💻 computer science

Naming the Concepts Classifiers Rely On: Language-Anchored Decomposition for Faithful Explanation

This paper introduces Language-Anchored Decomposition (LAD), a post-hoc framework that generates faithful, spatially precise, and human-interpretable explanations for deep neural networks by inverting non-negative matrix factorization to learn a concept basis constrained by language-grounded region maps, thereby achieving named and decision-relevant interpretations without modifying the original model.

Original authors: Ahsan Habib Akash, Dipkamal Bhusal, Stacey Jones, Donald A. Adjeroh, Binod Bhattarai, Prashnna Kumar Gyawali

Published 2026-07-09

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CC BY 4.0

Original authors: Ahsan Habib Akash, Dipkamal Bhusal, Stacey Jones, Donald A. Adjeroh, Binod Bhattarai, Prashnna Kumar Gyawali

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a super-smart AI that looks at photos and tells you what's in them. It's great at its job, but it's like a black box: you see the photo go in and the answer come out, but you have no idea why it made that choice.

Current methods to peek inside this black box have a problem. Some can tell you what the AI looked at (like "it saw a dog's ear"), but they can't tell you what that thing is called. Others can give you a name (like "Pointy Ears"), but they only do that by rebuilding the AI from scratch, which changes how the original AI works.

This paper introduces a new method called LAD (Language-Anchored Decomposition). Think of it as a "translator" that lets you peek inside the original, unmodified AI and get a clear, named explanation of its thinking.

Here is how it works, using a few simple analogies:

1. The Problem: The "Mystery Ingredient" Soup

Imagine the AI is a chef who makes a perfect soup (the prediction).

Old methods are like tasting the soup and saying, "It tastes like Ingredient #4." But you don't know if Ingredient #4 is "salt," "pepper," or "mystery spice." You have to guess the name after the fact, and it might be different every time you taste it.
Other methods are like asking the chef to write a recipe before cooking. But to do that, you have to hire a new chef and train them from scratch. The new chef might make a slightly different soup than the original one you wanted to understand.

2. The LAD Solution: The "Anchored" Recipe

LAD is different. It looks at the original chef's cooking process without changing a thing.

Step 1: The Menu (The Language Anchor)
First, LAD asks a smart language model (like a very knowledgeable food critic) to guess a list of possible ingredients for a specific dish. If the dish is "Cat," the critic suggests: "Pointy Ears," "Whiskers," "Green Eyes." These are the names we want to use.

Step 2: The Map (The CLIP Connection)
Next, LAD uses a tool called CLIP to look at the photo and find where those specific things are. It draws a map showing exactly where the "Pointy Ears" are in the picture.

Step 3: The Magic Trick (Inverting the Math)
Here is the clever part. Usually, when scientists try to break down an image, they try to guess both the ingredients and the recipe at the same time.
LAD does the opposite. It locks the names in place (the "Language Anchor"). It says, "We know the ingredients are 'Pointy Ears' and 'Whiskers.' Now, tell us: how much of each did the chef actually use to make this soup?"

It forces the math to find a recipe that fits the original AI's thinking, but only using the pre-chosen names.

3. Why the "Anchor" Matters

The paper proves that this "anchor" isn't just a fancy label stuck on later; it's essential.

Without the anchor: If you let the AI guess the names itself, it might find a pattern that helps it get the answer right, but the pattern might be something weird and unexplainable (like "a specific shade of blue in the corner"). The explanation would be accurate to the math, but useless to a human.
With the anchor: By forcing the AI to explain itself using human words, the method filters out the weird patterns. It only keeps the concepts that actually matter for the decision and have a name.

4. The Results: Clear, Named Explanations

The paper tested this on photos of animals, scenes, and even medical images (like eye scans).

For a picture of a guitar: Instead of saying "Factor 1 is important," LAD says, "The model is looking at the Maple Neck and the Tuning Pegs."
For a medical eye scan: Instead of a blurry red spot, it says, "The model sees Drusen-like structures near the optic disc."

The Bottom Line

LAD is a tool that lets you ask an AI, "Why did you think this was a cat?" and get an answer like, "Because I saw pointy ears and whiskers," without ever having to retrain the AI or change how it thinks. It makes the AI's "thought process" transparent, named, and trustworthy, all while keeping the original model exactly as it was.

Technical Summary: Language-Anchored Decomposition (LAD)

1. Problem Statement

Deep neural networks deployed in high-stakes visual applications require interpretability, yet existing explanation methods face a fundamental trade-off between faithfulness (alignment with the model's actual decision process) and naming (human-readable semantic labels).

Post-hoc concept discovery methods (e.g., TCAV, ACE, CRAFT, FACE) are faithful to the model's behavior but produce unnamed factors. The same factor index may correspond to different visual elements across images, requiring post-hoc labeling that lacks consistency.
Naming and by-design methods (e.g., Concept Bottleneck Models, neuron-naming approaches like LaViSE) provide human-readable names but often require retraining the model or altering its architecture. Consequently, the explained model is no longer the deployed one, or the named units are not verified as causally responsible for predictions.

