Locality-aware Concept Bottleneck Model (LCBM)

• LCBM is a framework that enforces spatial grounding by predicting concepts from spatially relevant local regions rather than diffuse global evidence.
• It integrates architectural strategies such as prototype learning, cross-attention, and specialized pooling to achieve precise concept localization.
• Empirical findings indicate that enforcing locality improves explanation quality and concept trustworthiness while sustaining competitive predictive accuracy.

Locality-aware Concept Bottleneck Model (LCBM) denotes a line of concept bottleneck modeling that explicitly constrains concept prediction to arise from spatially relevant local regions rather than from diffuse global evidence. In its most explicit formulation, LCBM is a framework that utilizes foundation models and prototype learning to ensure accurate spatial localization of the concepts (Jeon et al., 20 Aug 2025). Closely related work uses the same term for an enhanced CBM that predicts concepts from distinct parts of the feature map and evaluates whether concepts are derived from relevant regions through a concept trustworthiness score (Huang et al., 2024). The broader research program is motivated by a recurring limitation of conventional CBMs: although the concept bottleneck is interpretable, the mapping from input to concepts often lacks locality faithfulness and may rely on spurious cues (Zhang et al., 19 Jan 2026).

1. Historical motivation and problem formulation

Concept Bottleneck Models decompose prediction into an input-to-concept mapping and a concept-to-label mapping, so one might expect each concept to be predicted from a distinct region or feature subset of the input (Furby et al., 2023). Empirical analysis has shown that this expectation is often not met. In a study of end-to-end explanation in CBMs, saliency maps for the $x \rightarrow c$ pathway did not show distinct, localized regions for each concept; relevance was generally spread across the entire bird or concentrated on features like the eye regardless of the specific concept, and concepts with similar predicted values tended to produce similar input saliency maps (Furby et al., 2023).

This failure of locality is not merely cosmetic. The 2024 trustworthiness study argues that the mapping from the input to the intermediate concept remains a black box, so learned concepts may be predicted based on spurious cues, which greatly hampers interpretability (Huang et al., 2024). The 2026 semantic-locality extension makes the same diagnosis in terms of locality faithfulness, stating that existing CBMs often fail to spatially align concepts with meaningful image regions, which limits interpretability and reliability (Zhang et al., 19 Jan 2026). LCBM research therefore targets a more stringent notion of interpretability: not only must the concept bottleneck be human-understandable, but the evidence used to activate each concept must also be spatially grounded.

2. Architectural patterns

The locality-aware literature contains several closely related architectural strategies for spatially grounded concept prediction.

Framework	Core mechanism	Locality strategy
LCBM (Huang et al., 2024)	concept prediction head as a $1 \times 1$ convolution over the activation map	CLA, CIA, and PA modules
LCBM (Jeon et al., 20 Aug 2025)	one prototype for each concept, guided by CLIP patch–concept similarity	prototype learning and locality loss
SL-CBM (Zhang et al., 19 Jan 2026)	$1 \times 1$ convolution plus cross-attention	semantic locality and faithful saliency maps

In the 2024 locality-aware formulation, a concept prediction head $h_c$ is attached as a $1 \times 1$ convolutional layer over the spatial activation map $\mathbf{A} \in \mathbb{R}^{C \times H \times W}$ so that concept activation is predicted per spatial location:

$\hat{c}_{k,(i,j)} = h_{c,k}(\mathbf{A}_{:, i, j}).$

A spatial pooling mechanism then aggregates these local predictions, while the architecture and loss are designed so that only certain $(i,j)$ locations dominate the concept activation (Huang et al., 2024).

The 2025 LCBM framework instead combines concept bottlenecks, prototype learning, and CLIP-based guidance. A backbone extracts patchwise features $F \in \mathbb{R}^{HW \times D}$, each concept $c_k$ is assigned a dedicated prototype vector $1 \times 1$0, and cosine similarity between patches and prototypes yields

$1 \times 1$1

CLIP image-patch and text-concept similarities are used to select the most relevant concepts for each patch, so prototype assignment is constrained by foundation-model priors (Jeon et al., 20 Aug 2025).

SL-CBM extends the same locality agenda by integrating a $1 \times 1$2 convolutional layer with a cross-attention mechanism. The $1 \times 1$3 convolution directly produces $1 \times 1$4 concept saliency maps $1 \times 1$5, and cross-attention fuses these maps with the concept-based projection of the image summary to reinforce both locality and concept faithfulness (Zhang et al., 19 Jan 2026). Final class logits are computed through a classifier $1 \times 1$6, while class-level saliency inherits spatial structure from concept-level maps.

3. Locality enforcement and training objectives

A central technical issue is how locality is enforced during training rather than assessed only post hoc. In the 2024 LCBM, three modules are introduced: cross-layer alignment (CLA), cross-image alignment (CIA), and prediction alignment (PA). CLA encourages spatial position $1 \times 1$7 to remain semantically consistent across layers; CIA aligns the same spatial site across different images when the same concept is present there; and PA enforces that each concept is predicted from only a single or small subset of spatial locations through a peaky spatial distribution (Huang et al., 2024). The PA mechanism uses

$1 \times 1$8

followed by

$1 \times 1$9

and an entropy regularizer

$1 \times 1$0

to penalize diffuse spatial assignments (Huang et al., 2024).

The 2025 prototype-based LCBM introduces a different locality objective. It computes a concept-wise gradient-based attribution for each spatial location,

$1 \times 1$1

and then minimizes KL divergence between normalized concept attribution and masked prototype similarity:

$1 \times 1$2

Its total objective is

$1 \times 1$3

where the auxiliary classification loss encourages prototypes to encode discriminative, class-relevant region features (Jeon et al., 20 Aug 2025).

