Adrian Weller

Longhui Yu, Weisen Jiang, Han Shi et al. · cambridge

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.

Vedant Nanda, Till Speicher, Camila Kolling et al. · cambridge

A major challenge in studying robustness in deep learning is defining the set of ``meaningless'' perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model to define such perturbations. Our work offers a new view on robustness by using another reference NN to define the set of perturbations a given NN should be invariant to, thus generalizing the reliance on a reference ``human NN'' to any NN. This makes measuring robustness equivalent to measuring the extent to which two NNs share invariances, for which we propose a measure called STIR. STIR re-purposes existing representation similarity measures to make them suitable for measuring shared invariances. Using our measure, we are able to gain insights into how shared invariances vary with changes in weight initialization, architecture, loss functions, and training dataset. Our implementation is available at: \url{https://github.com/nvedant07/STIR}.

Zeju Qiu, Weiyang Liu, Haiwen Feng et al. · cambridge

Large text-to-image diffusion models have impressive capabilities in generating photorealistic images from text prompts. How to effectively guide or control these powerful models to perform different downstream tasks becomes an important open problem. To tackle this challenge, we introduce a principled finetuning method -- Orthogonal Finetuning (OFT), for adapting text-to-image diffusion models to downstream tasks. Unlike existing methods, OFT can provably preserve hyperspherical energy which characterizes the pairwise neuron relationship on the unit hypersphere. We find that this property is crucial for preserving the semantic generation ability of text-to-image diffusion models. To improve finetuning stability, we further propose Constrained Orthogonal Finetuning (COFT) which imposes an additional radius constraint to the hypersphere. Specifically, we consider two important finetuning text-to-image tasks: subject-driven generation where the goal is to generate subject-specific images given a few images of a subject and a text prompt, and controllable generation where the goal is to enable the model to take in additional control signals. We empirically show that our OFT framework outperforms existing methods in generation quality and convergence speed.

Lance Ying, Katherine M. Collins, Megan Wei et al. · cambridge, mit

Human beings are social creatures. We routinely reason about other agents, and a crucial component of this social reasoning is inferring people's goals as we learn about their actions. In many settings, we can perform intuitive but reliable goal inference from language descriptions of agents, actions, and the background environments. In this paper, we study this process of language driving and influencing social reasoning in a probabilistic goal inference domain. We propose a neuro-symbolic model that carries out goal inference from linguistic inputs of agent scenarios. The "neuro" part is a large language model (LLM) that translates language descriptions to code representations, and the "symbolic" part is a Bayesian inverse planning engine. To test our model, we design and run a human experiment on a linguistic goal inference task. Our model closely matches human response patterns and better predicts human judgements than using an LLM alone.

Ilia Sucholutsky, Lukas Muttenthaler, Adrian Weller et al. · berkeley, cambridge

Biological and artificial information processing systems form representations of the world that they can use to categorize, reason, plan, navigate, and make decisions. How can we measure the similarity between the representations formed by these diverse systems? Do similarities in representations then translate into similar behavior? If so, then how can a system's representations be modified to better match those of another system? These questions pertaining to the study of representational alignment are at the heart of some of the most promising research areas in contemporary cognitive science, neuroscience, and machine learning. In this Perspective, we survey the exciting recent developments in representational alignment research in the fields of cognitive science, neuroscience, and machine learning. Despite their overlapping interests, there is limited knowledge transfer between these fields, so work in one field ends up duplicated in another, and useful innovations are not shared effectively. To improve communication, we propose a unifying framework that can serve as a common language for research on representational alignment, and map several streams of existing work across fields within our framework. We also lay out open problems in representational alignment where progress can benefit all three of these fields. We hope that this paper will catalyze cross-disciplinary collaboration and accelerate progress for all communities studying and developing information processing systems.

Katherine M. Collins, Albert Q. Jiang, Simon Frieder et al. · cambridge

There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs relies on static pairs of inputs and outputs, and is insufficient for making an informed decision about which LLMs and under which assistive settings can they be sensibly used. Static assessment fails to account for the essential interactive element in LLM deployment, and therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we garner a more granular understanding of GPT-4 mathematical problem-solving through a series of case studies, contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models that communicate uncertainty respond well to user corrections, and are more interpretable and concise may constitute better assistants. Interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models' algebraic fallibility and discern where they are appropriate to use.

Katherine M. Collins, Ilia Sucholutsky, Umang Bhatt et al. · mit

What do we want from machine intelligence? We envision machines that are not just tools for thought, but partners in thought: reasonable, insightful, knowledgeable, reliable, and trustworthy systems that think with us. Current artificial intelligence (AI) systems satisfy some of these criteria, some of the time. In this Perspective, we show how the science of collaborative cognition can be put to work to engineer systems that really can be called ``thought partners,'' systems built to meet our expectations and complement our limitations. We lay out several modes of collaborative thought in which humans and AI thought partners can engage and propose desiderata for human-compatible thought partnerships. Drawing on motifs from computational cognitive science, we motivate an alternative scaling path for the design of thought partners and ecosystems around their use through a Bayesian lens, whereby the partners we construct actively build and reason over models of the human and world.