No prior method successfully delivers concepts that are simultaneously named, faithful to the frozen classifier, and obtained without modifying the model.

2. Methodology: Language-Anchored Decomposition (LAD)

LAD addresses this gap by inverting the standard Non-Negative Matrix Factorization (NMF) process. Instead of learning latent coefficients and labeling them later, LAD fixes the coefficients to language-grounded maps and learns only the concept basis.

Core Framework:

Setup: Given a frozen pretrained encoder $f$ and classifier head $g$ , LAD operates on the spatial feature maps $Z$ produced by the encoder. Unlike methods that pool features globally, LAD unfolds activations to preserve spatial locality, treating each spatial location as an independent observation.
Language-Anchored Coefficients ( $S$ ):
- For a target class, a Large Language Model (LLM) generates a class-specific vocabulary of visually grounded concepts (e.g., "pointy ears," "green eyes").
- CLIP image-text similarity is used to localize these concepts across image regions, creating spatial similarity maps.
- These maps are flattened and stacked to form a fixed coefficient matrix $S \in \mathbb{R}^{(nhw) \times r}$ , where rows represent spatial locations and columns represent named concepts.
Inverted Factorization:
- Standard NMF learns both coefficients ( $U$ ) and basis ( $W$ ) such that $A \approx UW^\top$ .
- LAD fixes the coefficients to the language-grounded matrix $S$ and learns only the concept basis $W$ to reconstruct the encoder's activations: $\hat{\bar{A}} \approx SW^\top$ .
- The optimization minimizes the reconstruction error $\|\bar{A} - SW^\top\|_F^2$ under non-negativity constraints using Projected Gradient Descent (PGD).
Inference: For new images, the basis $W$ is fixed, and non-negative coefficients $\hat{S}$ are estimated via non-negative least squares. These coefficients are reshaped into spatial heatmaps, providing localized, named explanations.

Key Mechanism: The language anchor acts as a structural constraint. The frozen encoder's feature geometry determines which named concepts are retained (by assigning them non-zero basis weights), while concepts inconsistent with the encoder's evidence are suppressed.

3. Key Contributions

A Novel Post-hoc Framework: LAD is the first framework to produce concepts that are named, faithful, and obtained without retraining the model. It achieves this by fixing language-grounded CLIP similarity maps as the coefficient matrix in an NMF-like decomposition.
Functional Language Anchor: The paper demonstrates that the language anchor is not merely cosmetic. Removing the anchor (reverting to standard unsupervised NMF) preserves classification accuracy but causes a sharp collapse in attribution faithfulness (specifically in concept deletion tests). This proves that the anchor steers the discovery toward classifier-meaningful structures.
Per-Image Named Concept Rollouts: Unlike baselines that output anonymous factors, LAD enables per-image rollouts where the specific named concepts used for a prediction are localized, ranked by importance, and annotated with their contribution to the reconstruction.
Comprehensive Evaluation: The method is evaluated across natural images (ImageNet), scenes (Places365), and a clinical domain (retinal fundus images), demonstrating robustness across diverse visual tasks.

4. Results

Faithfulness: Across ImageNet and Places365, LAD preserves top-1 accuracy (comparable to baselines) while achieving the highest Concept Insertion (C-Ins) scores, indicating its named concepts are sufficient to restore predictions.
Deletion Performance: While the FACE method (which jointly optimizes coefficients and basis) slightly outperforms LAD in Concept Deletion (C-Del) on natural images, LAD significantly outperforms all baselines in the clinical domain (retinal fundus). In clinical settings, where disease signatures are spatially focal, LAD's named concepts are the most causally decisive, leading to a C-Del score of 0.954 compared to 0.863 for FACE.
Ablation Studies:
- Language Anchor: Replacing fixed language coefficients with learned ones drops C-Del from 0.902 to 0.507, confirming the anchor's role in discovering faithful directions.
- Concept Budget: Increasing the number of concepts ( $r$ ) improves faithfulness monotonically without sacrificing accuracy.
Efficiency: LAD is computationally efficient, fitting a class in 0.03 seconds on an RTX A4500, significantly faster than FACE (2.6s) and CRAFT (0.5s).

5. Significance and Claims

The paper claims that LAD successfully bridges the gap between faithful attribution and human interpretability without compromising the integrity of the deployed model.

Structural vs. Cosmetic Naming: The authors emphasize that naming in LAD is a structural property of the factorization, not a post-hoc label. The model's own feature geometry determines which concepts are relevant, mitigating known biases in CLIP-style models by suppressing concepts inconsistent with the encoder's evidence.
Auditable Evidence: In high-stakes domains like medical imaging, LAD provides an "auditable record" where a reader can inspect not only where the model looks but what it attributes to that region (e.g., "drusen-like structures"). This allows for the detection of disagreements between the model's visual evidence and its semantic attribution.
Generalizability: The approach is shown to be effective across natural images, scene understanding, and clinical diagnostics, suggesting that fixing language-grounded coefficients is a viable strategy for creating transparent vision models where the content of a decision is as critical as its accuracy.