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Researcher profile

Thomas Icard

Thomas Icard contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Artificial IntelligenceMachine LearningComputation and Languagecs.CYLogic in Computer Sciencemath.STMethodologyStatistics Theory

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Published work

7 published item(s)

preprint2026arXiv

Bucketing the Good Apples: A Method for Diagnosing and Improving Causal Abstraction

We present a method for diagnosing interpretation in neural networks by identifying an input subspace where a proposed interpretation is highly faithful. Our method is particularly useful for causal-abstraction-style interpretability, where a high-level causal hypothesis is evaluated by interchange interventions. Rather than treating interchange intervention accuracy as a single global summary, we refine this framework by partitioning the input space into well-interpreted and under-interpreted regions according to pairwise interchange-intervention behavior. This turns causal abstraction from a purely global evaluation into a more diagnostic tool: it not only measures whether an interpretation works, but also reveals where it works, where it fails, and what distinguishes the two cases. This diagnostic view also provides practical heuristics for improving interpretations. By analyzing the structure of the well-interpreted and under-interpreted regions, we can identify missing distinctions in a high-level hypothesis, discover previously unmodeled intermediate variables, and combine complementary partial interpretations into a stronger one. We instantiate this idea as a simple four-step recipe and show that it yields informative error analyses across multiple causal abstraction settings. In a toy logic task, recursively applying the recipe recovers a high-level hypothesis from scratch. More broadly, our results suggest that partitioning the input space is a useful step toward more precise, constructive, and scalable mechanistic interpretability.

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preprint2026arXiv

Counterfactual Spaces

We mathematically axiomatise the stochastics of counterfactuals, by introducing two related frameworks, called counterfactual probability spaces and counterfactual causal spaces, which we collectively term counterfactual spaces. They are, respectively, probability and causal spaces whose underlying measurable spaces are products of world-specific measurable spaces. In contrast to more familiar accounts of counterfactuals founded on causal models, we do not view interventions as a necessary component of a theory of counterfactuals. As an alternative to Pearl's celebrated ladder of causation, we view counterfactuals and interventions are orthogonal concepts, respectively mathematised in counterfactual probability spaces and causal spaces. The two concepts are then combined to form counterfactual causal spaces. At the heart of our theory is the notion of shared information between the worlds, encoded completely within the probability measure and causal kernels, and whose extremes are characterised by independence and synchronisation of worlds. Compared to existing frameworks, counterfactual spaces enable the mathematical treatment of a strictly broader spectrum of counterfactuals.

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preprint2022arXiv

A Topological Perspective on Causal Inference

This paper presents a topological learning-theoretic perspective on causal inference by introducing a series of topologies defined on general spaces of structural causal models (SCMs). As an illustration of the framework we prove a topological causal hierarchy theorem, showing that substantive assumption-free causal inference is possible only in a meager set of SCMs. Thanks to a known correspondence between open sets in the weak topology and statistically verifiable hypotheses, our results show that inductive assumptions sufficient to license valid causal inferences are statistically unverifiable in principle. Similar to no-free-lunch theorems for statistical inference, the present results clarify the inevitability of substantial assumptions for causal inference. An additional benefit of our topological approach is that it easily accommodates SCMs with infinitely many variables. We finally suggest that the framework may be helpful for the positive project of exploring and assessing alternative causal-inductive assumptions.

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preprint2022arXiv

Causal Distillation for Language Models

Distillation efforts have led to language models that are more compact and efficient without serious drops in performance. The standard approach to distillation trains a student model against two objectives: a task-specific objective (e.g., language modeling) and an imitation objective that encourages the hidden states of the student model to be similar to those of the larger teacher model. In this paper, we show that it is beneficial to augment distillation with a third objective that encourages the student to imitate the causal computation process of the teacher through interchange intervention training(IIT). IIT pushes the student model to become a causal abstraction of the teacher model - a simpler model with the same causal structure. IIT is fully differentiable, easily implemented, and combines flexibly with other objectives. Compared with standard distillation of BERT, distillation via IIT results in lower perplexity on Wikipedia (masked language modeling) and marked improvements on the GLUE benchmark (natural language understanding), SQuAD (question answering), and CoNLL-2003 (named entity recognition).

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preprint2022arXiv

Inducing Causal Structure for Interpretable Neural Networks

In many areas, we have well-founded insights about causal structure that would be useful to bring into our trained models while still allowing them to learn in a data-driven fashion. To achieve this, we present the new method of interchange intervention training (IIT). In IIT, we (1) align variables in a causal model (e.g., a deterministic program or Bayesian network) with representations in a neural model and (2) train the neural model to match the counterfactual behavior of the causal model on a base input when aligned representations in both models are set to be the value they would be for a source input. IIT is fully differentiable, flexibly combines with other objectives, and guarantees that the target causal model is a causal abstraction of the neural model when its loss is zero. We evaluate IIT on a structural vision task (MNIST-PVR), a navigational language task (ReaSCAN), and a natural language inference task (MQNLI). We compare IIT against multi-task training objectives and data augmentation. In all our experiments, IIT achieves the best results and produces neural models that are more interpretable in the sense that they more successfully realize the target causal model.

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preprint2022arXiv

On the Opportunities and Risks of Foundation Models

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.

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preprint2020arXiv

Intention as Commitment toward Time

In this paper we address the interplay among intention, time, and belief in dynamic environments. The first contribution is a logic for reasoning about intention, time and belief, in which assumptions of intentions are represented by preconditions of intended actions. Intentions and beliefs are coherent as long as these assumptions are not violated, i.e. as long as intended actions can be performed such that their preconditions hold as well. The second contribution is the formalization of what-if scenarios: what happens with intentions and beliefs if a new (possibly conflicting) intention is adopted, or a new fact is learned? An agent is committed to its intended actions as long as its belief-intention database is coherent. We conceptualize intention as commitment toward time and we develop AGM-based postulates for the iterated revision of belief-intention databases, and we prove a Katsuno-Mendelzon-style representation theorem.

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