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We present NeuralMag, a flexible and high-performance open-source Python library for micromagnetic simulations. NeuralMag leverages modern machine learning frameworks, such as PyTorch and JAX, to perform efficient tensor operations on various parallel hardware, including CPUs, GPUs, and TPUs. The library implements a novel nodal finite-difference discretization scheme that provides improved accuracy over traditional finite-difference methods without increasing computational complexity. NeuralMag is particularly well-suited for solving inverse problems, especially those with time-dependent objectives, thanks to its automatic differentiation capabilities. Performance benchmarks show that NeuralMag is competitive with state-of-the-art simulation codes while offering enhanced flexibility through its Python interface and integration with high-level computational backends.

Digital Twins (DTs) are computational models that simulate the states and temporal dynamics of real-world systems, playing a crucial role in prediction, understanding, and decision-making across diverse domains. However, existing approaches to DTs often struggle to generalize to unseen conditions in data-scarce settings, a crucial requirement for such models. To address these limitations, our work begins by establishing the essential desiderata for effective DTs. Hybrid Digital Twins ($\textbf{HDTwins}$) represent a promising approach to address these requirements, modeling systems using a composition of both mechanistic and neural components. This hybrid architecture simultaneously leverages (partial) domain knowledge and neural network expressiveness to enhance generalization, with its modular design facilitating improved evolvability. While existing hybrid models rely on expert-specified architectures with only parameters optimized on data, $\textit{automatically}$ specifying and optimizing HDTwins remains intractable due to the complex search space and the need for flexible integration of domain priors. To overcome this complexity, we propose an evolutionary algorithm ($\textbf{HDTwinGen}$) that employs Large Language Models (LLMs) to autonomously propose, evaluate, and optimize HDTwins. Specifically, LLMs iteratively generate novel model specifications, while offline tools are employed to optimize emitted parameters. Correspondingly, proposed models are evaluated and evolved based on targeted feedback, enabling the discovery of increasingly effective hybrid models. Our empirical results reveal that HDTwinGen produces generalizable, sample-efficient, and evolvable models, significantly advancing DTs' efficacy in real-world applications., Comment: Accepted as Spotlight at NeurIPS2024

Offline preference optimization is a key method for enhancing and controlling the quality of Large Language Model (LLM) outputs. Typically, preference optimization is approached as an offline supervised learning task using manually-crafted convex loss functions. While these methods are based on theoretical insights, they are inherently constrained by human creativity, so the large search space of possible loss functions remains under explored. We address this by performing LLM-driven objective discovery to automatically discover new state-of-the-art preference optimization algorithms without (expert) human intervention. Specifically, we iteratively prompt an LLM to propose and implement new preference optimization loss functions based on previously-evaluated performance metrics. This process leads to the discovery of previously-unknown and performant preference optimization algorithms. The best performing of these we call Discovered Preference Optimization (DiscoPOP), a novel algorithm that adaptively blends logistic and exponential losses. Experiments demonstrate the state-of-the-art performance of DiscoPOP and its successful transfer to held-out tasks.

Inferring unbiased treatment effects has received widespread attention in the machine learning community. In recent years, our community has proposed numerous solutions in standard settings, high-dimensional treatment settings, and even longitudinal settings. While very diverse, the solution has mostly relied on neural networks for inference and simultaneous correction of assignment bias. New approaches typically build on top of previous approaches by proposing new (or refined) architectures and learning algorithms. However, the end result -- a neural-network-based inference machine -- remains unchallenged. In this paper, we introduce a different type of solution in the longitudinal setting: a closed-form ordinary differential equation (ODE). While we still rely on continuous optimization to learn an ODE, the resulting inference machine is no longer a neural network. Doing so yields several advantages such as interpretability, irregular sampling, and a different set of identification assumptions. Above all, we consider the introduction of a completely new type of solution to be our most important contribution as it may spark entirely new innovations in treatment effects in general. We facilitate this by formulating our contribution as a framework that can transform any ODE discovery method into a treatment effects method., Comment: Published in The Twelfth International Conference on Learning Representations (ICLR). Copyright 2024 by the author(s)

