Interpretable and Steerable Concept Bottleneck Sparse Autoencoders¶

Conference: CVPR 2026
arXiv: 2512.10805
Code: GitHub
Area: Image Generation
Keywords: Sparse Autoencoders, Concept Bottleneck, Interpretability, Steerability, Mechanistic Interpretability

TL;DR¶

This work reveals that a majority of neurons (~81%) in Sparse Autoencoders (SAEs) suffer from insufficient interpretability or steerability. It proposes the CB-SAE framework—by pruning low-utility SAE neurons and integrating a concept bottleneck module, it improves interpretability by +32.1% and steerability by +14.5% in LVLM and image generation tasks, respectively.

Background & Motivation¶

Sparse Autoencoders (SAEs) have become a foundational tool for mechanistic interpretability, used to decompose dense polysemantic activations in LLMs/VLMs into sparse monosemantic latent variables. However, for practical applications, SAE features must simultaneously satisfy two conditions: being interpretable (humans can understand the meaning of each neuron) and steerable (intervening in neuron activations reliably changes model output).

Through empirical analysis, this paper identifies two key limitations of SAEs: 1. Most neurons are impractical: Among 65,536 SAE neurons, only 18.84% possess both high interpretability and high steerability; 36.26% are low in both. 2. Insufficient coverage of user-required concepts: Despite the large dictionary size, 27-45% of ImageNet-related concepts cannot be represented by the SAE.

While Concept Bottleneck Models (CBMs) provide explicit concept control, they fail to discover new features. The Core Idea of this paper is to unify the unsupervised discovery capabilities of SAEs with the steerability of CBMs into a single framework.

Method¶

Overall Architecture¶

CB-SAE aims to resolve the dilemma where SAE dictionaries are "large but impractical": while having tens of thousands of neurons, only a few are both human-understandable and steerable, and concepts of user interest are often missing. Instead of retraining a better SAE from scratch, it performs "subtraction and addition" on a pretrained standard SAE. It first scores neurons and prunes the useless ones, then attaches a lightweight "Concept Bottleneck Autoencoder" (CB-AE) module to the freed-up dimensional space to specifically supplement missing user-specified concepts. The pipeline consists of four steps: train a standard SAE → quantify interpretability and steerability for each neuron → prune low-utility neurons based on total scores → train a CB-AE in parallel with the frozen pruned SAE. The final reconstruction is the sum of two parts: the retained SAE latents for unsupervised discovery, and the CB-AE for supervised alignment of specified concepts.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Pretrained Standard SAE<br/>65,536 Neurons"] --> B["Dual-axis Metric<br/>Interpretability (CLIP-Dissect) + Steerability (Intervention Test)"]
    B --> C["Low-utility Neuron Pruning<br/>Row/Column removal by total score 65K→30K"]
    C --> D["Pruned SAE (Frozen)<br/>Unsupervised Features"]
    C -->|Free dimensions for parallel attachment| E["Concept Bottleneck AE (CB-AE)<br/>Supplements Missing Concepts"]
    E --> F["Encoder E_cb: Understanding<br/>L_int Concept Alignment"]
    E --> G["Decoder D_cb: Control<br/>L_st Cycle Reconstruction"]
    D --> H["Combined Reconstruction<br/>SAE Latents + CB Concepts"]
    F --> H
    G --> H
    H --> I["Task-agnostic Downstream Steerable Generation<br/>LLaVA Text / UnCLIP Image"]

Key Designs¶

1. Dual-axis Metric for Interpretability and Steerability: Quantifying "Understandability" and "Controllability" Separately

The paper first addresses whether an SAE neuron is useful by scoring interpretability and steerability separately. Interpretability follows CLIP-Dissect, matching each neuron to the most similar concept in a predefined set and using that similarity as a score. Steerability is measured via an intervention test: setting the target neuron activation to a high value \(\alpha=50\) while zeroing others, then checking if the downstream model (LLaVA or UnCLIP) output moves toward the concept assigned by CLIP-Dissect via cosine similarity in the embedding space. Decoupling the two axes reveals that a highly interpretable neuron might have weak causal effects, while a steerable neuron might represent abstract or entangled features.

2. Low-utility Neuron Pruning: Directly removing rows and columns to make space for the CB

With dual-axis scores, pruning is straightforward: the sum of interpretability and steerability scores is used to rank and remove the bottom \(M\) neurons (retaining 30K out of 65K). Implementation-wise, the corresponding rows and columns in the encoder and decoder matrices are deleted: \(E'_{sae} = E_{sae}[[\omega]\setminus\mathcal{P},:]\) and \(D'_{sae} = D_{sae}[:,[\omega]\setminus\mathcal{P}]\), where \(\mathcal{P}\) is the set of pruned indices. This creates space for the concept bottleneck to supplement only the subset of user-desired concepts that the existing SAE cannot represent: \(\mathcal{C} = \mathcal{C}_{user} \setminus \mathcal{C}_{rsae}\).

