution, stationarity, and causal structure density. This analysis is then extended to the RCV method to see how it compares in these different situations. This examination helps confirm whether the results are consistent with existing literature and also reveals the strengths and weaknesses of the novel approaches. By tackling key methodological challenges, the study aims to enhance ABM validation with a more resilient valuation framework presented. These improvements increase the reliability of model-driven decision making processes in complex systems analysis.

arXiv:2410.19412v2 Announce Type: replace-cross Abstract: Time series causal discovery is essential for understanding dynamic systems, yet many existing methods remain sensitive to noise, non-stationarity, and sampling variability. We propose the Validated Consensus-Driven Framework (VCDF), a simple and method-agnostic layer that improves robustness by evaluating the stability of causal relations across blocked temporal subsets. VCDF requires no modification to base algorithms and can be applied to methods such as VAR-LiNGAM and PCMCI. Experiments on synthetic datasets show that VCDF improves VAR-LiNGAM by approximately 0.08-0.12 in both window and summary F1 scores across diverse data characteristics, with gains most pronounced for moderate-to-long sequences. The framework also benefits from longer sequences, yielding up to 0.18 absolute improvement on time series of length 1000 and above. Evaluations on simulated fMRI data and IT-monitoring scenarios further demonstrate enhanced stability and structural accuracy under realistic noise conditions. VCDF provides an effective reliability layer for time series causal discovery without altering underlying modeling assumptions.