Large Language Models (LLMs) have demonstrated the strong potential to assist both clinicians and the general public with their extensive medical knowledge. However, their application in healthcare is constrained due to concerns about the privacy of data used in training, which prevents the integration of private and personal information because of security and ethical issues. Moreover, if their capabilities can be enhanced with information retrieval to access up-to-date knowledge, the current integration of LLMs with Information retrieval lacks robustness to imperfect retrieval, which can hinder their effectiveness and even reduce overall performance. In this work, we address this challenge by introducing the Retrieval-Augmented Thought Process (RATP). Given access to external knowledge, RATP formulates the thought generation of LLMs as a multiple-step decision process. To optimise such a thought process, RATP leverages Monte-Carlo Tree Search and learns a proxy reward function that permits cost-efficient inference. On a private dataset of electronic medical records, deliberately excluded from any LLM training set, RATP achieves 35% additional accuracy compared to in-context retrieval-augmented generation for the question-answering task., Comment: 17 pages, 18 figures

Reinforcement Learning from Human Feedback (RLHF) has been credited as the key advance that has allowed Large Language Models (LLMs) to effectively follow instructions and produce useful assistance. Classically, this involves generating completions from the LLM in response to a query before using a separate reward model to assign a score to the full completion. As an auto-regressive process, the LLM has to take many "actions" (selecting individual tokens) and only receives a single, sparse reward at the end of an episode, a setup that is known to be difficult to optimise in traditional reinforcement learning. In this work we leverage the fact that the reward model contains more information than just its scalar output, in particular, it calculates an attention map over tokens as part of the transformer architecture. We use these attention weights to redistribute the reward along the whole completion, effectively densifying the signal and highlighting the most important tokens, all without incurring extra computational cost or requiring any additional modelling. We demonstrate that, theoretically, this approach is equivalent to potential-based reward shaping, ensuring that the optimal policy remains unchanged. Empirically, we show that it stabilises training, accelerates the rate of learning, and, in practical cases, may lead to better local optima.

Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex combinatorial search space. Existing methods, ranging from heuristic search to reinforcement learning, fail to scale with the number of input variables. We make the observation that closed-form equations often have structural characteristics and invariances (e.g., the commutative law) that could be further exploited to build more effective symbolic regression solutions. Motivated by this observation, our key contribution is to leverage pre-trained deep generative models to capture the intrinsic regularities of equations, thereby providing a solid foundation for subsequent optimization steps. We show that our novel formalism unifies several prominent approaches of symbolic regression and offers a new perspective to justify and improve on the previous ad hoc designs, such as the usage of cross-entropy loss during pre-training. Specifically, we propose an instantiation of our framework, Deep Generative Symbolic Regression (DGSR). In our experiments, we show that DGSR achieves a higher recovery rate of true equations in the setting of a larger number of input variables, and it is more computationally efficient at inference time than state-of-the-art RL symbolic regression solutions., Comment: In the proceedings of the Eleventh International Conference on Learning Representations (ICLR 2023). https://iclr.cc/virtual/2023/poster/11782

Transformer-based large language models (LLMs) are constrained by the fixed context window of the underlying transformer architecture, hindering their ability to produce long and coherent outputs. Memory-augmented LLMs are a promising solution, but current approaches cannot handle long output generation tasks since they (1) only focus on reading memory and reduce its evolution to the concatenation of new memories or (2) use very specialized memories that cannot adapt to other domains. This paper presents L2MAC, the first practical LLM-based general-purpose stored-program automatic computer (von Neumann architecture) framework, an LLM-based multi-agent system, for long and consistent output generation. Its memory has two components: the instruction registry, which is populated with a prompt program to solve the user-given task, and a file store, which will contain the final and intermediate outputs. Each instruction in turn is executed by a separate LLM agent, whose context is managed by a control unit capable of precise memory reading and writing to ensure effective interaction with the file store. These components enable L2MAC to generate extensive outputs, bypassing the constraints of the finite context window while producing outputs that fulfill a complex user-specified task. We empirically demonstrate that L2MAC achieves state-of-the-art performance in generating large codebases for system design tasks, significantly outperforming other coding methods in implementing the detailed user-specified task; we show that L2MAC works for general-purpose extensive text-based tasks, such as writing an entire book; and we provide valuable insights into L2MAC's performance improvement over existing methods., Comment: Published in The Twelfth International Conference on Learning Representations (ICLR), 2024. Copyright 2023 by the author(s)