3. Concept Bottleneck Autoencoder: Encoder for "Understanding" and Decoder for "Control" via Cycle Reconstruction

A linear concept bottleneck is attached in parallel to the frozen pruned SAE. The encoder \(E_{cb} \in \mathbb{R}^{|\mathcal{C}| \times d}\) maps features to concepts, and the decoder \(D_{cb} \in \mathbb{R}^{d \times |\mathcal{C}|}\) maps them back. The final reconstruction is:

\[\hat{v}' = D'_{sae}z' + b + D_{cb}\sigma_{cb}(c)\]

where \(\sigma_{cb}\) applies top-k sparsification (\(k=5\)). Crucially, the encoder and decoder are optimized with different objectives. Three objectives are alternated: reconstruction loss \(\mathcal{L}_r\) updates both; interpretability loss \(\mathcal{L}_{int}\) updates only \(E_{cb}\) using CLIP zero-shot pseudo-labels; and steerability loss \(\mathcal{L}_{st}\) updates only \(D_{cb}\) via a cycle reconstruction—passing the reconstructed \(\hat{v}'\) back through \(E_{cb}\) to match the pseudo-labels. This cycle reconstruction ensures task-agnosticism.

Loss & Training¶

Three objectives are optimized using independent Adam optimizers to adaptively scale gradients without manual weighting:

\(\mathcal{L}_r = \|v - \hat{v}'\|_2^2\): Reconstruction fidelity, updates \(E_{cb}, D_{cb}\).
\(\mathcal{L}_{int}\): Cosine-cubed similarity loss, updates \(E_{cb}\) (Interpretability).
\(\mathcal{L}_{st}\): Cycle cosine-cubed similarity loss, updates \(D_{cb}\) (Steerability).

Key Experimental Results¶

Main Results — LLaVA/UnCLIP Steerable Generation¶

Downstream Model	Method	CLIP-Dissect↑	Monosemanticity↑	Unit Vector↑	White Image↑
LLaVA-1.5-7B	SAE	0.154	0.517	0.198	0.203
LLaVA-1.5-7B	CB-SAE	0.244	0.556	0.261	0.250
LLaVA-MORE	SAE	0.194	0.553	0.179	0.177
LLaVA-MORE	CB-SAE	0.291	0.598	0.192	0.189
UnCLIP	SAE	0.058	0.540	0.642	0.654
UnCLIP	CB-SAE	0.092	0.594	0.659	0.664

Average interpretability gain: +32.1%; steerability gain: +14.5%.

Ablation Study — Neuron Type Analysis¶

Neuron Type	CLIP-Dissect	Unit Vector	White Image
All SAE Neurons	0.154	0.198	0.203
Pruned SAE Neurons	0.084	0.144	0.162
Retained SAE Neurons	0.238	0.263	0.252
CB Neurons	0.323	0.231	0.219
All CB-SAE Neurons	0.244	0.261	0.250

Key Findings¶

Four-quadrant distribution of SAE neurons: High Interpretability + High Steerability accounts for only 18.84%, while Low Interpretability + Low Steerability accounts for 36.26%.
SAE concept coverage drops sharply as the concept set expands: from 96.3% on Broden to only 28.0% on a 20K English vocabulary.
CB neurons exhibit significantly higher interpretability than SAE neurons (0.323 vs 0.154), validating the necessity of concept supervision.
Steerability loss \(\mathcal{L}_{st}\) contributes a +2.9% gain in steerability without affecting interpretability.
30K retained neurons offer a reasonable balance, as keeping too few hurts reconstruction.

Highlights & Insights¶

Systematically reveals the trade-off between SAE interpretability and steerability and quantifies the concept coverage gap.
Unifying SAE (unsupervised discovery) and CBM (supervised alignment) is a natural and effective design.
Cycle reconstruction steerability loss is a clever task-agnostic design, allowing the same CB-SAE to control both text and image generation.
The concept selection strategy (adding only missing concepts) avoids redundancy.

Limitations & Future Work¶

Dependency on CLIP-Dissect for concept assignment, which might be inherently inaccurate.
Steerability of CB neurons is still lower than that of retained SAE neurons, requiring better or task-specific losses.
Only validated on CLIP vision encoders; applicability to others (e.g., DINOv2) needs exploration.
The relationship between the "feature splitting" phenomenon in SAEs and concept coverage gaps remains under-investigated.
Training depends on pseudo-labels from CLIP zero-shot classifiers, which limits accuracy.

vs Standard SAE: SAEs are purely unsupervised and offer no guarantee of finding specific concepts; CB-SAE solves this via pruning and enhancement.
vs CBM: CBMs are limited to predefined concepts; CB-SAE retains the ability to discover new features.
vs AlignSAE: A concurrent work. AlignSAE uses orthogonality loss to separate supervised/unsupervised concepts, whereas CB-SAE uses direct pruning. AlignSAE targets text LLMs, while CB-SAE focus on vision models.

Rating¶

Novelty: ⭐⭐⭐⭐ Unifying SAE and CBM is effective; the dual-axis analysis has independent value.
Experimental Thoroughness: ⭐⭐⭐⭐ Two downstream tasks and detailed ablations, though datasets are limited (mostly ImageNet).
Writing Quality: ⭐⭐⭐⭐ Clear problem analysis, logical progression, and intuitive visualizations.
Value: ⭐⭐⭐⭐ Significant push toward practical SAE applications, especially for scenarios requiring specific concept control.