概念解释

Concept shift occurs when the distribution of labels conditioned on the features changes between domains, which can make even a well-tuned ML model miscalibrated on a new domain. Identifying these shifted features provides unique insight into how feature-label relationships differ between domains, considering the difference may be across a scientifically relevant dimension, such as time, disease status, population, etc. In this paper, we propose SGShift, a method for attributing performance degradation under concept shift in tabular data to a sparse set of shifted features. We frame concept shift as a feature selection task to learn the features that can explain performance differences between models in the source and target domain. This framework enables SGShift to adapt powerful statistical tools such as generalized additive models, knockoffs, and absorption towards identifying these shifted features. We conduct extensive experiments in synthetic and real data across various ML models and find SGShift can identify shifted features much more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases of concept shift.

Concept Embedding Models (CEMs) advance interpretable AI by extending Concept Bottleneck Models (CBMs) through semantic concept embeddings, providing an important solution in high-stakes domains such as medical diagnosis where accuracy and interpretability are critical. However, a fundamental limitation persists: existing CEMs inherently assume concept independence, critically overlooking the highly complex dependencies among concepts. To address this, we propose an Evidential Copula Concept Embedding Model (EC-CEM) that redefines the joint distribution over concepts, capturing inter-concept dependencies while maintaining a flexible structure that decouples the marginal concept distributions from their dependency structure. In particular, EC-CEM relaxes the concept independence assumption and uniquely integrates Copula theory with evidential deep learning to define a joint distribution over concepts. The proposed EC-CEM also develops two training objectives that aim at classification and concept modeling simultaneously. We provide theoretical justification via variational inference and demonstrate empirical superiority through extensive experiments.

Explanations of model behavior are commonly evaluated via proxy properties weakly tied to the purposes explanations serve in practice. We contribute a decision theoretic framework that treats explanations as information signals valued by the expected improvement they enable on a specified decision task. This approach yields three distinct estimands: (i) a theoretical benchmark that upper-bounds achievable performance by any agent with the explanation, (ii) a human-complementary value that quantifies the theoretically attainable value that is not already captured by a baseline human decision policy, and (iii) a behavioral value representing the causal effect of providing the explanation to human decision-makers. We instantiate these definitions in a practical validation workflow, and apply them to assess explanation potential and interpret behavioral effects in human–AI decision support and mechanistic interpretability.

Large Multimodal Models (LMMs) integrate unimodal encoders with Large Language Models (LLMs) to execute complex multimodal tasks. Despite progress in the field, understanding the internal representations of these models through interpretable logic remains an open problem. To address this, we present a framework utilizing a Human-Inspired (Neuro-fuzzy) approach for learning token representations. In this method, we leverage fuzzy rules to compute activation firing strengths, which are subsequently defuzzified to extract distinct concepts. This mechanism allows for the interpretation of learned representations directly through explicit logic. Consequently, we derive "multimodal concepts" that are both semantically coherent and interpretable. We validate our approach through rigorous qualitative and quantitative experiments, demonstrating the utility of these concepts in interpreting test samples. Additionally, we evaluate the disentanglement of the learned concepts and the efficacy of their grounding in both visual and textual domains.

The Massart noise condition is a central model in Probably Approximately Correct (PAC) learning theory. Its importance lies in it being an interpolation condition between realizable and the agnostic settings, under which one can attain faster rates than in the latter, and, under strict conditions, recover the rates of the former. Despite its importance, the Massart condition has not yet been fully explored in emerging extensions of statistical learning theory beyond the classical PAC framework. In this work, we present two such extensions. First, we revisit the transductive empirical risk minimization (TERM) algorithm of (Hanneke & Moran, 2026), and derive sharper excess error bounds under Massart noise using offset Rademacher techniques and local metric entropy introduced by (Zhivotovskiy & Hanneke, 2018). We then leverage this analysis to obtain new sample complexity bounds for PAC learning with partial concept classes and complete the characterization of universal rates under Massart noise.