The Bloch point is a point singularity in the magnetisation configuration, where the magnetisation vanishes. It can exist as an equilibrium configuration and plays an important role in many magnetisation reversal processes. In the present work, we focus on manipulating Bloch points in a system that can host stable Bloch points - a two-layer FeGe nanostrip with opposite chirality of the two layers. We drive Bloch points using spin-transfer torques and find that Bloch points can move collectively without any Hall effect and report that Bloch points are repelled from the sample boundaries and each other. We study pinning of Bloch points at wedge-shaped constrictions (notches) in the nanostrip and demonstrate that arrays of Bloch points can be moved past a series of notches in a controlled manner by applying consecutive current pulses of different strength. Finally, we simulate a T-shaped geometry and demonstrate that a Bloch point can be moved along different paths by applying current between suitable strip ends., Comment: 12 pages, 7 figures

We report a case study where an existing materials science course was modified to include numerical simulation projects on the micromagnetic behavior of materials. The Ubermag micromagnetic simulation software package is used in order to solve problems computationally. The simulation software is controlled through Python code in Jupyter notebooks. Our experience is that the self-paced problem-solving nature of the project work can facilitate a better in-depth exploration of the course contents. We discuss which aspects of the Ubermag and the project Jupyter ecosystem have been beneficial for the students' learning experience and which could be transferred to similar teaching activities in other subject areas., Comment: Main article: 9 pages; supplementary material: 24 pages. Accepted for publication in American Journal of Physics

Many real-world offline reinforcement learning (RL) problems involve continuous-time environments with delays. Such environments are characterized by two distinctive features: firstly, the state x(t) is observed at irregular time intervals, and secondly, the current action a(t) only affects the future state x(t + g) with an unknown delay g > 0. A prime example of such an environment is satellite control where the communication link between earth and a satellite causes irregular observations and delays. Existing offline RL algorithms have achieved success in environments with irregularly observed states in time or known delays. However, environments involving both irregular observations in time and unknown delays remains an open and challenging problem. To this end, we propose Neural Laplace Control, a continuous-time model-based offline RL method that combines a Neural Laplace dynamics model with a model predictive control (MPC) planner--and is able to learn from an offline dataset sampled with irregular time intervals from an environment that has a inherent unknown constant delay. We show experimentally on continuous-time delayed environments it is able to achieve near expert policy performance., Comment: Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS) 2023, Valencia, Spain. PMLR: Volume 206. Copyright 2023 by the author(s)

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks. However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in engineering and biological systems. Broader classes of differential equations (DE) have been proposed as remedies, including delay differential equations and integro-differential equations. Furthermore, Neural ODE suffers from numerical instability when modelling stiff ODEs and ODEs with piecewise forcing functions. In this work, we propose Neural Laplace, a unified framework for learning diverse classes of DEs including all the aforementioned ones. Instead of modelling the dynamics in the time domain, we model it in the Laplace domain, where the history-dependencies and discontinuities in time can be represented as summations of complex exponentials. To make learning more efficient, we use the geometrical stereographic map of a Riemann sphere to induce more smoothness in the Laplace domain. In the experiments, Neural Laplace shows superior performance in modelling and extrapolating the trajectories of diverse classes of DEs, including the ones with complex history dependency and abrupt changes., Comment: Proceedings of the 39th International Conference on Machine Learning, Baltimore, Maryland, USA, PMLR 162, 2022. Copyright 2022 by the author(s)

We show Bitcoin implied volatility on a 5 minute time horizon is modestly predictable from price, volatility momentum and alternative data including sentiment and engagement. Lagged Bitcoin index price and volatility movements contribute to the model alongside Google Trends with markets responding often several hours later. The code and datasets used in this paper can be found at https://github.com/Globe-Research/bitfear., Comment: 9 pages, 3 figures