SL-CBM uses a composite objective that jointly targets class accuracy, concept accuracy, sparsity, and optional concept consistency. The overall loss is

$1 \times 1$4

with class cross-entropy, a concept accuracy loss, entropy regularization for saliency sparsity, and an optional contrastive loss for concept consistency (Zhang et al., 19 Jan 2026). The ablation results reported for SL-CBM indicate that entropy loss controls sparsity, while contrastive loss stabilizes concept embedding and reduces irrelevant attributions.

4. Explanation mechanisms and evaluation protocols

LCBM work evaluates explanations at the level of both concept prediction and class decision. In SL-CBM, concept saliency maps are produced directly by the architecture rather than by a post-hoc attribution method. If $1 \times 1$5 denotes the classifier weights for class $1 \times 1$6, the class-level saliency map is formed as

$1 \times 1$7

This makes the class saliency map a linear combination of concept saliency maps, so the class decision can be inspected in terms of how the model assembles concepts into a prediction (Zhang et al., 19 Jan 2026).

The 2024 trustworthiness framework formalizes reliability through a concept trustworthiness score,

$1 \times 1$8

together with aggregated trustworthiness over images and locations (Huang et al., 2024). This score is intended to gauge whether a concept prediction at a spatial site is reliable and aligned with the relevant region.

Evaluation protocols in this area are heterogeneous but systematically locality-oriented. With annotations such as masks or segmentation labels, SL-CBM reports IoU, Dice, and Compact IoU (C-IoU), the last of which penalizes over-large saliency maps (Zhang et al., 19 Jan 2026). Without annotations, it reports Average Drop (AD), Average Increase (AI), and Average Gain (AG), with AG described as the most robust for explanation evaluation. The prototype-based LCBM evaluates localization through Inclusion, mIoU, REP, and Deletion, and also evaluates explanation precision through whether the most contributing concepts actually exist in the image (Jeon et al., 20 Aug 2025).

Earlier diagnostic work supplied an additional perspective by adapting the pointing game into a distance-based metric. For each concept saliency map, the most salient pixel is identified and its Euclidean distance to the ground-truth part location is measured; lower distance indicates more local prediction (Furby et al., 2023). The same paper introduced the proportion of relevance metric for the $1 \times 1$9 mapping,

$h_c$0

to quantify concept importance in the final prediction.

5. Empirical findings

Across the locality-aware literature, the reported empirical pattern is consistent: enforcing spatial grounding improves explanation quality and localization while preserving competitive predictive performance. The 2024 LCBM study reports experiments on five datasets across ten architectures and states that, without using any concept localization annotations during training, the model improves concept trustworthiness by a large margin while achieving superior accuracy to the state of the art (Huang et al., 2024). Its detailed summary further reports increased locality, calibrated trustworthiness, cross-image consistency, and nearly unchanged end-task prediction accuracy.

The 2025 prototype-based LCBM reports that it effectively identifies present concepts in the images and exhibits improved localization while maintaining comparable classification performance (Jeon et al., 20 Aug 2025). On CUB-200-2011, the reported Inclusion score is 72.4% for LCBM versus 65.3% for LfCBM and 53.8% for VLG-CBM, and the paper states that LCBM outperforms all baselines across Inclusion, mIoU, and REP on all datasets. Deletion tests show that removing the local region for a concept causes a larger drop in concept scores for LCBM than for baselines, which the paper interprets as evidence that the model focuses on the correct regions.

SL-CBM reports a stronger claim at the level of both concepts and classes. It achieves the highest class and concept accuracy compared to PCBM and CSS baselines, outperforms all baselines across IoU, Dice, and C-IoU with annotation and AG, AI, and AD without annotation, and produces visualizations in which semantically correct and spatially tight regions are highlighted (Zhang et al., 19 Jan 2026). It also reports improved intervention efficacy: when human-corrected concepts are supplied, SL-CBM maintains or improves model performance, whereas competing models that do not enforce locality sometimes degrade when intervened, which is described as a sign of non-faithful concept representation.

These results support a narrow empirical conclusion: accuracy alone does not diagnose whether a concept bottleneck is trustworthy. Locality-aware evaluation exposes deficiencies in concept grounding that are otherwise hidden by strong classification performance.

6. Scope, related variants, and terminology

The term LCBM is not used uniformly across the literature. In the locality-aware line, it refers to CBMs that predict concepts from distinct parts of the feature map or from prototype-aligned local regions (Huang et al., 2024, Jeon et al., 20 Aug 2025). SL-CBM should be understood as a semantic-locality extension within this line: it enhances concept bottleneck models with semantic locality for better interpretability by generating spatially coherent saliency maps at both concept and class levels (Zhang et al., 19 Jan 2026).

A separate 2025 paper uses the acronym LCBM for “Learnable Concept-Based Model,” an unsupervised concept-based model for image classification that models concepts as random variables within a Bernoulli latent space (Santis et al., 2 Jun 2025). In that usage, locality-awareness refers to a local linear combination of concepts with sample-dependent weights rather than to spatial localization of concepts in image regions. The model comprises a concept encoder $h_c$1, an interpretable local classifier, and a concept decoder; prediction takes the form

$h_c$2

where the weight $h_c$3 is predicted as a function of the concept embedding (Santis et al., 2 Jun 2025).

This acronym reuse has practical significance for reading the literature. In vision-centered explainability papers, “locality-aware” usually denotes spatial grounding of concepts in relevant image patches or regions; in the unsupervised learnable-model paper, “locality-aware” denotes sample-dependent local linear explanations. A plausible implication is that the field is converging on a broader requirement for concept-based interpretability: concepts should be both semantically meaningful and operationally tied to the evidence actually used by the model.