Large language models (LLMs) are increasingly deployed in high-stakes domains, where free-text explanations such as chain-of-thought and post-hoc rationales are used to justify model outputs. Yet it remains unclear whether these explanations are _sufficient_, i.e., if they contain enough information to explain the model’s output-generating process. We generalize classical sufficiency from feature attributions to arbitrary explanations and prove that explanation sufficiency can change depending on the input distribution, which must be explicitly defined for LLM explanations. We propose using the LLM itself to generate alternative inputs conditioned on an explanation, capturing its beliefs about possible inputs. We formalize _self-consistent sufficiency_ as a goal for free-text explanations and introduce an information-theoretic metric, SCSuff, that enables evaluation of free-text explanations without relying on predefined biases or shortcuts. Our experiments show that SCSuff agrees with targeted perturbation tests where applicable and demonstrate that explanation sufficiency can vary with the input distribution. We find LLM explanations are generally insufficient and weakly correlated with model size, accuracy, or output entropy. Analysis of final-token hidden states shows that top and bottom SCSuff scores can be predicted from internal representations, suggesting that SCSuff can guide detection and improvement of sufficient LLM explanations. The code for this paper is available at https://github.com/rajesh-lab/self-consistent-sufficiency.

While *Prover-Verifier Games* (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, expressive *concept encodings* effectively allow to translate such data into interpretable concepts but are often utilised in the context of low-capacity linear predictors. In this work, we push towards real-world verifiability by combining the strengths of both approaches. We introduce *Neural Concept Verifier (NCV)*, a unified framework combining PVGs for formal verifiability with concept encodings to handle complex, high-dimensional inputs in an interpretable way. NCV achieves this by utilizing recent minimally supervised concept discovery models to extract structured concept encodings from raw inputs. A *prover* then selects a subset of these encodings, which a *verifier*, implemented as a nonlinear predictor, uses exclusively for decision-making. Our evaluations show that NCV outperforms classic concept-based models and pixel-based PVG classifier baselines on high-dimensional, logically complex datasets and helps mitigate shortcut behavior. Overall, we demonstrate NCV as a promising step toward concept-level, verifiable AI.

The expansion of text-to-image diffusion models has raised concerns about harmful outputs, from fabricated depictions of public figures to sexually explicit imagery. To mitigate such risks, prior work has proposed concept erasure methods that aim to sever unwanted concepts from the model via fine-tuning, yet it remains unclear whether these approaches truly remove all links to the harmful concept or merely conceal superficial connections. In this work, we reveal a critical vulnerability, the Erasure Evasion Backdoor (EEB): an adversary binds a backdoor trigger to a concept slated for removal, and this malicious link survives subsequent erasure. We show that both black-box and white-box adversaries can instantiate this threat. Across six state-of-the-art erasure methods, including robust ones that explicitly search for alternative representations of the target concept, EEB consistently exposes harmful content: up to 82% success against celebrity-identity unlearning, up to 94% for object erasure, and up to 16$\times$ amplification of explicit-content exposure. While EEB uncovers a blind spot in current erasure methods, it also provides a diagnostic tool for stress-testing future concept erasure techniques.

Federated Continual Learning (FCL) enables the continuous acquisition of knowledge from streaming tasks, but inherently struggles with the temporal dynamics of client data distributions. These dynamics naturally induce asynchronous concept drift, where distribution shifts occur independently across clients at unsynchronized times and with varying magnitudes. Such asynchrony generates conflicting updates that destabilize global convergence and exacerbate catastrophic forgetting. However, existing FCL research focuses on static or incremental settings, typically treating all incoming updates uniformly, which obscures concept drift under divergent distributions and fails to adapt to the evolution of learned concepts. To address these limitations, we propose RC-FCL, a retrospective calibration framework for FCL that can effectively distinguish asynchronous concept drift and adjust the learning strategy adaptively. Specifically, RC-FCL leverages a conditional generative model to synthesize class-conditional reference distributions of previously learned concepts for local drift detection. It calibrates local adaptation using a weighting mechanism driven by the local discriminator to prioritize informative samples, and executes a global aggregation strategy based on drift magnitude. Our experimental results demonstrate that RC-FCL achieves competitive performance against state-of-the-art methods.