This paper shows that temporal CNNs accurately predict bitcoin spot price movements from limit order book data. On a 2 second prediction time horizon we achieve 71\% walk-forward accuracy on the popular cryptocurrency exchange coinbase. Our model can be trained in less than a day on commodity GPUs which could be installed into colocation centers allowing for model sync with existing faster orderbook prediction models. We provide source code and data at https://github.com/Globe-Research/deep-orderbook., Comment: 9 pages, 7 figures

Cryptocurrency markets have many of the characteristics of 20th century commodities markets, making them an attractive candidate for trend following strategies. We present a decade of evidence from the infancy of bitcoin, showcasing the potential investor returns in cryptocurrency trend following, 255% walkforward annualised returns. We find that cryptocurrencies offer similar returns characteristics to commodities with similar risk-adjusted returns, and strong bear market diversification against traditional equities. Code available at https://github.com/Globe-Research/bittrends., Comment: 8 pages, 6 figures

The GaV$_4$S$_{8-y}$Se$_y$ $(y = 0$ to $8)$ family of materials have been synthesized in both polycrystalline and single crystal form, and their structural and magnetic properties thoroughly investigated. Each of these materials crystallizes in the $F\bar{4}3m$ space group at ambient temperature. However, in contrast to the end members GaV$_4$S$_8$ and GaV$_4$Se$_8$, that undergo a structural transition to the $R3m$ space group at 42 and 41 K respectively, the solid solutions $(y = 1$ to $7)$ retain cubic symmetry down to 1.5 K. In zero applied field the end members of the family order ferromagnetically at 13 K (GaV$_4$S$_8$) and 18 K (GaV$_4$Se$_8$), while the intermediate compounds exhibit a spin-glass-like ground state. We demonstrate that the magnetic structure of GaV$_4$S$_8$ shows localization of spins on the V cations, indicating that a charge ordering mechanism drives the structural phase transition. We conclude that the observation of both structural and ferromagnetic transitions in the end members of the series in zero field is a prerequisite for the stabilization of a skyrmion phase, and discuss how the absence of these transitions in the $y = 1$ to $7$ materials can be explained by their structural properties., Comment: Main text: 14 pages, 5 figures, 1 table. Supplementary information: 10 pages, 6 figures, 6 tables

NASA has titled its 2020 thrust for the Moon, Artemis. The increased focus on the Moon as a destination for future human and robotic expeditions necessitates general purpose navigational and communications infrastructure reducing their complexity to help establish a sustained presence. A framework through which Lunar missions can relay communications and localize their positions shifts the burden from the individual mission and enables resource allocation tailored to mission-specific goals. During the summer of 2020, student interns under the Innovation to Flight (i2F) program at the National Aeronautics and Space Administration’s (NASA) Jet Propulsion Laboratory (JPL) in collaboration with the University of Colorado Boulder designed, built, and tested a prototype framework capable of providing surface assets with communication and positioning services. The team utilized the existing i2F CubeSat bus in addition to developing several CubeSat engineering development units (EDUs), a ground vehicle, and a ground station to simulate a scenario in which a lunar surface mission is supported by these services. A primary goal of the summer was to develop a method for localizing the ground vehicle through trilateration. Distances are inferred from the round-trip time of flight (ToF) of radio signals between an asset and several elements. Signals were sent and received using LimeSDR software defined radios on-board both the ground vehicle and the EDUs; ToF and trilateration were calculated on a Qualcomm Snapdragon development board located within the LA MOON payload data system. The ModalAI chipset on the Qualcomm was instrumental in executing visual based position estimation. Communications was facilitated through a bent-pipe approach addressing the NASA requirement to provide solutions for in communication denied locations. The ground vehicle relayed information to other surface assets in addition to its ground station through the supporting constellation. This project demonstrates the feasibility of a lunar CubeSat constellation for the support of surface assets and explores packaging and operations of the components critical to trilateration and bent-pipe communication into a standard CubeSat form factor. When implemented, this framework will open a door for new surface missions designed with lower power requirements and increased operational access.