Draft:Concept Bottleneck Model

Concept bottleneck models are a class of interpretable machine learning models that make predictions through human-understandable intermediate variables called concepts. Rather than mapping an input directly to an output label, a concept bottleneck model first predicts a set of concepts and then uses those concepts to make the final prediction. This design is intended to make the model's reasoning process more transparent and allow users to inspect or intervene on intermediate concepts in some cases.

Overview and motivation

A concept bottleneck model (CBM) factors prediction into two stages: an input $x$ is first mapped to a set of human-understandable concepts $c$, and those concepts are then used to predict the target label $y$. This is often summarized as $x\rightarrow c\rightarrow y$. Unlike conventional end-to-end neural networks, which learn a direct mapping from raw inputs to labels, CBMs require the final prediction to pass through a concept layer. In principle, this allows a prediction to be related to intermediate attributes that humans can understand.

Concept bottleneck models were proposed in 2020 by Pang Wei Koh and colleagues as an interpretable-by-design approach to machine learning. The framework was motivated by the difficulty of interpreting, auditing, and correcting the internal representations of deep neural networks. CBMs build interpretability into the model architecture itself rather than relying only on post-hoc explanations after training. The concepts are usually chosen to correspond to attributes used by domain experts, such as clinical findings in medical imaging or visual attributes in fine-grained image classification.

One motivation for CBMs is that they support concept interventions at test time. Since the label predictor uses concept scores rather than raw features, a human expert can inspect the predicted concepts for an example, correct values that appear wrong, and then propagate the corrected concept vector through the label predictor. In medical imaging applications, for example, a clinician may correct an incorrectly predicted clinical concept before the final prediction is recomputed. Unlike many post-hoc explanation methods, CBMs include the interpretable concept layer as part of the predictive model itself.

The original CBM paper evaluated the framework on two benchmark applications: knee osteoarthritis severity grading from x-ray images, using clinical concepts such as joint space narrowing and bone spurs, and fine-grained bird classification on the Caltech-UCSD Birds-200-2011 dataset, where concepts correspond to visual attributes such as wing color, bill shape, and breast pattern. In both settings, concept predictions provided a human-readable account of model behavior, and correcting individual concept values improved final task accuracy.

A limitation of the original formulation is the cost of concept supervision. Standard CBMs require training data annotated not only with labels $y$, but also with ground-truth concepts $c$. Such annotations can be expensive, especially when they require clinical or scientific expertise. This limitation has motivated later work on post-hoc and label-free variants that reduce the need for manually labeled concepts.

Architecture and training

Concept bottleneck models decompose prediction into two stages: a concept predictor and a label predictor. Given an input $x$, the model first predicts a vector of concepts ${\hat {c}}$, and then uses these concepts to predict the final label ${\hat {y}}$. The general architecture can be written as:

$x\rightarrow g(x)={\hat {c}}\rightarrow f({\hat {c}})={\hat {y}}$

where $g$ maps inputs to concepts and $f$ maps concepts to labels.

In standard supervised CBMs, the model is trained on triplets $(x,c,y)$, where $x$ is the input, $c$ is the concept vector, and $y$ is the target label. The bottleneck is intended to enforce that the information used for prediction passes through the concept representation, enabling interpretability and concept-level intervention.

CBMs are commonly trained using three strategies: independent training, sequential training, and joint training. In independent training, the concept predictor is trained to predict concepts from inputs, while the label predictor is trained separately using ground-truth concepts. At inference time, predicted concepts are passed to the label predictor. This approach can introduce error when the predicted concepts differ from the true concepts.

In sequential training, the concept predictor is trained first, and the label predictor is then trained using the predicted concepts produced by the concept predictor. In joint training, both the concept predictor and the label predictor are optimized together using a combined concept and label loss. A typical joint objective has the form:$$\min _{f,g}\sum _{i}\left[L_{Y}(f(g(x^{(i)})),y^{(i)})+\lambda \sum _{j}L_{C}(g_{j}(x^{(i)}),c_{j}^{(i)})\right]$$where $L_{C}$ is the concept loss, $L_{Y}$ is the task loss, and $\lambda$ controls the tradeoff between concept prediction and task prediction.