James Jordon, Lukasz Szpruch, Florimond Houssiau et al. · cambridge

This explainer document aims to provide an overview of the current state of the rapidly expanding work on synthetic data technologies, with a particular focus on privacy. The article is intended for a non-technical audience, though some formal definitions have been given to provide clarity to specialists. This article is intended to enable the reader to quickly become familiar with the notion of synthetic data, as well as understand some of the subtle intricacies that come with it. We do believe that synthetic data is a very useful tool, and our hope is that this report highlights that, while drawing attention to nuances that can easily be overlooked in its deployment.

Weiyang Liu, Longhui Yu, Adrian Weller et al. · cambridge

The neural collapse (NC) phenomenon describes an underlying geometric symmetry for deep neural networks, where both deeply learned features and classifiers converge to a simplex equiangular tight frame. It has been shown that both cross-entropy loss and mean square error can provably lead to NC. We remove NC's key assumption on the feature dimension and the number of classes, and then present a generalized neural collapse (GNC) hypothesis that effectively subsumes the original NC. Inspired by how NC characterizes the training target of neural networks, we decouple GNC into two objectives: minimal intra-class variability and maximal inter-class separability. We then use hyperspherical uniformity (which characterizes the degree of uniformity on the unit hypersphere) as a unified framework to quantify these two objectives. Finally, we propose a general objective -- hyperspherical uniformity gap (HUG), which is defined by the difference between inter-class and intra-class hyperspherical uniformity. HUG not only provably converges to GNC, but also decouples GNC into two separate objectives. Unlike cross-entropy loss that couples intra-class compactness and inter-class separability, HUG enjoys more flexibility and serves as a good alternative loss function. Empirical results show that HUG works well in terms of generalization and robustness.

Hector Zenil, Jesper Tegnér, Felipe S. Abrahão et al. · cambridge

Recent advances in machine learning and AI, including Generative AI and LLMs, are disrupting technological innovation, product development, and society as a whole. AI's contribution to technology can come from multiple approaches that require access to large training data sets and clear performance evaluation criteria, ranging from pattern recognition and classification to generative models. Yet, AI has contributed less to fundamental science in part because large data sets of high-quality data for scientific practice and model discovery are more difficult to access. Generative AI, in general, and Large Language Models in particular, may represent an opportunity to augment and accelerate the scientific discovery of fundamental deep science with quantitative models. Here we explore and investigate aspects of an AI-driven, automated, closed-loop approach to scientific discovery, including self-driven hypothesis generation and open-ended autonomous exploration of the hypothesis space. Integrating AI-driven automation into the practice of science would mitigate current problems, including the replication of findings, systematic production of data, and ultimately democratisation of the scientific process. Realising these possibilities requires a vision for augmented AI coupled with a diversity of AI approaches able to deal with fundamental aspects of causality analysis and model discovery while enabling unbiased search across the space of putative explanations. These advances hold the promise to unleash AI's potential for searching and discovering the fundamental structure of our world beyond what human scientists have been able to achieve. Such a vision would push the boundaries of new fundamental science rather than automatize current workflows and instead open doors for technological innovation to tackle some of the greatest challenges facing humanity today.

Valerie Chen, Umang Bhatt, Hoda Heidari et al. · cambridge, cmu

Machine learning (ML) practitioners are increasingly tasked with developing models that are aligned with non-technical experts' values and goals. However, there has been insufficient consideration on how practitioners should translate domain expertise into ML updates. In this paper, we consider how to capture interactions between practitioners and experts systematically. We devise a taxonomy to match expert feedback types with practitioner updates. A practitioner may receive feedback from an expert at the observation- or domain-level, and convert this feedback into updates to the dataset, loss function, or parameter space. We review existing work from ML and human-computer interaction to describe this feedback-update taxonomy, and highlight the insufficient consideration given to incorporating feedback from non-technical experts. We end with a set of open questions that naturally arise from our proposed taxonomy and subsequent survey.

Weiyang Liu, Zhen Liu, Liam Paull et al. · cambridge

This paper considers the problem of unsupervised 3D object reconstruction from in-the-wild single-view images. Due to ambiguity and intrinsic ill-posedness, this problem is inherently difficult to solve and therefore requires strong regularization to achieve disentanglement of different latent factors. Unlike existing works that introduce explicit regularizations into objective functions, we look into a different space for implicit regularization -- the structure of latent space. Specifically, we restrict the structure of latent space to capture a topological causal ordering of latent factors (i.e., representing causal dependency as a directed acyclic graph). We first show that different causal orderings matter for 3D reconstruction, and then explore several approaches to find a task-dependent causal factor ordering. Our experiments demonstrate that the latent space structure indeed serves as an implicit regularization and introduces an inductive bias beneficial for reconstruction.

Umang Bhatt, Valerie Chen, Katherine M. Collins et al. · cambridge, cmu

Individual human decision-makers may benefit from different forms of support to improve decision outcomes, but when each form of support will yield better outcomes? In this work, we posit that personalizing access to decision support tools can be an effective mechanism for instantiating the appropriate use of AI assistance. Specifically, we propose the general problem of learning a decision support policy that, for a given input, chooses which form of support to provide to decision-makers for whom we initially have no prior information. We develop $\texttt{Modiste}$, an interactive tool to learn personalized decision support policies. $\texttt{Modiste}$ leverages stochastic contextual bandit techniques to personalize a decision support policy for each decision-maker and supports extensions to the multi-objective setting to account for auxiliary objectives like the cost of support. We find that personalized policies outperform offline policies, and, in the cost-aware setting, reduce the incurred cost with minimal degradation to performance. Our experiments include various realistic forms of support (e.g., expert consensus and predictions from a large language model) on vision and language tasks. Our human subject experiments validate our computational experiments, demonstrating that personalization can yield benefits in practice for real users, who interact with $\texttt{Modiste}$.