We study the Probably Approximately Correct (PAC) learnability of partial concept classes in the multiclass setting, where the label space can be infinite. While the Natarajan dimension characterizes learnability for finite label spaces, we show it fails when the label space is unbounded. Instead, we prove that the Daniely-Shalev (DS) dimension provides a characterization of learnability for partial concept classes in the general multiclass setting. Furthermore, our analysis reveals a surprising phenomenon we call the ``Disambiguation Paradox'': disambiguation schemes with simple label space can destroy learnability, while richer labeling may preserves it. We further characterize how the number and structure of disambiguation labels control the induced DS dimension, yielding a trade-off between label complexity and sample complexity.

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-CBEs), 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.

Many visual explanation methods in computer vision highlight pixel importance but struggle to link these low-level cues to semantically meaningful concepts, limiting their interpretability and trustworthiness. We introduce Concept-based Explanations (ConEx), a novel framework that bridges saliency visualization with concept-based reasoning to provide both faithfulness and interpretability. ConEx automatically discovers class-specific concepts and represents them through concept activation vectors (CAVs), learned without manual supervision using an architecture-specific masking mechanism that reduces noise introduced by the segmentation masks to enhance concept purity. ConEx generates faithful saliency maps that reveal where each concept appears in the image and how it contributes to the prediction. To evaluate the reliability of these learned concepts, we propose two complementary metrics, Vector-Concept Match (VCM) and Concept-Class Match (CCM), that quantify concept alignment and enable direct comparison with existing methods. Extensive experiments across diverse settings demonstrate that ConEx achieves state-of-the-art performance on faithfulness, segmentation, and concept-quality benchmarks. Overall, ConEx advances the field toward truly interpretable and concept-grounded explanations in vision models.

One of the most pressing challenges in artificial intelligence is to make models more transparent to their users. Recently, explainable artificial intelligence has come up with numerous methods to tackle this challenge. A promising avenue is to use concept-based explanations, that is, high-level concepts instead of plain feature importance scores. Among this class of methods, Concept Activation Vectors (CAVs, Kim et al., 2018) stand out as one of the main protagonists. One interesting aspect of CAVs is that their computation requires sampling random examples from the train set. Therefore, the actual vectors obtained may vary depending on the randomness of this sampling. In this paper, we propose a fine-grained theoretical analysis of CAV construction in order to quantify their variability. Our results, confirmed by experiments on several real-life datasets of four different modalities, point to an universal result: the variance of CAVs declines roughly as $1/N$, where $N$ is the number of random examples. Based on this, we give practical recommendations for a resource-efficient application of the method.

Real-world knowledge is often organized as hierarchies such as product taxonomies, medical ontologies, and label trees, yet learning hierarchical representations is challenging due to asymmetric structure and noisy semantics. We introduce Polaris, a polar hyperspherical embedding framework that separates semanticity from hierarchy using angular geometry and radius, enabling the learning of meaning and structure without interference. To map latent representation onto the sphere, we project it to the tangent space at the north pole, apply the exponential map, and learn unit-norm representations using spherical linear layers. Polaris then combines robust local constraints, global regularization that prevents geometric collapse, and uncertainty-aware asymmetric objectives that encourage directional containment. At inference time, Polaris uses structure-guided retrieval to efficiently narrow down candidate parents before final ranking. We evaluate Polaris on different settings of taxonomy expansion -- spanning trees, multi-parent DAGs, and multimodal hierarchies, showing consistent improvements of up to $\sim$19 points in top-$K$ retrieval and up to $\sim$ 60\% reduction in mean rank over fourteen strong baselines.

Generalization under distribution shift remains a core challenge in modern machine learning, yet existing learning bound theory is limited to narrow, idealized settings and is non-estimable from samples. In this paper, we bridge the gap between theory and practical applications. We first show that existing definition of concept shift breaks when the source and target supports mismatch. Leveraging entropic optimal transport, we propose a key notion: $\gamma^\ast$-concept shifts, and derive a general error bound unifying covariate and $\gamma^\ast$-concept shifts, which applies to broad loss functions, label spaces, and stochastic labeling. We further develop estimators for these shifts with concentration guarantees, and the DataShifts algorithm, which can quantify distribution shifts and estimate the error bound in most applications - a rigorous and general tool for analyzing learning error under distribution shift.