Some CBMs use hard concepts, such as binary or discrete attributes, while others use soft concepts, such as predicted concept probabilities. Soft concept representations can improve predictive performance, but they may also make it harder to determine whether the concept layer contains only the intended semantic information.

A related issue is concept leakage, in which the concept predictor encodes additional information about the label into the concept representation. In this case, the label predictor may use information beyond the intended concept set, reducing the faithfulness of the bottleneck. Havasi, Parbhoo, and Doshi-Velez studied this problem and proposed architectural modifications, including side-channel and autoregressive approaches, to improve concept faithfulness while maintaining predictive performance.

Variants and extensions

Several variants of concept bottleneck models have been proposed to preserve interpretability while reducing the need for dense concept annotations or expensive retraining.

Post-hoc concept bottleneck models

Post-hoc concept bottleneck models (PCBMs) extend CBMs to already-trained neural networks. Rather than training a model from scratch with concept labels, a PCBM attaches a concept-based layer to a pretrained backbone. Its general pipeline is:$${\text{input}}\rightarrow {\text{backbone embedding}}\rightarrow {\text{concept subspace}}\rightarrow {\text{interpretable predictor}}\rightarrow {\text{prediction}}.$$A pretrained backbone first maps an input to an embedding, which is then projected onto a concept subspace. A sparse predictor then maps the resulting concept scores to the final label. This allows concept-based interpretation without retraining the full model from scratch.

In the PCBM formulation, a pretrained model $f:X\rightarrow \mathbb {R} ^{d}$ maps an input $x$ to an embedding $f(x)$. A concept bank contains concept vectors, which may be learned using Concept Activation Vectors or derived from multimodal models such as CLIP. The embedding is projected onto the concept subspace to produce concept scores, and an interpretable predictor maps those concept scores to the final label.

Yuksekgonul, Wang, and Zou also proposed PCBM-h, a hybrid version that adds a residual predictor using the original backbone embedding. This can improve accuracy when the concept bank is incomplete, but it makes the prediction less purely concept-based because part of the prediction comes from non-concept features. PCBMs also support concept-level editing, where users inspect concept weights and remove spurious associations between concepts and labels.

Label-free concept bottleneck models

Label-free concept bottleneck models (LF-CBMs) address another limitation of standard CBMs: the need for manually labeled concept data. LF-CBMs use foundation models to generate, filter, and learn concepts without requiring ground-truth concept labels for every training example.

The LF-CBM pipeline first generates an initial concept set using a language model. Concepts are then filtered to remove entries that are overly long, duplicated, too similar to class names, absent from the data, or poorly represented. The model learns a projection from backbone features into a concept bottleneck layer:$$f_{c}(x)=W_{c}f(x)$$where each dimension of $f_{c}(x)$ is intended to correspond to a human-readable concept.

To train this projection without concept labels, LF-CBM uses CLIP image and text encoders to form a concept activation matrix:$$P_{i,j}=E_{I}(x_{i})\cdot E_{T}(t_{j})$$where $E_{I}$ is the image encoder, $E_{T}$ is the text encoder, $x_{i}$ is an image, and $t_{j}$ is a concept text description. The projection is optimized so that each concept neuron's activation pattern matches the CLIP-based activation pattern for its target concept. After this layer is fixed, LF-CBM trains a sparse final linear layer using an elastic-net objective.

Interpretability in LF-CBMs comes from both the bottleneck and the sparse final layer. The bottleneck maps backbone features into concept activations, while the final layer indicates how those concepts influence each class. LF-CBMs also allow model editing by modifying concept weights directly when concept activations are correct but the final prediction is wrong.

Related query-based methods

Variational information pursuit (V-IP) is a related interpretable prediction framework. Instead of using a fixed concept bottleneck, V-IP makes predictions by sequentially asking human-understandable queries about an input. Queries may correspond to visual attributes, image patches, words in a document, or patient symptoms. The final prediction is based only on the observed query-answer history, making that history the explanation.

V-IP builds on information pursuit, where the next query is chosen to maximize information about the label. This can be written as:$$q_{k+1}=\arg \max _{q\in Q}I(q(X);Y\mid q_{1:k}(x))$$Rather than estimating this quantity using expensive generative models and sampling procedures, V-IP directly learns a querier and a classifier. The querier selects the next query, and the classifier predicts from the updated query-answer history. Later work has used large language and vision models to bootstrap V-IP for interpretable image classification.

