arXiv subjects

Mateo Espinosa Zarlenga

Publications and source records attributed to Mateo Espinosa Zarlenga.

At least 19 recordsLinked to original sources

arXiv2026

Harmful Partial Interventions and Benign Leakage in Concept-based Models

Artificial intelligence systems deployed in high-risk settings increasingly require models that support meaningful human oversight. Concept-based models (CMs) offer a promising framework by enabling users to inspect and intervene on intermediate, human-understandable concepts. However, concept interventions can counterintuitively worsen downstream predictions, a failure mode we formalise as intervention harm. We distinguish harm after all concepts have been intervened on from harm under partial interventions, the more likely practical use case. Modern CMs often achieve high accuracy by encoding, or leaking, additional task-relevant information in their intermediate concept representations. Recent work argues that such leakage can be benign with respect to intervention harm when concept representations satisfy two conditions: sufficiency and localisation. We prove that these criteria are not sufficient to guarantee that concept interventions improve downstream performance. Across controlled and real-world settings, we find that concept supervision incompleteness is associated with increased intervention harm. Importantly, optimising the model when all concepts are intervened on, a previously proposed leakage mitigation objective, reduces endpoint harm but does not reliably prevent harmful partial corrections. Hence, we introduce a complementary monotonic intervention objective that directly penalises increases in task loss along partial intervention trajectories. Combining endpoint and monotonic intervention training substantially reduces the prevalence and magnitude of partial intervention harm while preserving concept and task predictive performance.

cs.LG↗

arXiv2026

Persistent Sparse Autoencoders: Learning Feature-Specific Timescales in Language Model Representations

Sparse autoencoders (SAEs) decompose language model activations into sparse features, yet these models traditionally encode each token independently, failing to expose information that persists across a sequence. We first show that temporal persistence can naturally emerge in standard SAE features: after a feature activates, the hidden state remains aligned with its direction, and past activations help reconstruct later hidden states. How long this lasts varies widely across features. We therefore introduce Persistent Sparse Autoencoders (Persistent SAEs), an extension of standard SAEs that learns a persistence coefficient for each feature, allowing the model to learn feature-specific timescales from reconstruction alone. Our experiments show that Persistent SAEs retain competitive reconstruction quality while learning a spectrum of timescales: short-timescale (fast) features stay locally interpretable, whereas long-timescale (slow) features accumulate information that identifies the current context. Moreover, we show in a prompt-injection monitoring case study that slow features preserve injection-related signals and remain causally effective over long contexts. These results suggest that Persistent SAEs offer new opportunities for interpreting and monitoring language models via persistent sparse features.

cs.LG↗

arXiv2026

The Standard Interpretable Model: A general theory of interpretable machine learning to deductively design interpretable methods using Lagrangian mechanics

As Artificial Intelligence models grow in complexity, interpretability has become an indispensable tool for understanding, debugging, and controlling their computations. However, interpretability lacks general theories to deductively design interpretable methods. This gap between theories and methods results in a fragmented literature and inconsistent evaluation protocols. To fill this gap, we introduce the Standard Interpretable Model (SIM), a general theory grounded in Lagrangian mechanics that enables the deductive design of interpretable methods. Specifically, the SIM summarises, in a set of premises, what interpretability is for a target user. From these premises, the SIM systematically derives interpretability symmetries and corresponding constraints, which shape the landscape of a Lagrangian whose minima correspond to optimal interpretable models. To reach the minima, one can either update the parameter values of an opaque model to make it more interpretable or compile constraints into an interpretable architecture. We empirically show that the SIM identifies and solves limitations of existing methods (including traditional, concept-based, and mechanistic interpretability), highlights underexplored research directions, and informs the design of core programming interfaces. Beyond being a research method, the deductive nature of the SIM offers pedagogical grounding for interpretability curricula and may shift the scientific community's perspective of a discipline that has long been fragmented.

cs.LG↗

arXiv2026

Actionable Interpretability Must Be Defined in Terms of Symmetries

This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit that actionable definitions of interpretability must be formulated in terms of *symmetries* that inform model design and lead to testable conditions. Under a probabilistic view, we hypothesise that four symmetries (inference equivariance, information invariance, concept-closure invariance, and structural invariance) suffice to (i) formalise interpretable models as a subclass of probabilistic models, (ii) yield a unified formulation of interpretable inference (e.g., alignment, interventions, and counterfactuals) as a form of Bayesian inversion, and (iii) provide a formal framework to verify compliance with safety standards and regulations.

cs.AI↗

arXiv2026

In Defense of Information Leakage in Concept-based Models

Concept-based models (CMs), deep neural networks that ground their predictions on representations aligned with human-understandable concepts (e.g., "round", "stripes", etc.), have been shown to learn representations that leak concept-irrelevant information. As the traditional narrative goes, this leakage is undesirable and should be eradicated as it leads to uninterpretable models. In this paper, we posit that this conventional view of leakage in CMs is not only ill-posed, as the evidence of how leakage makes a model less interpretable is often inconclusive, but also bound to lead to impractical CMs under common real-world constraints. Specifically, we argue that in real-world settings where concept incompleteness is the norm, some leakage is often necessary for constructing accurate and intervenable CMs. To this end, we propose that there is such a thing as benign leakage and show that, by optimizing a reframing of the typical CM training objective, CMs can encourage and exploit this form of leakage without sacrificing accuracy or intervenability.