Learning semantics is essential for deep learning models to be interpretable and better aligned with human reasoning. Concept-based models approach this by representing classes through meaningful semantic abstractions, but typically treat all concepts as a flat, unstructured set learned at a single neural network layer. This overlooks a fundamental property of human semantic understanding: concepts being organized hierarchically, from general to specific. While deep networks do learn a hierarchy of visual features, this structure is rarely aligned with explicit semantic hierarchies. Drawing on Formal Concept Analysis, we demonstrate that formal concept lattices provide principled semantic scaffolds to guide neural network learning. These lattices naturally identify where in the network concepts should be learned based on their level of generality. This allows the model to develop staged, semantically grounded representations throughout its depth. Empirical results on real-world datasets show that our models produce more interpretable embeddings, support more effective interventions, and learn concept representations that are both meaningful and hierarchically structured.

In this paper, we study a structured class of nonconvex constrained stochastic problems with difference-of-convex (DC) regularization, where the feasible set is possibly nonconvex and the concave part of the DC regularizer is allowed to be nonsmooth. The fundamental challenge lies in maintaining feasibility for nonconvex constraints while achieving favorable oracle complexity. Although single-loop algorithms efficiently solve unconstrained DC optimization problems, their potential for constrained optimization with DC structure remains largely unexplored. To address this gap, we develop **MoSSP**, a **Mo**mentum-based **S**ingle-loop **S**tochastic **P**enalty method for such problems with provable complexity guarantees. The key idea is to apply a single stochastic proximal-gradient step to the Moreau envelope of the penalty plus the convex DC part, with the concave part's proximal mapping computed in parallel. We derive two algorithm variants: a Polyak-momentum version with $\mathcal{O}(\varepsilon^{-4})$ oracle complexity for finding stochastic $\varepsilon$-KKT points, and an improved $\mathcal{O}(\varepsilon^{-3})$ version incorporating recursive momentum. Experimental results demonstrate the effectiveness of the proposed algorithms.

Building reliable applications that leverage large language models (LLMs) remains a significant challenge. While LLMs offer impressive capabilities across diverse tasks, their outputs often lack accuracy and provide no clear measure of confidence. This uncertainty compounds in flows of multiple calls to LLMs and other tools, making it difficult for developers and end-users to trust the results. This paper introduces a probabilistic language for programming LLM-based flows. It enables developers to quantify and propagate uncertainty throughout the application's flow, and experiment with different inference scaling techniques without adding a single line of code beyond the flow's logic. We present an experimental study to demonstrate this capability, and a case study building a theorem proving agent for the Rocq theorem prover.

Concept Bottleneck Models (CBMs) aim to improve interpretability in Deep Learning by structuring predictions through human-understandable concepts, but they provide no way to verify whether learned concepts align with the human's intended meaning, hurting interpretability. We introduce Prototype-Grounded Concept Models (PGCMs), which ground concepts in learned visual prototypes: image parts that serve as explicit evidence for the concepts. This grounding enables direct inspection of concept semantics and supports targeted human intervention at the prototype level to correct misalignments. Empirically, PGCMs achieve similar predictive performance as state-of-the-art CBMs while substantially improving transparency, interpretability, and intervenability.

We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value. For any smooth $f:\mathbb R^n\to\mathbb R$, $\mathbf{x}\in\mathbb R^n$, and $\varepsilon>0$, we design a gradient testing algorithm that determines whether the normalized gradient $\nabla f(\mathbf{x})/\lVert\nabla f(\mathbf{x})\rVert$ is $\varepsilon$-close or $2\varepsilon$-far from a given unit vector $\mathbf{v}$ using $O(1)$ queries, as well as a gradient estimation algorithm that outputs an $\varepsilon$-estimate of $\nabla f(\mathbf{x})/\lVert\nabla f(\mathbf{x})\rVert$ using $O(n\log(1/\varepsilon))$ queries which we prove to be optimal. Furthermore, we study gradient estimation in the quantum comparison oracle model where queries can be made in superpositions, and develop a quantum algorithm using $O(\log (n/\varepsilon))$ queries.