Applications

Concept bottleneck models have been applied in domains where intermediate human-interpretable concepts can make model behavior easier to inspect. They were first studied mainly in supervised classification settings, especially image classification. In these tasks, the intermediate concepts often describe visible attributes of an object, such as parts, colors, or other human-labeled properties. The final class is then predicted from the concept representation rather than directly from the raw input. This makes image classification a natural application area, since predicted concepts can be inspected and, in some cases, corrected before the final prediction is made.

Several later methods focus on computer vision while reducing the amount of direct concept supervision required. Label-free concept bottleneck models use image and text representations to construct concept-based classifiers without requiring a fully labeled concept dataset. Similarly, vision-language-guided concept bottleneck models use vision-language models to help build concept bottlenecks, with the goal of preserving interpretability while reducing reliance on manually annotated concepts. Other work connects concept bottleneck methods with information pursuit, where the model selects informative concepts or queries for visual prediction. These approaches retain the basic idea of using human-understandable intermediate variables, but adapt it to settings where manually defining and labeling each concept is difficult.

Concept bottleneck models have also been extended to language models. Concept Bottleneck Large Language Models introduce a bottleneck structure into large language models so that predictions can be connected to intermediate concept-level information. In this setting, concepts are used not only as visual attributes, but also as a way to analyze or control model behavior in natural language tasks.

Another application is protein design. Concept bottleneck language models for protein design use intermediate concepts to represent meaningful properties related to proteins during generation. In this setting, the concept bottleneck is intended to support interpretation and intervention. Rather than reasoning only through output sequences, users may analyze or modify generated proteins through concept values.

Concept bottlenecks have also been used with generative models. Post-hoc concept bottlenecks for generative models add concept-based interpretation to pre-trained generative models without requiring the full model to be trained from scratch. This allows generated outputs to be analyzed and guided using human-understandable concepts. Spatially-aware concept bottleneck models further extend the visual use case by linking concepts with image regions, so that explanations can indicate not only which concepts are important, but also where they appear in the image.

Limitations

A fundamental limitation of standard CBMs is the cost and scalability of concept supervision. Training a fully supervised CBM requires examples of the form $(x,c,y)$, where each input is annotated with both the final label and the relevant intermediate concepts. In domains such as medical imaging, scientific data analysis, and natural language understanding, concept labels may require expert judgment and can be costly to collect at large scale. This restricts standard CBMs to settings where high-quality concept annotations already exist or can be produced reliably.

A related challenge is how to choose the concept set. The usefulness of a CBM depends on whether the predefined concepts are meaningful, non-redundant, and sufficiently predictive of the target. If important task-relevant information is missing from the concept set, the bottleneck may reduce accuracy or encourage the model to rely on unintended information. If the concept set contains ambiguous or overlapping concepts, the resulting explanations may be difficult for users to interpret. Post-hoc and label-free CBM variants reduce the need for manual annotation, but automatically generated concepts still require evaluation for semantic quality and reliability.

CBMs also involve an interpretability-accuracy tradeoff. A strict bottleneck can improve transparency because the label predictor is constrained to use only concept information, but it may discard predictive signals that are not captured by the chosen concepts. Jointly trained or soft-concept models can improve task performance, but they may weaken the faithfulness of the bottleneck if the concept layer carries information beyond the intended concept semantics.

Concept leakage is one example of this problem. Leakage occurs when concept predictions encode unintended information about the label, allowing the label predictor to exploit information that is not represented in the human-interpretable concept set. This can undermine interpretability and reduce the reliability of concept-level interventions.

Several research directions remain open. One is automated concept discovery: identifying useful bottleneck concepts without relying entirely on domain experts. Another is extending CBMs to less structured domains such as free-form text, video, protein design, and generative modeling, where concepts may be context-dependent or difficult to ground directly in the input. A further theoretical issue is the relationship between concept interventions and causal reasoning, since intervening on a model's concept score is not always equivalent to intervening on the corresponding real-world attribute.

Recent work has also explored hierarchical concept-based interpretable models, which aim to organize concepts at multiple levels of abstraction rather than using a flat concept set.

See also

• Explainable artificial intelligence
• Artificial neural network
• Machine learning