Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge. While CBMs use supervision to align activations with human-labeled concepts, SAEs rely on sparse coding to uncover emergent ones. We show that both paradigms instantiate the same geometric structure: each learns a set of linear directions in activation space whose nonnegative combinations form a concept cone. Supervised and unsupervised methods thus differ not in kind but in how they select this cone. Building on this view, we propose an operational bridge between the two paradigms. CBMs provide human-defined reference geometries, while SAEs can be evaluated by how well their learned cones approximate or contain those of CBMs. This containment framework yields quantitative metrics linking inductive biases -- such as SAE type, sparsity, or expansion ratio -- to emergence of plausible\footnote{We adopt the terminology of \citet{jacovi2020towards}, who distinguish between faithful explanations (accurately reflecting model computations) and plausible explanations (aligning with human intuition and domain knowledge). CBM concepts are plausible by construction -- selected or annotated by humans -- though not necessarily faithful to the true latent factors that organise the data manifold.} concepts. Using these metrics, we uncover a ``sweet spot'' in both sparsity and expansion factor that maximizes both geometric and semantic alignment with CBM concepts. Overall, our work unifies supervised and unsupervised concept discovery through a shared geometric framework, providing principled metrics to measure SAE progress and assess how well discovered concept align with plausible human concepts.

Concept-based explanations have emerged as an effective approach within Explainable Artificial Intelligence, enabling interpretable insights by aligning model decisions with human-understandable concepts. However, existing methods rely on computationally intensive procedures and struggle to efficiently capture complex, semantic concepts. This work introduces the Concept Directions via Latent Clustering (CDLC), which extracts global, class-specific concept directions by clustering latent difference vectors derived from factual and diffusion-generated counterfactual image pairs. CDLC reduces storage requirements by 4.6 and accelerates concept discovery by 5.3 compared to the baseline method, while requiring no GPU for clustering, thereby enabling efficient extraction of multidimensional semantic concepts across latent dimensions. This approach is validated on a real-world skin lesion dataset, demonstrating that the extracted concept directions align with clinically recognized dermoscopic features and, in some cases, reveal dataset-specific biases or unknown biomarkers. These results highlight that CDLC is interpretable, scalable, and applicable across high-stakes domains and diverse data modalities. Introduction In high-stakes applications, such as medical diagnosis, financial risk assessment, and autonomous driving, understanding the rationale behind a neural network's decision is often as important as the decision itself. Explainable Artificial Intelligence (XAI) [1, 2] has emerged as a critical research area, aiming to bridge the gap between high-performing black-box models and human interpretability. Among the various XAI paradigms, concept-based explanations [3, 4] have gained particular attention due to their ability to express model behavior in terms of high-level, semantically meaningful concepts, rather than low-level feature weights or pixel-based saliency maps [5, 6]. By aligning explanations with concepts recognized by domain experts, these methods facilitate trust [7, 8], debugging [9], and regulatory compliance [10, 11].

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

Large Language Models (LLMs) are being used for a wide variety of tasks.

Concept Activation Vectors (CAVs) are widely used to model human-understandable concepts as directions within the latent space of neural networks. They are trained by identifying directions from the activations of concept samples to those of non-concept samples. However, this method often produces similar, non-orthogonal directions for correlated concepts, such as "beard" and "necktie" within the CelebA dataset, which frequently co-occur in images of men. This entanglement complicates the interpretation of concepts in isolation and can lead to undesired effects in CAV applications, such as activation steering. To address this issue, we introduce a post-hoc concept disentanglement method that employs a non-orthogonality loss, facilitating the identification of orthogonal concept directions while preserving directional correctness. We evaluate our approach with real-world and controlled correlated concepts in CelebA and a synthetic FunnyBirds dataset with VGG16 and ResNet18 architectures. We further demonstrate the superiority of orthogonalized concept representations in activation steering tasks, allowing (1) the insertion of isolated concepts into input images through generative models and (2) the removal of concepts for effective shortcut suppression with reduced impact on correlated concepts in comparison to baseline CAVs.