Matthew Barker, Emma Kallina, Dhananjay Ashok et al. · cambridge, cmu

Even though machine learning (ML) pipelines affect an increasing array of stakeholders, there is little work on how input from stakeholders is recorded and incorporated. We propose FeedbackLogs, addenda to existing documentation of ML pipelines, to track the input of multiple stakeholders. Each log records important details about the feedback collection process, the feedback itself, and how the feedback is used to update the ML pipeline. In this paper, we introduce and formalise a process for collecting a FeedbackLog. We also provide concrete use cases where FeedbackLogs can be employed as evidence for algorithmic auditing and as a tool to record updates based on stakeholder feedback.

Zeju Qiu, Weiyang Liu, Tim Z. Xiao et al. · cambridge

We consider the problem of iterative machine teaching, where a teacher sequentially provides examples based on the status of a learner under a discrete input space (i.e., a pool of finite samples), which greatly limits the teacher's capability. To address this issue, we study iterative teaching under a continuous input space where the input example (i.e., image) can be either generated by solving an optimization problem or drawn directly from a continuous distribution. Specifically, we propose data hallucination teaching (DHT) where the teacher can generate input data intelligently based on labels, the learner's status and the target concept. We study a number of challenging teaching setups (e.g., linear/neural learners in omniscient and black-box settings). Extensive empirical results verify the effectiveness of DHT.

Mateo Espinosa Zarlenga, Pietro Barbiero, Gabriele Ciravegna et al. · cambridge

Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an intermediate level of human-like concepts. This enables human interventions which can correct mispredicted concepts to improve the model's performance. However, existing concept bottleneck models are unable to find optimal compromises between high task accuracy, robust concept-based explanations, and effective interventions on concepts -- particularly in real-world conditions where complete and accurate concept supervisions are scarce. To address this, we propose Concept Embedding Models, a novel family of concept bottleneck models which goes beyond the current accuracy-vs-interpretability trade-off by learning interpretable high-dimensional concept representations. Our experiments demonstrate that Concept Embedding Models (1) attain better or competitive task accuracy w.r.t. standard neural models without concepts, (2) provide concept representations capturing meaningful semantics including and beyond their ground truth labels, (3) support test-time concept interventions whose effect in test accuracy surpasses that in standard concept bottleneck models, and (4) scale to real-world conditions where complete concept supervisions are scarce.

Katherine M. Collins, Umang Bhatt, Adrian Weller · cambridge

The labels used to train machine learning (ML) models are of paramount importance. Typically for ML classification tasks, datasets contain hard labels, yet learning using soft labels has been shown to yield benefits for model generalization, robustness, and calibration. Earlier work found success in forming soft labels from multiple annotators' hard labels; however, this approach may not converge to the best labels and necessitates many annotators, which can be expensive and inefficient. We focus on efficiently eliciting soft labels from individual annotators. We collect and release a dataset of soft labels (which we call CIFAR-10S) over the CIFAR-10 test set via a crowdsourcing study (N=248). We demonstrate that learning with our labels achieves comparable model performance to prior approaches while requiring far fewer annotators -- albeit with significant temporal costs per elicitation. Our elicitation methodology therefore shows nuanced promise in enabling practitioners to enjoy the benefits of improved model performance and reliability with fewer annotators, and serves as a guide for future dataset curators on the benefits of leveraging richer information, such as categorical uncertainty, from individual annotators.

Katherine M. Collins, Matthew Barker, Mateo Espinosa Zarlenga et al. · cambridge

Placing a human in the loop may abate the risks of deploying AI systems in safety-critical settings (e.g., a clinician working with a medical AI system). However, mitigating risks arising from human error and uncertainty within such human-AI interactions is an important and understudied issue. In this work, we study human uncertainty in the context of concept-based models, a family of AI systems that enable human feedback via concept interventions where an expert intervenes on human-interpretable concepts relevant to the task. Prior work in this space often assumes that humans are oracles who are always certain and correct. Yet, real-world decision-making by humans is prone to occasional mistakes and uncertainty. We study how existing concept-based models deal with uncertain interventions from humans using two novel datasets: UMNIST, a visual dataset with controlled simulated uncertainty based on the MNIST dataset, and CUB-S, a relabeling of the popular CUB concept dataset with rich, densely-annotated soft labels from humans. We show that training with uncertain concept labels may help mitigate weaknesses of concept-based systems when handling uncertain interventions. These results allow us to identify several open challenges, which we argue can be tackled through future multidisciplinary research on building interactive uncertainty-aware systems. To facilitate further research, we release a new elicitation platform, UElic, to collect uncertain feedback from humans in collaborative prediction tasks.

Katherine M. Collins, Simon Frieder, Jonas Bayer et al.

