Language agents [1-4] are AI agents [5] that integrate LLMs [6-8] as core components. LLMs excel at zero-shot generalization [9, 10], providing a notable advantage over traditional AI agents, such as those based on handcrafted rules or reinforcement learning, which often struggle to generalize to new environments [11]. While LLMs can exhibit flawed reasoning and logic when used in isolation [12-14], constructing a language agent by grounding LLMs in an environment with observational feedback can mitigate these issues. Early work on language agents used LLMs to directly output actions in the external environment [15-17], while more recently, language agents have been augmented with internal reasoning [18, 19] and planning [20, 21] procedures, as well as long-term memory storage [22, 23]. An emergent research challenge is to pose a theoretical description of the learning problem solved by language agents [4, 24] and to develop efficient methods to optimize the components of a language agent [24-26]. Here, we define common language agent tasks as language decision processes (LDPs) and frame language agents as stochastic computation graphs [27] that may be trained to solve LDPs. We show that pre-existing agents [18, 19, 21] can be implemented within our stochastic computation graph framework and introduce a simple and extensible software package named LDP that enables modular interchange of environments, agents, and optimizers, simplifying experimentation across a variety of settings. These authors jointly supervise technical work at FutureHouse.

The suite of datasets commonly used to train and evaluate the mathematical capabilities of AI-based mathematical copilots (primarily large language models) exhibit several shortcomings. These limitations include a restricted scope of mathematical complexity, typically not exceeding lower undergraduate-level mathematics, binary rating protocols and other issues, which makes comprehensive proof-based evaluation suites difficult. We systematically explore these limitations and contend that enhancing the capabilities of large language models, or any forthcoming advancements in AI-based mathematical assistants (copilots or "thought partners"), necessitates a paradigm shift in the design of mathematical datasets and the evaluation criteria of mathematical ability: It is necessary to move away from result-based datasets (theorem statement to theorem proof) and convert the rich facets of mathematical research practice to data LLMs can train on. Examples of these are mathematical workflows (sequences of atomic, potentially subfield-dependent tasks that are often performed when creating new mathematics), which are an important part of the proof-discovery process. Additionally, we advocate for mathematical dataset developers to consider the concept of "motivated proof", introduced by G. P\'olya in 1949, which can serve as a blueprint for datasets that offer a better proof learning signal, alleviating some of the mentioned limitations. Lastly, we introduce math datasheets for datasets, extending the general, dataset-agnostic variants of datasheets: We provide a questionnaire designed specifically for math datasets that we urge dataset creators to include with their datasets. This will make creators aware of potential limitations of their datasets while at the same time making it easy for readers to assess it from the point of view of training and evaluating mathematical copilots.

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, either cover only elementary mathematics or are very small. We address this by publicly releasing two new datasets: GHOSTS and miniGHOSTS. These are the first natural-language datasets curated by working researchers in mathematics that (1) aim to cover graduate-level mathematics, (2) provide a holistic overview of the mathematical capabilities of language models, and (3) distinguish multiple dimensions of mathematical reasoning. These datasets also test whether ChatGPT and GPT-4 can be helpful assistants to professional mathematicians by emulating use cases that arise in the daily professional activities of mathematicians. We benchmark the models on a range of fine-grained performance metrics. For advanced mathematics, this is the most detailed evaluation effort to date. We find that ChatGPT can be used most successfully as a mathematical assistant for querying facts, acting as a mathematical search engine and knowledge base interface. GPT-4 can additionally be used for undergraduate-level mathematics but fails on graduate-level difficulty. Contrary to many positive reports in the media about GPT-4 and ChatGPT's exam-solving abilities (a potential case of selection bias), their overall mathematical performance is well below the level of a graduate student. Hence, if your goal is to use ChatGPT to pass a graduate-level math exam, you would be better off copying from your average peer!

In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in synthetic chemistry and materials science is time and cost-intensive to collect. On the other hand, knowledge about the data-generation mechanism is often available in the sciences, such as the measurement error of a piece of laboratory apparatus. Both characteristics, small data and knowledge of the underlying physics, make Gaussian processes (GPs) ideal candidates for fitting such datasets. GPs can make predictions with consideration of uncertainty, for example in the virtual screening of molecules and materials, and can also make inferences about incomplete data such as the latent emission signature from a black hole accretion disc. Furthermore, GPs are currently the workhorse model for Bayesian optimisation, a methodology foreseen to be a guide for laboratory experiments in scientific discovery campaigns. The first contribution of this thesis is to use GP modelling to reason about the latent emission signature from the Seyfert galaxy Markarian 335, and by extension, to reason about the applicability of various theoretical models of black hole accretion discs. The second contribution is to extend the GP framework to molecular and chemical reaction representations and to provide an open-source software library to enable the framework to be used by scientists. The third contribution is to leverage GPs to discover novel and performant photoswitch molecules. The fourth contribution is to introduce a Bayesian optimisation scheme capable of modelling aleatoric uncertainty to facilitate the identification of material compositions that possess intrinsic robustness to large scale fabrication processes.

