Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning

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.

VisualPredicator: Learning Abstract World Models with Neuro-Symbolic Predicates for Robot Planning

Broadly intelligent agents should form task-specific abstractions that selectively expose the essential elements of a task, while abstracting away the complexity of the raw sensorimotor space. In this work, we present Neuro-Symbolic Predicates, a first-order abstraction language that combines the strengths of symbolic and neural knowledge representations. We outline an online algorithm for inventing such predicates and learning abstract world models. We compare our approach to hierarchical reinforcement learning, vision-language model planning, and symbolic predicate invention approaches, on both in- and out-of-distribution tasks across five simulated robotic domains. Results show that our approach offers better sample complexity, stronger out-of-distribution generalization, and improved interpretability.

Countering Autonomous Cyber Threats

With the capability to write convincing and fluent natural language and generate code, Foundation Models present dual-use concerns broadly and within the cyber domain specifically. Generative AI has already begun to impact cyberspace through a broad illicit marketplace for assisting malware development and social engineering attacks through hundreds of malicious-AI-as-a-services tools. More alarming is that recent research has shown the potential for these advanced models to inform or independently execute offensive cyberspace operations. However, these previous investigations primarily focused on the threats posed by proprietary models due to the until recent lack of strong open-weight model and additionally leave the impacts of network defenses or potential countermeasures unexplored. Critically, understanding the aptitude of downloadable models to function as offensive cyber agents is vital given that they are far more difficult to govern and prevent their misuse. As such, this work evaluates several state-of-the-art FMs on their ability to compromise machines in an isolated network and investigates defensive mechanisms to defeat such AI-powered attacks. Using target machines from a commercial provider, the most recently released downloadable models are found to be on par with a leading proprietary model at conducting simple cyber attacks with common hacking tools against known vulnerabilities. To mitigate such LLM-powered threats, defensive prompt injection (DPI) payloads for disrupting the malicious cyber agent's workflow are demonstrated to be effective. From these results, the implications for AI safety and governance with respect to cybersecurity is analyzed.

ALVIN: Active Learning Via INterpolation

Active Learning aims to minimize annotation effort by selecting the most useful instances from a pool of unlabeled data. However, typical active learning methods overlook the presence of distinct example groups within a class, whose prevalence may vary, e.g., in occupation classification datasets certain demographics are disproportionately represented in specific classes. This oversight causes models to rely on shortcuts for predictions, i.e., spurious correlations between input attributes and labels occurring in well-represented groups. To address this issue, we propose Active Learning Via INterpolation (ALVIN), which conducts intra-class interpolations between examples from under-represented and well-represented groups to create anchors, i.e., artificial points situated between the example groups in the representation space. By selecting instances close to the anchors for annotation, ALVIN identifies informative examples exposing the model to regions of the representation space that counteract the influence of shortcuts. Crucially, since the model considers these examples to be of high certainty, they are likely to be ignored by typical active learning methods. Experimental results on six datasets encompassing sentiment analysis, natural language inference, and paraphrase detection demonstrate that ALVIN outperforms state-of-the-art active learning methods in both in-distribution and out-of-distribution generalization.

Gridded Transformer Neural Processes for Large Unstructured Spatio-Temporal Data

Many important problems require modelling large-scale spatio-temporal datasets, with one prevalent example being weather forecasting. Recently, transformer-based approaches have shown great promise in a range of weather forecasting problems. However, these have mostly focused on gridded data sources, neglecting the wealth of unstructured, off-the-grid data from observational measurements such as those at weather stations. A promising family of models suitable for such tasks are neural processes (NPs), notably the family of transformer neural processes (TNPs). Although TNPs have shown promise on small spatio-temporal datasets, they are unable to scale to the quantities of data used by state-of-the-art weather and climate models. This limitation stems from their lack of efficient attention mechanisms. We address this shortcoming through the introduction of gridded pseudo-token TNPs which employ specialised encoders and decoders to handle unstructured observations and utilise a processor containing gridded pseudo-tokens that leverage efficient attention mechanisms. Our method consistently outperforms a range of strong baselines on various synthetic and real-world regression tasks involving large-scale data, while maintaining competitive computational efficiency. The real-life experiments are performed on weather data, demonstrating the potential of our approach to bring performance and computational benefits when applied at scale in a weather modelling pipeline.