For centuries, human mathematicians have written proofs to substantiate their mathematical arguments; yet, the ability to automatically verify the validity of proofs has long been a challenge. Advances in AI systems' ability to generate code and engage in increasingly high-level mathematical reasoning promise to transform people's ability to formalize and thereby verify proofs. While many works focus on benchmarking the current frontier, we instead study how people use these tools. We conduct a mixed-methods analysis into the initial impact of AI on people's formalization workflows: what people claim they want, what they see as the barriers to those visions, and how they actually use and adapt AI in practice. A qualitative survey shows that people's preferences are diverse, but with a general desire for AI assistance in formalization that preserves high-level human control over the proof discovery process. To assess how people actually engage with AI for formalization under such limitations, we conduct a controlled user study in which participants formalize informal math problems and their proofs, with and without AI, across a range of mathematical problems at varying levels of difficulty and domains. Despite limitations of the tools at the time for autoformalization, participants tend to attain higher formalization accuracy when allowed access to AI tools than when formalizing on their own, with most participants flexibly choosing to use multiple different AI tools. Taken together, our work sheds light on the early stages of AI integration into formalization workflows, involving an intimate interplay of human and AI engagement.

Mateo Espinosa Zarlenga, Katherine M. Collins, Krishnamurthy Dvijotham et al. · cambridge

Concept Bottleneck Models (CBMs) tackle the opacity of neural architectures by constructing and explaining their predictions using a set of high-level concepts. A special property of these models is that they permit concept interventions, wherein users can correct mispredicted concepts and thus improve the model's performance. Recent work, however, has shown that intervention efficacy can be highly dependent on the order in which concepts are intervened on and on the model's architecture and training hyperparameters. We argue that this is rooted in a CBM's lack of train-time incentives for the model to be appropriately receptive to concept interventions. To address this, we propose Intervention-aware Concept Embedding models (IntCEMs), a novel CBM-based architecture and training paradigm that improves a model's receptiveness to test-time interventions. Our model learns a concept intervention policy in an end-to-end fashion from where it can sample meaningful intervention trajectories at train-time. This conditions IntCEMs to effectively select and receive concept interventions when deployed at test-time. Our experiments show that IntCEMs significantly outperform state-of-the-art concept-interpretable models when provided with test-time concept interventions, demonstrating the effectiveness of our approach.

Varun Babbar, Umang Bhatt, Adrian Weller · cambridge

Research on human-AI teams usually provides experts with a single label, which ignores the uncertainty in a model's recommendation. Conformal prediction (CP) is a well established line of research that focuses on building a theoretically grounded, calibrated prediction set, which may contain multiple labels. We explore how such prediction sets impact expert decision-making in human-AI teams. Our evaluation on human subjects finds that set valued predictions positively impact experts. However, we notice that the predictive sets provided by CP can be very large, which leads to unhelpful AI assistants. To mitigate this, we introduce D-CP, a method to perform CP on some examples and defer to experts. We prove that D-CP can reduce the prediction set size of non-deferred examples. We show how D-CP performs in quantitative and in human subject experiments ($n=120$). Our results suggest that CP prediction sets improve human-AI team performance over showing the top-1 prediction alone, and that experts find D-CP prediction sets are more useful than CP prediction sets.

Isabel Chien, Nina Deliu, Richard E. Turner et al. · cambridge

While interest in the application of machine learning to improve healthcare has grown tremendously in recent years, a number of barriers prevent deployment in medical practice. A notable concern is the potential to exacerbate entrenched biases and existing health disparities in society. The area of fairness in machine learning seeks to address these issues of equity; however, appropriate approaches are context-dependent, necessitating domain-specific consideration. We focus on clinical trials, i.e., research studies conducted on humans to evaluate medical treatments. Clinical trials are a relatively under-explored application in machine learning for healthcare, in part due to complex ethical, legal, and regulatory requirements and high costs. Our aim is to provide a multi-disciplinary assessment of how fairness for machine learning fits into the context of clinical trials research and practice. We start by reviewing the current ethical considerations and guidelines for clinical trials and examine their relationship with common definitions of fairness in machine learning. We examine potential sources of unfairness in clinical trials, providing concrete examples, and discuss the role machine learning might play in either mitigating potential biases or exacerbating them when applied without care. Particular focus is given to adaptive clinical trials, which may employ machine learning. Finally, we highlight concepts that require further investigation and development, and emphasize new approaches to fairness that may be relevant to the design of clinical trials.

Mateo Espinosa Zarlenga, Pietro Barbiero, Zohreh Shams et al. · cambridge

Recent work on interpretability has focused on concept-based explanations, where deep learning models are explained in terms of high-level units of information, referred to as concepts. Concept learning models, however, have been shown to be prone to encoding impurities in their representations, failing to fully capture meaningful features of their inputs. While concept learning lacks metrics to measure such phenomena, the field of disentanglement learning has explored the related notion of underlying factors of variation in the data, with plenty of metrics to measure the purity of such factors. In this paper, we show that such metrics are not appropriate for concept learning and propose novel metrics for evaluating the purity of concept representations in both approaches. We show the advantage of these metrics over existing ones and demonstrate their utility in evaluating the robustness of concept representations and interventions performed on them. In addition, we show their utility for benchmarking state-of-the-art methods from both families and find that, contrary to common assumptions, supervision alone may not be sufficient for pure concept representations.

