Actionable Interpretability Must Be Defined in Terms of Symmetries

This paper argues that interpretability research in Artificial Intelligence is fundamentally ill-posed as existing definitions of interpretability are not *actionable*: they fail to provide formal principles from which concrete modelling and inferential rules can be derived. We posit that for a definition of interpretability to be actionable, it must be given in terms of *symmetries*. We hypothesise that four symmetries suffice to (i) motivate core interpretability properties, (ii) characterize the class of interpretable models, and (iii) derive a unified formulation of interpretable inference (e.g., alignment, interventions, and counterfactuals) as a form of Bayesian inversion.

An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making

This paper compares three methodological categories of neural reasoning: LLM reasoning, supervised learning-based reasoning, and explicit model-based reasoning. LLMs remain unreliable and struggle with simple decision-making that animals can master without extensive corpora training. Through disjunctive syllogistic reasoning testing, we show that reasoning via supervised learning is less appealing than reasoning via explicit model construction. Concretely, we show that an Euler Net trained to achieve 100.00% in classic syllogistic reasoning can be trained to reach 100.00% accuracy in disjunctive syllogistic reasoning. However, the retrained Euler Net suffers severely from catastrophic forgetting (its performance drops to 6.25% on already-learned classic syllogistic reasoning), and its reasoning competence is limited to the pattern level. We propose a new version of Sphere Neural Networks that embeds concepts as circles on the surface of an n-dimensional sphere. These Sphere Neural Networks enable the representation of the negation operator via complement circles and achieve reliable decision-making by filtering out illogical statements that form unsatisfiable circular configurations. We demonstrate that the Sphere Neural Network can master 16 syllogistic reasoning tasks, including rigorous disjunctive syllogistic reasoning, while preserving the rigour of classical syllogistic reasoning. We conclude that neural reasoning with explicit model construction is the most reliable among the three methodological categories of neural reasoning.

A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models

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.

Oruga: An Avatar of Representational Systems Theory

Humans use representations flexibly. We draw diagrams, change representations and exploit creative analogies across different domains. We want to harness this kind of power and endow machines with it to make them more compatible with human use. Previously we developed Representational Systems Theory (RST) to study the structure and transformations of representations. In this paper we present Oruga (caterpillar in Spanish; a symbol of transformation), an implementation of various aspects of RST. Oruga consists of a core of data structures corresponding to concepts in RST, a language for communicating with the core, and an engine for producing transformations using a method we call structure transfer. In this paper we present an overview of the core and language of Oruga, with a brief example of the kind of transformation that structure transfer can execute.

Avoiding Leakage Poisoning: Concept Interventions Under Distribution Shifts

In this paper, we investigate how concept-based models (CMs) respond to out-of-distribution (OOD) inputs. CMs are interpretable neural architectures that first predict a set of high-level concepts (e.g., stripes, black) and then predict a task label from those concepts. In particular, we study the impact of concept interventions (i.e., operations where a human expert corrects a CM's mispredicted concepts at test time) on CMs' task predictions when inputs are OOD. Our analysis reveals a weakness in current state-of-the-art CMs, which we term leakage poisoning, that prevents them from properly improving their accuracy when intervened on for OOD inputs. To address this, we introduce MixCEM, a new CM that learns to dynamically exploit leaked information missing from its concepts only when this information is in-distribution. Our results across tasks with and without complete sets of concept annotations demonstrate that MixCEMs outperform strong baselines by significantly improving their accuracy for both in-distribution and OOD samples in the presence and absence of concept interventions.

RO-FIGS: Efficient and Expressive Tree-Based Ensembles for Tabular Data

Tree-based models are often robust to uninformative features and can accurately capture non-smooth, complex decision boundaries. Consequently, they often outperform neural network-based models on tabular datasets at a significantly lower computational cost. Nevertheless, the capability of traditional tree-based ensembles to express complex relationships efficiently is limited by using a single feature to make splits. To improve the efficiency and expressiveness of tree-based methods, we propose Random Oblique Fast Interpretable Greedy-Tree Sums (RO-FIGS). RO-FIGS builds on Fast Interpretable Greedy-Tree Sums, and extends it by learning trees with oblique or multivariate splits, where each split consists of a linear combination learnt from random subsets of features. This helps uncover interactions between features and improves performance. The proposed method is suitable for tabular datasets with both numerical and categorical features. We evaluate RO-FIGS on 22 real-world tabular datasets, demonstrating superior performance and much smaller models over other tree- and neural network-based methods. Additionally, we analyse their splits to reveal valuable insights into feature interactions, enriching the information learnt from SHAP summary plots, and thereby demonstrating the enhanced interpretability of RO-FIGS models. The proposed method is well-suited for applications, where balance between accuracy and interpretability is essential.