On Evaluating LLMs' Capabilities as Functional Approximators: A Bayesian Perspective

Recent works have successfully applied Large Language Models (LLMs) to function modeling tasks. However, the reasons behind this success remain unclear. In this work, we propose a new evaluation framework to comprehensively assess LLMs' function modeling abilities. By adopting a Bayesian perspective of function modeling, we discover that LLMs are relatively weak in understanding patterns in raw data, but excel at utilizing prior knowledge about the domain to develop a strong understanding of the underlying function. Our findings offer new insights about the strengths and limitations of LLMs in the context of function modeling.

Linear Transformer Topological Masking with Graph Random Features

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in a graph. In this paper, we propose to parameterise topological masks as a learnable function of a weighted adjacency matrix -- a novel, flexible approach which incorporates a strong structural inductive bias. By approximating this mask with graph random features (for which we prove the first known concentration bounds), we show how this can be made fully compatible with linear attention, preserving $\mathcal{O}(N)$ time and space complexity with respect to the number of input tokens. The fastest previous alternative was $\mathcal{O}(N \log N)$ and only suitable for specific graphs. Our efficient masking algorithms provide strong performance gains for tasks on image and point cloud data, including with $>30$k nodes.

On the Weaknesses of Backdoor-based Model Watermarking: An Information-theoretic Perspective

Safeguarding the intellectual property of machine learning models has emerged as a pressing concern in AI security. Model watermarking is a powerful technique for protecting ownership of machine learning models, yet its reliability has been recently challenged by recent watermark removal attacks. In this work, we investigate why existing watermark embedding techniques particularly those based on backdooring are vulnerable. Through an information-theoretic analysis, we show that the resilience of watermarking against erasure attacks hinges on the choice of trigger-set samples, where current uses of out-distribution trigger-set are inherently vulnerable to white-box adversaries. Based on this discovery, we propose a novel model watermarking scheme, In-distribution Watermark Embedding (IWE), to overcome the limitations of existing method. To further minimise the gap to clean models, we analyze the role of logits as watermark information carriers and propose a new approach to better conceal watermark information within the logits. Experiments on real-world datasets including CIFAR-100 and Caltech-101 demonstrate that our method robustly defends against various adversaries with negligible accuracy loss (< 0.1%).

Mutual Information Multinomial Estimation

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data distribution can dramatically help estimate. This preliminary estimate serves as a bridge between the joint and the marginal distribution, and by comparing with this bridge distribution we can easily obtain the true difference between the joint distributions and the marginal distributions. Experiments on diverse tasks including non-Gaussian synthetic problems with known ground-truth and real-world applications demonstrate the advantages of our method.

Can Large Language Models Understand Symbolic Graphics Programs?

Assessing the capabilities of large language models (LLMs) is often challenging, in part, because it is hard to find tasks to which they have not been exposed during training. We take one step to address this challenge by turning to a new task: focusing on symbolic graphics programs, which are a popular representation for graphics content that procedurally generates visual data. LLMs have shown exciting promise towards program synthesis, but do they understand symbolic graphics programs? Unlike conventional programs, symbolic graphics programs can be translated to graphics content. Here, we characterize an LLM's understanding of symbolic programs in terms of their ability to answer questions related to the graphics content. This task is challenging as the questions are difficult to answer from the symbolic programs alone -- yet, they would be easy to answer from the corresponding graphics content as we verify through a human experiment. To understand symbolic programs, LLMs may need to possess the ability to imagine how the corresponding graphics content would look without directly accessing the rendered visual content. We use this task to evaluate LLMs by creating a large benchmark for the semantic understanding of symbolic graphics programs. This benchmark is built via program-graphics correspondence, hence requiring minimal human efforts. We evaluate current LLMs on our benchmark to elucidate a preliminary assessment of their ability to reason about visual scenes from programs. We find that this task distinguishes existing LLMs and models considered good at reasoning perform better. Lastly, we introduce Symbolic Instruction Tuning (SIT) to improve this ability. Specifically, we query GPT4-o with questions and images generated by symbolic programs. Such data are then used to finetune an LLM. We also find that SIT data can improve the general instruction following ability of LLMs.