Matthew Wicker, Juyeon Heo, Luca Costabello et al. · cambridge

Post-hoc explanation methods are used with the intent of providing insights about neural networks and are sometimes said to help engender trust in their outputs. However, popular explanations methods have been found to be fragile to minor perturbations of input features or model parameters. Relying on constraint relaxation techniques from non-convex optimization, we develop a method that upper-bounds the largest change an adversary can make to a gradient-based explanation via bounded manipulation of either the input features or model parameters. By propagating a compact input or parameter set as symbolic intervals through the forwards and backwards computations of the neural network we can formally certify the robustness of gradient-based explanations. Our bounds are differentiable, hence we can incorporate provable explanation robustness into neural network training. Empirically, our method surpasses the robustness provided by previous heuristic approaches. We find that our training method is the only method able to learn neural networks with certificates of explanation robustness across all six datasets tested.

Valerii Likhosherstov, Krzysztof Choromanski, Avinava Dubey et al. · cambridge

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on the trigonometric maps. We present variants of CRTs where RFs are positive, a key requirement for applications in recent low-rank Transformers. Further variance reduction is possible by leveraging statistics which are simple to compute. One instantiation of CRTs, the optimal positive random features (OPRFs), is to our knowledge the first RF method for unbiased softmax kernel estimation with positive and bounded RFs, resulting in exponentially small tails and much lower variance than its counterparts. As we show, orthogonal random features applied in OPRFs provide additional variance reduction for any dimensionality $d$ (not only asymptotically for sufficiently large $d$, as for RKS). We test CRTs on many tasks ranging from non-parametric classification to training Transformers for text, speech and image data, obtaining new state-of-the-art results for low-rank text Transformers, while providing linear space and time complexity.

Zeju Qiu, Weiyang Liu, Haiwen Feng et al.

Against the backdrop of enthusiasm for large language models (LLMs), there is a growing need to scientifically assess their capabilities and shortcomings. This is nontrivial in part because it is difficult to find tasks which the models have not encountered during training. Utilizing symbolic graphics programs, we propose a domain well-suited to test multiple spatial-semantic reasoning skills of LLMs. Popular in computer graphics, these programs procedurally generate visual data. While LLMs exhibit impressive skills in general program synthesis and analysis, symbolic graphics programs offer a new layer of evaluation: they allow us to test an LLM's ability to answer semantic questions about the images or 3D geometries without a vision encoder. To semantically understand the symbolic programs, LLMs would need to possess the ability to "imagine" and reason how the corresponding graphics content would look with only the symbolic description of the local curvatures and strokes. We use this task to evaluate LLMs by creating a large benchmark for the semantic visual understanding of symbolic graphics programs, built procedurally with minimal human effort. Particular emphasis is placed on transformations of images that leave the image level semantics invariant while introducing significant changes to the underlying program. We evaluate commercial and open-source LLMs on our benchmark to assess their ability to reason about visual output of programs, finding that LLMs considered stronger at reasoning generally perform better. Lastly, we introduce a novel method to improve this ability -- Symbolic Instruction Tuning (SIT), in which the LLM is finetuned with pre-collected instruction data on symbolic graphics programs. Interestingly, we find that SIT not only improves LLM's understanding on symbolic programs, but it also improves general reasoning ability on various other benchmarks.

Longhui Yu, Tianyang Hu, Lanqing Hong et al. · cambridge

It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To address this issue, memory-based continual learning has been actively studied and stands out as one of the best-performing methods. We examine memory-based continual learning and identify that large variation in the representation space is crucial for avoiding catastrophic forgetting. Motivated by this, we propose to diversify representations by using two types of perturbations: model-agnostic variation (i.e., the variation is generated without the knowledge of the learned neural network) and model-based variation (i.e., the variation is conditioned on the learned neural network). We demonstrate that enlarging representational variation serves as a general principle to improve continual learning. Finally, we perform empirical studies which demonstrate that our method, as a simple plug-and-play component, can consistently improve a number of memory-based continual learning methods by a large margin.

Krzysztof Marcin Choromanski, Shanda Li, Valerii Likhosherstov et al. · cambridge

We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for sequential data, as well as novel RPEs operating on geometric data embedded in higher-dimensional Euclidean spaces. FLTs construct the optimal RPE mechanism implicitly by learning its spectral representation. As opposed to other architectures combining efficient low-rank linear attention with RPEs, FLTs remain practical in terms of their memory usage and do not require additional assumptions about the structure of the RPE mask. Besides, FLTs allow for applying certain structural inductive bias techniques to specify masking strategies, e.g. they provide a way to learn the so-called local RPEs introduced in this paper and give accuracy gains as compared with several other linear Transformers for language modeling. We also thoroughly test FLTs on other data modalities and tasks, such as image classification, 3D molecular modeling, and learnable optimizers. To the best of our knowledge, for 3D molecular data, FLTs are the first Transformer architectures providing linear attention and incorporating RPE masking.

Isaac Reid, Krzysztof Choromanski, Valerii Likhosherstov et al. · cambridge

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

Katherine M. Collins, Umang Bhatt, Weiyang Liu et al. · cambridge

Aligning model representations to humans has been found to improve robustness and generalization. However, such methods often focus on standard observational data. Synthetic data is proliferating and powering many advances in machine learning; yet, it is not always clear whether synthetic labels are perceptually aligned to humans -- rendering it likely model representations are not human aligned. We focus on the synthetic data used in mixup: a powerful regularizer shown to improve model robustness, generalization, and calibration. We design a comprehensive series of elicitation interfaces, which we release as HILL MixE Suite, and recruit 159 participants to provide perceptual judgments along with their uncertainties, over mixup examples. We find that human perceptions do not consistently align with the labels traditionally used for synthetic points, and begin to demonstrate the applicability of these findings to potentially increase the reliability of downstream models, particularly when incorporating human uncertainty. We release all elicited judgments in a new data hub we call H-Mix.