How Well Does Your Tabular Generator Learn the Structure of Tabular Data?

Heterogeneous tabular data poses unique challenges in generative modelling due to its fundamentally different underlying data structure compared to homogeneous modalities, such as images and text. Although previous research has sought to adapt the successes of generative modelling in homogeneous modalities to the tabular domain, defining an effective generator for tabular data remains an open problem. One major reason is that the evaluation criteria inherited from other modalities often fail to adequately assess whether tabular generative models effectively capture or utilise the unique structural information encoded in tabular data. In this paper, we carefully examine the limitations of the prevailing evaluation framework and introduce $\textbf{TabStruct}$, a novel evaluation benchmark that positions structural fidelity as a core evaluation dimension. Specifically, TabStruct evaluates the alignment of causal structures in real and synthetic data, providing a direct measure of how effectively tabular generative models learn the structure of tabular data. Through extensive experiments using generators from eight categories on seven datasets with expert-validated causal graphical structures, we show that structural fidelity offers a task-independent, domain-agnostic evaluation dimension. Our findings highlight the importance of tabular data structure and offer practical guidance for developing more effective and robust tabular generative models. Code is available at https://github.com/SilenceX12138/TabStruct.

LLM Embeddings for Deep Learning on Tabular Data

Tabular deep-learning methods require embedding numerical and categorical input features into high-dimensional spaces before processing them. Existing methods deal with this heterogeneous nature of tabular data by employing separate type-specific encoding approaches. This limits the cross-table transfer potential and the exploitation of pre-trained knowledge. We propose a novel approach that first transforms tabular data into text, and then leverages pre-trained representations from LLMs to encode this data, resulting in a plug-and-play solution to improv ing deep-learning tabular methods. We demonstrate that our approach improves accuracy over competitive models, such as MLP, ResNet and FT-Transformer, by validating on seven classification datasets.

Measuring Cross-Modal Interactions in Multimodal Models

Integrating AI in healthcare can greatly improve patient care and system efficiency. However, the lack of explainability in AI systems (XAI) hinders their clinical adoption, especially in multimodal settings that use increasingly complex model architectures. Most existing XAI methods focus on unimodal models, which fail to capture cross-modal interactions crucial for understanding the combined impact of multiple data sources. Existing methods for quantifying cross-modal interactions are limited to two modalities, rely on labelled data, and depend on model performance. This is problematic in healthcare, where XAI must handle multiple data sources and provide individualised explanations. This paper introduces InterSHAP, a cross-modal interaction score that addresses the limitations of existing approaches. InterSHAP uses the Shapley interaction index to precisely separate and quantify the contributions of the individual modalities and their interactions without approximations. By integrating an open-source implementation with the SHAP package, we enhance reproducibility and ease of use. We show that InterSHAP accurately measures the presence of cross-modal interactions, can handle multiple modalities, and provides detailed explanations at a local level for individual samples. Furthermore, we apply InterSHAP to multimodal medical datasets and demonstrate its applicability for individualised explanations.

PATHS: A Hierarchical Transformer for Efficient Whole Slide Image Analysis

Computational analysis of whole slide images (WSIs) has seen significant research progress in recent years, with applications ranging across important diagnostic and prognostic tasks such as survival or cancer subtype prediction. Many state-of-the-art models process the entire slide - which may be as large as $150,000 \times 150,000$ pixels - as a bag of many patches, the size of which necessitates computationally cheap feature aggregation methods. However, a large proportion of these patches are uninformative, such as those containing only healthy or adipose tissue, adding significant noise and size to the bag. We propose Pathology Transformer with Hierarchical Selection (PATHS), a novel top-down method for hierarchical weakly supervised representation learning on slide-level tasks in computational pathology. PATHS is inspired by the cross-magnification manner in which a human pathologist examines a slide, recursively filtering patches at each magnification level to a small subset relevant to the diagnosis. Our method overcomes the complications of processing the entire slide, enabling quadratic self-attention and providing a simple interpretable measure of region importance. We apply PATHS to five datasets of The Cancer Genome Atlas (TCGA), and achieve superior performance on slide-level prediction tasks when compared to previous methods, despite processing only a small proportion of the slide.