cs.LG↗

arXiv2026

Mixture of Concept Bottleneck Experts

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically constrain their task predictor to a single expression whose functional form is set a priori, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBE), a framework that generalizes existing CBMs along two dimensions: the number of expressions, referred to as experts, employed by the task predictor to map concepts to the task, and the functional form each expression takes, thus exposing an underexplored region of this design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data subject to user-specified operator vocabularies. Empirical evaluation demonstrates that varying the number of expressions and their functional form provides a robust framework for navigating the accuracy-interpretability trade-off.

cs.LG↗

arXiv2026

CB-SLICE: Concept-Based Interpretable Error Slice Discovery

Despite strong average-case performance, deep learning models often exhibit systematic errors on specific population groups, known as error slices. Identifying these groups and the root causes of their failures is critical for model debugging and bias mitigation. However, existing error Slice Discovery Methods (SDMs) typically generate explanations disconnected from the model's inference process, thus only approximating the underlying error source and may be inaccurate. We address this limitation by leveraging Concept Bottleneck Models (CBMs), whose predictions are directly dependent on human-understandable semantic concepts. Since downstream task failures in CBMs commonly arise from concept mispredictions, concept representations provide a strong candidate for error slice identification, offering fine-grained explanations directly linked to the error source. Building on this insight, we introduce CB-SLICE, a concept-based SDM that groups samples with shared concept prediction failures and identifies the keyword concepts most responsible for each slice's failure mode. Across multiple benchmarks, we show that CB-SLICE outperforms state-of-the-art methods in uncovering well-known biases while providing richer and more faithful explanations of model errors.

cs.LG↗

arXiv2026

Don't Lose Focus: Activation Steering via Key-Orthogonal Projections

Activation steering controls LLM behaviour towards target behaviour by intervening in internal representations, yet it often degrades reasoning and retrieval performance. We argue that a primary cause of this trade-off is attention rerouting: steering vectors alter query-key matching, shifting attention away from contextually important tokens toward less informative ones. To address this, we propose Steering via Key-Orthogonal Projections (SKOP), a steering method that constrains harmful attention rerouting without eliminating steering efficacy. SKOP achieves this by preserving attention patterns on a small set of focus tokens the model relies on for reasoning and retrieval, while allowing redistribution among less critical tail tokens. Across multiple steering benchmarks, we show that SKOP achieves the best joint steering-utility trade-off, reducing utility degradation by 5-7x while retaining over 95% of vanilla steering efficacy. Our results further suggest that, in long-context retrieval settings where vanilla steering approaches are ineffective, SKOP can maintain robust performance by avoiding attention rerouting.

cs.CL↗

arXiv2026

Digging Deeper: Learning Multi-Level Concept Hierarchies

Although concept-based models promise interpretability by explaining predictions with human-understandable concepts, they typically rely on exhaustive annotations and treat concepts as flat and independent. To circumvent this, recent work has introduced Hierarchical Concept Embedding Models (HiCEMs) to explicitly model concept relationships, and Concept Splitting to discover sub-concepts using only coarse annotations. However, both HiCEMs and Concept Splitting are restricted to shallow hierarchies. We overcome this limitation with Multi-Level Concept Splitting (MLCS), which discovers multi-level concept hierarchies from only top-level supervision, and Deep-HiCEMs, an architecture that represents these discovered hierarchies and enables interventions at multiple levels of abstraction. Experiments across multiple datasets show that MLCS discovers human-interpretable concepts absent during training and that Deep-HiCEMs maintain high accuracy while supporting test-time concept interventions that can improve task performance.

cs.LG↗

arXiv2026

Hierarchical Concept-based Interpretable Models

Modern deep neural networks remain challenging to interpret due to the opacity of their latent representations, impeding model understanding, debugging, and debiasing. Concept Embedding Models (CEMs) address this by mapping inputs to human-interpretable concept representations from which tasks can be predicted. Yet, CEMs fail to represent inter-concept relationships and require concept annotations at different granularities during training, limiting their applicability. In this paper, we introduce Hierarchical Concept Embedding Models (HiCEMs), a new family of CEMs that explicitly model concept relationships through hierarchical structures. To enable HiCEMs in real-world settings, we propose Concept Splitting, a method for automatically discovering finer-grained sub-concepts from a pretrained CEM's embedding space without requiring additional annotations. This allows HiCEMs to generate fine-grained explanations from limited concept labels, reducing annotation burdens. Our evaluation across multiple datasets, including a user study and experiments on PseudoKitchens, a newly proposed concept-based dataset of 3D kitchen renders, demonstrates that (1) Concept Splitting discovers human-interpretable sub-concepts absent during training that can be used to train highly accurate HiCEMs, and (2) HiCEMs enable powerful test-time concept interventions at different granularities, leading to improved task accuracy.