Yanzhi Chen, Weihao Sun, Yingzhen Li et al. · cambridge

The task of infomin learning aims to learn a representation with high utility while being uninformative about a specified target, with the latter achieved by minimising the mutual information between the representation and the target. It has broad applications, ranging from training fair prediction models against protected attributes, to unsupervised learning with disentangled representations. Recent works on infomin learning mainly use adversarial training, which involves training a neural network to estimate mutual information or its proxy and thus is slow and difficult to optimise. Drawing on recent advances in slicing techniques, we propose a new infomin learning approach, which uses a novel proxy metric to mutual information. We further derive an accurate and analytically computable approximation to this proxy metric, thereby removing the need of constructing neural network-based mutual information estimators. Experiments on algorithmic fairness, disentangled representation learning and domain adaptation verify that our method can effectively remove unwanted information with limited time budget.

Matthew Barker, Katherine M. Collins, Krishnamurthy Dvijotham et al. · cambridge

Concept-based models perform prediction using a set of concepts that are interpretable to stakeholders. However, such models often involve a fixed, large number of concepts, which may place a substantial cognitive load on stakeholders. We propose Selective COncept Models (SCOMs) which make predictions using only a subset of concepts and can be customised by stakeholders at test-time according to their preferences. We show that SCOMs only require a fraction of the total concepts to achieve optimal accuracy on multiple real-world datasets. Further, we collect and release a new dataset, CUB-Sel, consisting of human concept set selections for 900 bird images from the popular CUB dataset. Using CUB-Sel, we show that humans have unique individual preferences for the choice of concepts they prefer to reason about, and struggle to identify the most theoretically informative concepts. The customisation and concept selection provided by SCOM improves the efficiency of interpretation and intervention for stakeholders.

Bradley Butcher, Miri Zilka, Darren Cook et al. · cambridge

While humans can extract information from unstructured text with high precision and recall, this is often too time-consuming to be practical. Automated approaches, on the other hand, produce nearly-immediate results, but may not be reliable enough for high-stakes applications where precision is essential. In this work, we consider the benefits and drawbacks of various human-only, human-machine, and machine-only information extraction approaches. We argue for the utility of a human-in-the-loop approach in applications where high precision is required, but purely manual extraction is infeasible. We present a framework and an accompanying tool for information extraction using weak-supervision labelling with human validation. We demonstrate our approach on three criminal justice datasets. We find that the combination of computer speed and human understanding yields precision comparable to manual annotation while requiring only a fraction of time, and significantly outperforms fully automated baselines in terms of precision.

Krzysztof Choromanski, Arijit Sehanobish, Han Lin et al. · cambridge

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Sunghwan Joo, Seokhyeon Jeong, Juyeon Heo et al. · cambridge

Neural network interpretation methods, particularly feature attribution methods, are known to be fragile with respect to adversarial input perturbations. To address this, several methods for enhancing the local smoothness of the gradient while training have been proposed for attaining \textit{robust} feature attributions. However, the lack of considering the normalization of the attributions, which is essential in their visualizations, has been an obstacle to understanding and improving the robustness of feature attribution methods. In this paper, we provide new insights by taking such normalization into account. First, we show that for every non-negative homogeneous neural network, a naive $\ell_2$-robust criterion for gradients is \textit{not} normalization invariant, which means that two functions with the same normalized gradient can have different values. Second, we formulate a normalization invariant cosine distance-based criterion and derive its upper bound, which gives insight for why simply minimizing the Hessian norm at the input, as has been done in previous work, is not sufficient for attaining robust feature attribution. Finally, we propose to combine both $\ell_2$ and cosine distance-based criteria as regularization terms to leverage the advantages of both in aligning the local gradient. As a result, we experimentally show that models trained with our method produce much more robust interpretations on CIFAR-10 and ImageNet-100 without significantly hurting the accuracy, compared to the recent baselines. To the best of our knowledge, this is the first work to verify the robustness of interpretation on a larger-scale dataset beyond CIFAR-10, thanks to the computational efficiency of our method.

Yichao Liang, Dat Nguyen, Cambridge Yang et al. · cambridge

Long-horizon embodied planning is challenging because the world does not only change through an agent's actions: exogenous processes (e.g., water heating, dominoes cascading) unfold concurrently with the agent's actions. We propose a framework for abstract world models that jointly learns (i) symbolic state representations and (ii) causal processes for both endogenous actions and exogenous mechanisms. Each causal process models the time course of a stochastic cause-effect relation. We learn these world models from limited data via variational Bayesian inference combined with LLM proposals. Across five simulated tabletop robotics environments, the learned models enable fast planning that generalizes to held-out tasks with more objects and more complex goals, outperforming a range of baselines.

Zhengyang Hu, Yanzhi Chen, Hanxiang Ren et al.

