In cosmology, emulators play a crucial role by providing fast and accurate predictions of complex physical models, enabling efficient exploration of high-dimensional parameter spaces that would be computationally prohibitive with direct numerical simulations. Symbolic emulators have emerged as promising alternatives to numerical approaches, delivering comparable accuracy with significantly faster evaluation times. While previous symbolic emulators were limited to relatively narrow prior ranges, we expand these to cover the parameter space relevant for current cosmological analyses. We introduce approximations to hypergeometric functions used for the $Λ$CDM comoving distance and linear growth factor which are accurate to better than 0.001% and 0.05%, respectively, for all redshifts and for $Ω_{\rm m} \in [0.1, 0.5]$. We show that integrating symbolic emulators into a Dark Energy Survey-like $3\times2$pt analysis produces cosmological constraints consistent with those obtained using standard numerical methods. Our symbolic emulators offer substantial improvements in speed and memory usage, demonstrating their practical potential for scalable, likelihood-based inference.

Machine learning enables powerful cosmological inference but typically requires many high-fidelity simulations covering many cosmological models. Transfer learning offers a way to reduce the simulation cost by reusing knowledge across models. We show that pre-training on the standard model of cosmology, $Λ$CDM, and fine-tuning on various beyond-$Λ$CDM scenarios -- including massive neutrinos, modified gravity, and primordial non-Gaussianities -- can enable inference with significantly fewer beyond-$Λ$CDM simulations. However, we also show that negative transfer can occur when strong physical degeneracies exist between $Λ$CDM and beyond-$Λ$CDM parameters. We consider various transfer architectures, finding that including bottleneck structures provides the best performance. Our findings illustrate the opportunities and pitfalls of foundation-model approaches in physics: pre-training can accelerate inference, but may also hinder learning new physics.

We propose a novel regularization loss that enforces standard Gaussianity, encouraging samples to align with a standard Gaussian distribution. This facilitates a range of downstream tasks involving optimization in the latent space of text-to-image models. We treat elements of a high-dimensional sample as one-dimensional standard Gaussian variables and define a composite loss that combines moment-based regularization in the spatial domain with power spectrum-based regularization in the spectral domain. Since the expected values of moments and power spectrum distributions are analytically known, the loss promotes conformity to these properties. To ensure permutation invariance, the losses are applied to randomly permuted inputs. Notably, existing Gaussianity-based regularizations fall within our unified framework: some correspond to moment losses of specific orders, while the previous covariance-matching loss is equivalent to our spectral loss but incurs higher time complexity due to its spatial-domain computation. We showcase the application of our regularization in generative modeling for test-time reward alignment with a text-to-image model, specifically to enhance aesthetics and text alignment. Our regularization outperforms previous Gaussianity regularization, effectively prevents reward hacking and accelerates convergence.

ReLU networks, while prevalent for visual data, have sharp transitions, sometimes relying on individual pixels for predictions, making vanilla gradient-based explanations noisy and difficult to interpret. Existing methods, such as Grad-CAM, smooth these explanations by producing surrogate models at the cost of faithfulness. W e introduce a unifying spectral framework to systematically analyze and quantify smoothness, faithfulness, and their trade-off in explanations. Using this framework, we quantify and regularize the contribution of ReLU networks to high-frequency information, providing a principled approach to identifying this trade-off. Our analysis characterizes how surrogate-based smoothing distorts explanations, leading to an "explanation gap" that we formally define and measure for different post-hoc methods.

We introduce CLAPP (CLASS LLM Agent for Pair Programming), an interactive AI assistant designed to support researchers working with the Einstein-Boltzmann solver CLASS. CLAPP leverages large language models (LLMs) and domain-specific retrieval to provide conversational coding support for CLASS-answering questions, generating code, debugging errors, and producing plots. Its architecture combines multi-agent LLM orchestration, semantic search across CLASS documentation, and a live Python execution environment. Deployed as a user-friendly web application, CLAPP lowers the entry barrier for scientists unfamiliar with AI tools and enables more productive human-AI collaboration in computational and numerical cosmology. The app is available at https://classclapp.streamlit.app

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibits spatiotemporal chaos. We introduce a novel methodology that integrates ESNs with transfer learning, aiming to enhance predictive performance across various parameter regimes of the gKS model. Our research focuses on predicting changes in long-term statistical patterns of the gKS model that result from varying the dispersion relation or the length of the spatial domain. We use transfer learning to adapt ESNs to different parameter settings and successfully capture changes in the underlying chaotic attractor.

How many simulations do we need to train machine learning methods to extract information available from summary statistics of the cosmological density field? Neural methods have shown the potential to extract non-linear information available from cosmological data. Success depends critically on having sufficient simulations for training the networks and appropriate network architectures. In the first detailed convergence study of neural network training for cosmological inference, we show that currently available simulation suites, such as the Quijote Latin Hypercube(LH) with 2000 simulations, do not provide sufficient training data for a generic neural network to reach the optimal regime, even for the dark matter power spectrum, and in an idealized case. We discover an empirical neural scaling law that predicts how much information a neural network can extract from a highly informative summary statistic, the dark matter power spectrum, as a function of the number of simulations used to train the network, for a wide range of architectures and hyperparameters. We combine this result with the Cramer-Rao information bound to forecast the number of training simulations needed for near-optimal information extraction. To verify our method we created the largest publicly released simulation data set in cosmology, the Big Sobol Sequence(BSQ), consisting of 32,768 $\Lambda$CDM n-body simulations uniformly covering the $\Lambda$CDM parameter space. Our method enables efficient planning of simulation campaigns for machine learning applications in cosmology, while the BSQ dataset provides an unprecedented resource for studying the convergence behavior of neural networks in cosmological parameter inference. Our results suggest that new large simulation suites or new training approaches will be necessary to achieve information-optimal parameter inference from non-linear simulations.

Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first estimating the score function (the gradient of a smoothed log-distribution) and then applying a gradient-based sampling algorithm. The resulting distribution's correctness can be impacted by several factors: the generalization error due to a finite number of initial samples, the error in score matching, and the diffusion error introduced by the sampling algorithm. In this paper, we analyze the sampling process in a simple yet representative setting-sampling from Gaussian distributions using a Langevin diffusion sampler. We provide a sharp analysis of the Wasserstein sampling error that arises from the multiple sources of error throughout the pipeline. This allows us to rigorously track how the anisotropy of the data distribution (encoded by its power spectrum) interacts with key parameters of the end-to-end sampling method, including the noise amplitude, the step sizes in both score matching and diffusion, and the number of initial samples. Notably, we show that the Wasserstein sampling error can be expressed as a kernel-type norm of the data power spectrum, where the specific kernel depends on the method parameters. This result provides a foundation for further analysis of the tradeoffs involved in optimizing sampling accuracy, such as adapting the noise amplitude to the choice of step sizes.

Next-generation galaxy surveys promise unprecedented precision in testing gravity at cosmological scales. However, realising this potential requires accurately modelling the non-linear cosmic web. We address this challenge by exploring conditional generative modelling to create 3D dark matter density fields via score-based (diffusion) and flow-based methods. Our results demonstrate the power of diffusion models to accurately reproduce the matter power spectra and bispectra, even for unseen configurations. They also offer a significant speed-up with slightly reduced accuracy, when flow-based reconstructing the probability distribution function, but they struggle with higher-order statistics. To improve conditional generation, we introduce a novel multi-output model to develop feature representations of the cosmological parameters. Our findings offer a powerful tool for exploring deviations from standard gravity, combining high precision with reduced computational cost, thus paving the way for more comprehensive and efficient cosmological analyses null .