cs.LG↗

arXiv2025

Addressing Concept Mislabeling in Concept Bottleneck Models Through Preference Optimization

Concept Bottleneck Models (CBMs) propose to enhance the trustworthiness of AI systems by constraining their decisions on a set of human-understandable concepts. However, CBMs typically assume that datasets contain accurate concept labels-an assumption often violated in practice, which we show can significantly degrade performance (by 25% in some cases). To address this, we introduce the Concept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigates the negative impact of concept mislabeling on CBM performance. We provide an analysis of key properties of the CPO objective, showing it directly optimizes for the concept's posterior distribution, and contrast it against Binary Cross Entropy (BCE), demonstrating that CPO is inherently less sensitive to concept noise. We empirically confirm our analysis by finding that CPO consistently outperforms BCE on three real-world datasets, both with and without added label noise. We make our code available on Github.

cs.LG↗

arXiv2025

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.

cs.LG↗

arXiv2025

Foundations of Interpretable Models

We argue that existing definitions of interpretability are not actionable in that they fail to inform users about general, sound, and robust interpretable model design. This makes current interpretability research fundamentally ill-posed. To address this issue, we propose a definition of interpretability that is general, simple, and subsumes existing informal notions within the interpretable AI community. We show that our definition is actionable, as it directly reveals the foundational properties, underlying assumptions, principles, data structures, and architectural features necessary for designing interpretable models. Building on this, we propose a general blueprint for designing interpretable models and introduce the first open-sourced library with native support for interpretable data structures and processes.

cs.LG↗

arXiv2025

Do Concept Bottleneck Models Respect Localities?

Concept-based explainability methods use human-understandable intermediaries to produce explanations for machine learning models. These methods assume concept predictions can help understand a model's internal reasoning. In this work, we assess the degree to which such an assumption is true by analyzing whether concept predictors leverage "relevant" features to make predictions, a term we call locality. Concept-based models that fail to respect localities also fail to be explainable because concept predictions are based on spurious features, making the interpretation of the concept predictions vacuous. To assess whether concept-based models respect localities, we construct and use three metrics to characterize when models respect localities, complementing our analysis with theoretical results. Each of our metrics captures a different notion of perturbation and assess whether perturbing "irrelevant" features impacts the predictions made by a concept predictors. We find that many concept-based models used in practice fail to respect localities because concept predictors cannot always clearly distinguish distinct concepts. Based on these findings, we propose suggestions for alleviating this issue.

cs.LG↗

arXiv2025

Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning

Causal opacity denotes the difficulty in understanding the "hidden" causal structure underlying the decisions of deep neural network (DNN) models. This leads to the inability to rely on and verify state-of-the-art DNN-based systems, especially in high-stakes scenarios. For this reason, circumventing causal opacity in DNNs represents a key open challenge at the intersection of deep learning, interpretability, and causality. This work addresses this gap by introducing Causal Concept Graph Models (Causal CGMs), a class of interpretable models whose decision-making process is causally transparent by design. Our experiments show that Causal CGMs can: (i) match the generalisation performance of causally opaque models, (ii) enable human-in-the-loop corrections to mispredicted intermediate reasoning steps, boosting not just downstream accuracy after corrections but also the reliability of the explanations provided for specific instances, and (iii) support the analysis of interventional and counterfactual scenarios, thereby improving the model's causal interpretability and supporting the effective verification of its reliability and fairness.

cs.LG↗

arXiv2025

Deferring Concept Bottleneck Models: Learning to Defer Interventions to Inaccurate Experts

Concept Bottleneck Models (CBMs) are machine learning models that improve interpretability by grounding their predictions on human-understandable concepts, allowing for targeted interventions in their decision-making process. However, when intervened on, CBMs assume the availability of humans that can identify the need to intervene and always provide correct interventions. Both assumptions are unrealistic and impractical, considering labor costs and human error-proneness. In contrast, Learning to Defer (L2D) extends supervised learning by allowing machine learning models to identify cases where a human is more likely to be correct than the model, thus leading to deferring systems with improved performance. In this work, we gain inspiration from L2D and propose Deferring CBMs (DCBMs), a novel framework that allows CBMs to learn when an intervention is needed. To this end, we model DCBMs as a composition of deferring systems and derive a consistent L2D loss to train them. Moreover, by relying on a CBM architecture, DCBMs can explain why defer occurs on the final task. Our results show that DCBMs achieve high predictive performance and interpretability at the cost of deferring more to humans.

cs.LG↗

arXiv2025

Neural Interpretable Reasoning

We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of variables of the system, we show that this complexity can be mitigated by treating interpretability as a Markovian property and employing neural re-parametrization techniques. Building on these insights, we propose a new modeling paradigm -- neural generation and interpretable execution -- that enables scalable verification of equivariance. This paradigm provides a general approach for designing Neural Interpretable Reasoners that are not only expressive but also transparent.

cs.LG↗

arXiv2024

Learning to Receive Help: Intervention-Aware Concept Embedding Models

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.

cs.LG↗