Measuring statistical dependency between high-dimensional random variables is a fundamental task in data science and machine learning. Neural mutual information (MI) estimators offer a promising avenue, but they typically require costly iterative optimization for each new dataset, making them impractical for real-time applications. We present InfoAtlas, a foundation model-like architecture that eliminates this bottleneck by directly inferring MI in a single forward pass. Pretrained on large-scale synthetic data with rich dependence patterns, InfoAtlas learns to identify diverse dependence structures and predict MI directly from the dataset. Comprehensive experiments demonstrate that InfoAtlas matches state-of-the-art neural estimators in accuracy while achieving $100\times$ speedup, can flexibly handle varying dimensions and sample sizes through a single unified model, and generalizes effectively to complex, real-world scenarios. By reformulating MI estimation as an inference task, InfoAtlas establishes a foundation for real-time dependency analysis.

Ilia Sucholutsky, Ruairidh M. Battleday, Katherine M. Collins et al.

Supervised learning typically focuses on learning transferable representations from training examples annotated by humans. While rich annotations (like soft labels) carry more information than sparse annotations (like hard labels), they are also more expensive to collect. For example, while hard labels only provide information about the closest class an object belongs to (e.g., "this is a dog"), soft labels provide information about the object's relationship with multiple classes (e.g., "this is most likely a dog, but it could also be a wolf or a coyote"). We use information theory to compare how a number of commonly-used supervision signals contribute to representation-learning performance, as well as how their capacity is affected by factors such as the number of labels, classes, dimensions, and noise. Our framework provides theoretical justification for using hard labels in the big-data regime, but richer supervision signals for few-shot learning and out-of-distribution generalization. We validate these results empirically in a series of experiments with over 1 million crowdsourced image annotations and conduct a cost-benefit analysis to establish a tradeoff curve that enables users to optimize the cost of supervising representation learning on their own datasets.

Valerii Likhosherstov, Krzysztof Choromanski, Avinava Dubey et al. · cambridge

The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in important applications ranging from kernel methods to efficient Transformers. We propose parameterized, positive, non-trigonometric RFs which approximate Gaussian and softmax-kernels. In contrast to traditional RF approximations, parameters of these new methods can be optimized to reduce the variance of the approximation, and the optimum can be expressed in closed form. We show that our methods lead to variance reduction in practice ($e^{10}$-times smaller variance and beyond) and outperform previous methods in a kernel regression task. Using our proposed mechanism, we also present FAVOR#, a method for self-attention approximation in Transformers. We show that FAVOR# outperforms other random feature methods in speech modelling and natural language processing.

Juyeon Heo, Vihari Piratla, Matthew Wicker et al. · cambridge

Machine learning from explanations (MLX) is an approach to learning that uses human-provided explanations of relevant or irrelevant features for each input to ensure that model predictions are right for the right reasons. Existing MLX approaches rely on local model interpretation methods and require strong model smoothing to align model and human explanations, leading to sub-optimal performance. We recast MLX as a robustness problem, where human explanations specify a lower dimensional manifold from which perturbations can be drawn, and show both theoretically and empirically how this approach alleviates the need for strong model smoothing. We consider various approaches to achieving robustness, leading to improved performance over prior MLX methods. Finally, we show how to combine robustness with an earlier MLX method, yielding state-of-the-art results on both synthetic and real-world benchmarks.

Darren Cook, Miri Zilka, Heidi DeSandre et al. · cambridge

Social media's growing popularity raises concerns around children's online safety. Interactions between minors and adults with predatory intentions is a particularly grave concern. Research into online sexual grooming has often relied on domain experts to manually annotate conversations, limiting both scale and scope. In this work, we test how well-automated methods can detect conversational behaviors and replace an expert human annotator. Informed by psychological theories of online grooming, we label $6772$ chat messages sent by child-sex offenders with one of eleven predatory behaviors. We train bag-of-words and natural language inference models to classify each behavior, and show that the best performing models classify behaviors in a manner that is consistent, but not on-par, with human annotation.

Weiyang Liu, Zeju Qiu, Yao Feng et al.

Large foundation models are becoming ubiquitous, but training them from scratch is prohibitively expensive. Thus, efficiently adapting these powerful models to downstream tasks is increasingly important. In this paper, we study a principled finetuning paradigm -- Orthogonal Finetuning (OFT) -- for downstream task adaptation. Despite demonstrating good generalizability, OFT still uses a fairly large number of trainable parameters due to the high dimensionality of orthogonal matrices. To address this, we start by examining OFT from an information transmission perspective, and then identify a few key desiderata that enable better parameter-efficiency. Inspired by how the Cooley-Tukey fast Fourier transform algorithm enables efficient information transmission, we propose an efficient orthogonal parameterization using butterfly structures. We apply this parameterization to OFT, creating a novel parameter-efficient finetuning method, called Orthogonal Butterfly (BOFT). By subsuming OFT as a special case, BOFT introduces a generalized orthogonal finetuning framework. Finally, we conduct an extensive empirical study of adapting large vision transformers, large language models, and text-to-image diffusion models to various downstream tasks in vision and language.

Victoria Smith, Ali Shahin Shamsabadi, Carolyn Ashurst et al.