Linear representation hypothesis posits that high-level concepts are encoded as linear directions in the representation spaces of LLMs. Park et al. (2024) formalize this notion by unifying multiple interpretations of linear representation, such as 1-dimensional subspace representation and interventions, using a causal inner product. However, their framework relies on single-token counterfactual pairs and cannot handle ambiguous contrasting pairs, limiting its applicability to complex or context-dependent concepts. We introduce a new notion of binary concepts as unit vectors in a canonical representation space, and utilize LLMs' (neural) activation differences along with maximum likelihood estimation (MLE) to compute concept directions (i.e., steering vectors). Our method, Sum of Activation-base Normalized Difference (SAND), formalizes the use of activation differences modeled as samples from a von Mises-Fisher (vMF) distribution, providing a principled approach to derive concept directions. We extend the applicability of Park et al. (2024) by eliminating the dependency on unembedding representations and single-token pairs. Through experiments with LLaMA models across diverse concepts and benchmarks, we demonstrate that our lightweight approach offers greater flexibility, superior performance in activation engineering tasks like monitoring and manipulation.

Current advances in Natural Language Processing (NLP) have made it increasingly feasible to build applications leveraging textual data. Generally, the core of these applications rely on having a good semantic representation of text into vectors, via embedding models. However, it has been shown that these embeddings capture and perpetuate biases already present in text. While a few techniques have been proposed to debias embeddings, they do not take advantage of the recent advances in context understanding of modern embedding models. In this paper, we fill this gap by conducting a review of 19 embedding models by quantifying their biases and how well they respond to context injection as a mean of debiasing. We show that higher performing models are more prone to capturing biases, but are also better at incorporating context. Surprisingly, we find that while models can easily embed affirmative semantics, they fail at embedding neutral semantics. Finally, in a retrieval task, we show that biases in embeddings can lead to non-desirable outcomes. We use our new-found insights to design a simple algorithm for top $k$ retrieval, where $k$ is dynamically selected. We show that our algorithm is able to retrieve all relevant gendered and neutral chunks.

Large Language Models (LLMs) are being used for a wide variety of tasks. While they are capable of generating human-like responses, they can also produce undesirable output including potentially harmful information, racist or sexist language, and hallucinations. Alignment methods are designed to reduce such undesirable output, via techniques such as fine-tuning, prompt engineering, and representation engineering. However, existing methods face several challenges: some require costly fine-tuning for every alignment task; some do not adequately remove undesirable concepts, failing alignment; some remove benign concepts, lowering the linguistic capabilities of LLMs. To address these issues, we propose Parsimonious Concept Engineering (PaCE), a novel activation engineering framework for alignment. First, to sufficiently model the concepts, we construct a large-scale concept dictionary in the activation space, in which each atom corresponds to a semantic concept. Then, given any alignment task, we instruct a concept partitioner to efficiently annotate the concepts as benign or undesirable. Finally, at inference time, we decompose the LLM activations along the concept dictionary via sparse coding, to accurately represent the activation as a linear combination of the benign and undesirable components. By removing the latter ones from the activation, we reorient the behavior of LLMs towards alignment goals. We conduct experiments on tasks such as response detoxification, faithfulness enhancement, and sentiment revising, and show that PaCE achieves state-of-the-art alignment performance while maintaining linguistic capabilities.

Transformer language models (LMs) have been shown to represent concepts as directions in the latent space of hidden activations. However, for any given human-interpretable concept, how can we find its direction in the latent space? We present a technique called linear relational concepts (LRC) for finding concept directions corresponding to human-interpretable concepts at a given hidden layer in a transformer LM by first modeling the relation between subject and object as a linear relational embedding (LRE). While the LRE work was mainly presented as an exercise in understanding model representations, we find that inverting the LRE while using earlier object layers results in a powerful technique to find concept directions that both work well as a classifier and causally influence model outputs.