We introduce GAUCHE, a library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation. Extending Gaussian processes to chemical representations, however, is nontrivial, necessitating kernels defined over structured inputs such as graphs, strings and bit vectors. By defining such kernels in GAUCHE, we seek to open the door to powerful tools for uncertainty quantification and Bayesian optimisation in chemistry. Motivated by scenarios frequently encountered in experimental chemistry, we showcase applications for GAUCHE in molecular discovery and chemical reaction optimisation. The codebase is made available at https://github.com/leojklarner/gauche

Models of human motion commonly focus either on trajectory prediction or action classification but rarely both. The marked heterogeneity and intricate compositionality of human motion render each task vulnerable to the data degradation and distributional shift common to real-world scenarios. A sufficiently expressive generative model of action could in theory enable data conditioning and distributional resilience within a unified framework applicable to both tasks. Here we propose a novel architecture based on hierarchical variational autoencoders and deep graph convolutional neural networks for generating a holistic model of action over multiple time-scales. We show this Hierarchical Graph-convolutional Variational Autoencoder (HG-VAE) to be capable of generating coherent actions, detecting out-of-distribution data, and imputing missing data by gradient ascent on the model's posterior. Trained and evaluated on H3.6M and the largest collection of open source human motion data, AMASS, we show HG-VAE can facilitate downstream discriminative learning better than baseline models.

Bayesian optimisation presents a sample-efficient methodology for global optimisation. Within this framework, a crucial performance-determining subroutine is the maximisation of the acquisition function, a task complicated by the fact that acquisition functions tend to be non-convex and thus nontrivial to optimise. In this paper, we undertake a comprehensive empirical study of approaches to maximise the acquisition function. Additionally, by deriving novel, yet mathematically equivalent, compositional forms for popular acquisition functions, we recast the maximisation task as a compositional optimisation problem, allowing us to benefit from the extensive literature in this field. We highlight the empirical advantages of the compositional approach to acquisition function maximisation across 3958 individual experiments comprising synthetic optimisation tasks as well as tasks from Bayesmark. Given the generality of the acquisition function maximisation subroutine, we posit that the adoption of compositional optimisers has the potential to yield performance improvements across all domains in which Bayesian optimisation is currently being applied.

Built upon GPflow and RDKit, FlowMO enables the user to make predictions with well-calibrated uncertainty estimates, an output central to active learning and molecular design applications. Gaussian Processes are particularly attractive for modelling small molecular datasets, a characteristic of many real-world virtual screening campaigns where high-quality experimental data is scarce. Computational experiments across three small datasets demonstrate comparable predictive performance to deep learning methods but with superior uncertainty calibration.

The space of synthesizable molecules is greater than $10^{60}$, meaning only a vanishingly small fraction of these molecules have ever been realized in the lab. In order to prioritize which regions of this space to explore next, synthetic chemists need access to accurate molecular property predictions. While great advances in molecular machine learning have been made, there is a dearth of benchmarks featuring properties that are useful for the synthetic chemist. Focussing directly on the needs of the synthetic chemist, we introduce the Photoswitch Dataset, a new benchmark for molecular machine learning where improvements in model performance can be immediately observed in the throughput of promising molecules synthesized in the lab. Photoswitches are a versatile class of molecule for medical and renewable energy applications where a molecule's efficacy is governed by its electronic transition wavelengths. We demonstrate superior performance in predicting these wavelengths compared to both time-dependent density functional theory (TD-DFT), the incumbent first principles quantum mechanical approach, as well as a panel of human experts. Our baseline models are currently being deployed in the lab as part of the decision process for candidate synthesis. It is our hope that this benchmark can drive real discoveries in photoswitch chemistry and that future benchmarks can be introduced to pivot learning algorithm development to benefit more expansive areas of synthetic chemistry.

Bayesian optimisation is an important decision-making tool for high-stakes applications in drug discovery and materials design. An oft-overlooked modelling consideration however is the representation of input-dependent or heteroscedastic aleatoric uncertainty. The cost of misrepresenting this uncertainty as being homoscedastic could be high in drug discovery applications where neglecting heteroscedasticity in high throughput virtual screening could lead to a failed drug discovery program. In this paper, we propose a heteroscedastic Bayesian optimisation scheme which both represents and penalises aleatoric noise in the suggestions.Our scheme features a heteroscedastic Gaussian Process (GP) as the surrogate model in conjunction with two acquisition heuristics. First, we extend the augmented expected improvement (AEI) heuristic to the heteroscedastic setting and second, we introduce a new acquisition function, aleatoric-penalised expected improvement (ANPEI) based on a simple scalarisation of the performance and noise objective. Both methods penalise aleatoric noise in the suggestions and yield improved performance relative to a naive implementation of homoscedastic Bayesian optimisation on toy problems as well as a real-world optimisation problem.