Large Language Models (LLMs) have shown greatly enhanced performance in recent years, attributed to increased size and extensive training data. This advancement has led to widespread interest and adoption across industries and the public. However, training data memorization in Machine Learning models scales with model size, particularly concerning for LLMs. Memorized text sequences have the potential to be directly leaked from LLMs, posing a serious threat to data privacy. Various techniques have been developed to attack LLMs and extract their training data. As these models continue to grow, this issue becomes increasingly critical. To help researchers and policymakers understand the state of knowledge around privacy attacks and mitigations, including where more work is needed, we present the first SoK on data privacy for LLMs. We (i) identify a taxonomy of salient dimensions where attacks differ on LLMs, (ii) systematize existing attacks, using our taxonomy of dimensions to highlight key trends, (iii) survey existing mitigation strategies, highlighting their strengths and limitations, and (iv) identify key gaps, demonstrating open problems and areas for concern.

Cedegao E. Zhang, Katherine M. Collins, Adrian Weller et al.

Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by advances in large language models (LLMs), has sparked renewed, widespread interest in building such systems. In this work, we reflect on these goals from a \textit{cognitive science} perspective. We call attention to several classical and ongoing research directions from cognitive science, which we believe are valuable for AI practitioners to consider when seeking to build truly human (or superhuman)-level mathematical systems. We close with open discussions and questions that we believe necessitate a multi-disciplinary perspective -- cognitive scientists working in tandem with AI researchers and mathematicians -- as we move toward better mathematical AI systems which not only help us push the frontier of the mathematics, but also offer glimpses into how we as humans are even capable of such great cognitive feats.

Yandong Wen, Weiyang Liu, Yao Feng et al.

In this paper, we focus on a general yet important learning problem, pairwise similarity learning (PSL). PSL subsumes a wide range of important applications, such as open-set face recognition, speaker verification, image retrieval and person re-identification. The goal of PSL is to learn a pairwise similarity function assigning a higher similarity score to positive pairs (i.e., a pair of samples with the same label) than to negative pairs (i.e., a pair of samples with different label). We start by identifying a key desideratum for PSL, and then discuss how existing methods can achieve this desideratum. We then propose a surprisingly simple proxy-free method, called SimPLE, which requires neither feature/proxy normalization nor angular margin and yet is able to generalize well in open-set recognition. We apply the proposed method to three challenging PSL tasks: open-set face recognition, image retrieval and speaker verification. Comprehensive experimental results on large-scale benchmarks show that our method performs significantly better than current state-of-the-art methods.

Cedegao E. Zhang, Katherine M. Collins, Lionel Wong et al.

People can evaluate features of problems and their potential solutions well before we can effectively solve them. When considering a game we have never played, for instance, we might infer whether it is likely to be challenging, fair, or fun simply from hearing the game rules, prior to deciding whether to invest time in learning the game or trying to play it well. Many studies of game play have focused on optimality and expertise, characterizing how people and computational models play based on moderate to extensive search and after playing a game dozens (if not thousands or millions) of times. Here, we study how people reason about a range of simple but novel Connect-N style board games. We ask people to judge how fair and how fun the games are from very little experience: just thinking about the game for a minute or so, before they have ever actually played with anyone else, and we propose a resource-limited model that captures their judgments using only a small number of partial game simulations and almost no look-ahead search.

Arik Reuter, Anish Dhir, Cristiana Diaconu et al.

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism is the most effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

Shubhra Mishra, Yuka Machino, Gabriel Poesia et al.

The evolution of mathematics has been guided in part by interestingness. From researchers choosing which problems to tackle next, to students deciding which ones to engage with, people's choices are often guided by judgments about how interesting or challenging problems are likely to be. As AI systems, such as LLMs, increasingly participate in mathematics with people -- whether for advanced research or education -- it becomes important to understand how well their judgments align with human ones. Our work examines this alignment through two empirical studies of human and LLM assessment of mathematical interestingness and difficulty, spanning a range of mathematical experience. We study two groups: participants from a crowdsourcing platform and International Math Olympiad competitors. We show that while many LLMs appear to broadly agree with human notions of interestingness, they mostly do not capture the distribution observed in human judgments. Moreover, most LLMs only somewhat align with why humans find certain math problems interesting, showing weak correlation with human-selected interestingness rationales. Together, our findings highlight both the promises and limitations of current LLMs in capturing human interestingness judgments for mathematical AI thought partnerships.

Isaac Reid, Krzysztof Choromanski, Eli Berger et al.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Matthew Wicker, Vihari Piratia, Adrian Weller

Providing formal guarantees of algorithmic fairness is of paramount importance to socially responsible deployment of machine learning algorithms. In this work, we study formal guarantees, i.e., certificates, for individual fairness (IF) of neural networks. We start by introducing a novel convex approximation of IF constraints that exponentially decreases the computational cost of providing formal guarantees of local individual fairness. We highlight that prior methods are constrained by their focus on global IF certification and can therefore only scale to models with a few dozen hidden neurons, thus limiting their practical impact. We propose to certify distributional individual fairness which ensures that for a given empirical distribution and all distributions within a $γ$-Wasserstein ball, the neural network has guaranteed individually fair predictions. Leveraging developments in quasi-convex optimization, we provide novel and efficient certified bounds on distributional individual fairness and show that our method allows us to certify and regularize neural networks that are several orders of magnitude larger than those considered by prior works. Moreover, we study real-world distribution shifts and find our bounds to be a scalable, practical, and sound source of IF guarantees.