Mechanistic Topic Models (MTMs)

• Mechanistic Topic Models are a family of models that extract semantically rich and abstract features from LLM activations using sparse autoencoders, surpassing traditional bag-of-words methods.
• They utilize nearly orthogonal activation directions to build interpretable, feature-based topic representations that capture complex concepts like style and tone.
• MTMs enable controllable text generation by employing steering vectors to bias LLM outputs, offering nuanced intervention in generated content.

Mechanistic Topic Models (MTMs) are a modern family of topic models that move beyond traditional bag-of-words frameworks, instead defining topics over structured, interpretable features—often derived using sparse autoencoders and closely linked to the internal representations of LLMs. MTMs explicitly target the extraction of semantically abstract concepts, enabling both deeper interpretability and a novel form of controllable text generation through steering vectors in model activation space. This approach offers distinct methodological advantages and broadens the functional repertoire of topic modeling in natural language processing.

1. Concept and Motivation

MTMs differ from classical topic models, such as Latent Dirichlet Allocation (LDA), by abandoning the word-count representation in favor of more semantically expressive features. Instead of modeling documents as distributions over word lists, MTMs operate on high-level features learned from the distributed representations inside LLMs. These features are often represented as nearly orthogonal directions in activation space, learned via sparse autoencoders (SAEs). Each topic in an MTM comprises a weighted combination of these features, resulting in not just richer topic abstractions but also enhanced interpretability, as the features themselves are equipped with automatic textual descriptions.

This construction facilitates the modeling of complex, non-surface phenomena including style, tone, and abstract semantics—domains where bag-of-words approaches are known to struggle (Zheng et al., 31 Jul 2025). The approach is motivated by the empirical finding that LLMs encode key concepts and stylistic attributes as activation directions, suggesting that topics can be extracted and manipulated at this functional level.

2. Sparse Autoencoder-Based Feature Space

MTMs rely on SAEs to extract a structured representation of activation space. The SAE trains to reconstruct the hidden activations of a pretrained LLM subject to a sparsity constraint, resulting in feature vectors $w_1, w_2, ..., w_W$ and corresponding sparse activation coefficients $\alpha_1, ..., \alpha_W$ for any input:

$a = \sum_{i=1}^{W} \alpha_i w_i + b$

where $a$ is the original activation, $b$ is a bias, and only a small subset of the $\alpha_i$ are nonzero for a given input due to the $\ell_0$ sparsity penalty enforced in the reconstruction loss:

$$\mathcal{L}(a) = \frac{1}{2}\|\hat{a}(a) - a\|_2^2 + \lambda \|\bullet(a)\|_0$$

Each SAE feature direction often corresponds to an interpretable semantic or stylistic unit—"feature descriptions" are generated automatically using text associated with strong activations along that direction. Document representations in MTMs are defined as count vectors of these activated features, analogous to (but far richer than) word count vectors in classical models.

3. Topic Construction and Representation

Several adaptation strategies for traditional topic models are introduced for use over feature-count representations:

• mLDA: Adapts the Latent Dirichlet Allocation framework to work on SAE feature counts rather than raw word counts.
• mETM: An "Embedded Topic Model" variant with topics as vectors in activation space, distributed over SAE features.
• mBERTopic: Utilizes UMAP for dimensionality reduction and HDBSCAN for clustering to construct document-topic embeddings in feature space.

Topics in MTMs are represented by feature distributions (not word lists). For each topic $k$, the model identifies a sparse vector of feature weights $\beta_{k,i}$. The highest-weight features and their associated descriptions define the topic.

This mechanism is capable of capturing topics that align with abstract, contextual, or stylistic dimensions—not merely surface-word correlations.

4. Controllable Generation via Mechanistic Steering

MTMs introduce controllable generation by leveraging the functional connection between topics and LLM activation space. For a given topic $k$, a steering vector $s_k$ is constructed as:

$$s_k = \frac{\sum_i \beta_{k,i} w_i}{\|\sum_i \beta_{k,i} w_i\|_2}$$

Text generation is then controlled by decomposing the (centered) LLM activation $a$ into components parallel and perpendicular to $s_k$, scaling the parallel component by a strength parameter $\lambda$, and reassembling:

$a_{\text{steered}} = a_{\perp} + \lambda s_k + b$

This allows topic-level intervention in LLM output: the generated text is biased along the semantic direction characterizing topic $k$, facilitating nuanced control not available in word-based approaches.

5. Evaluation with LLM-based Topic Judge and Baseline Comparisons

Recognizing that conventional topic coherence metrics do not fully capture the value of feature-based topic models, the MTM framework employs a LLM "topic judge" for head-to-head evaluation (Zheng et al., 31 Jul 2025). For each test document, the top topics (via their feature-based descriptions) produced by competing models are compared by an LLM acting as a judge, scoring not just subject matter but also style and affect.

Performance across five datasets—including benchmark corpora (20NG, Bills, Wiki) and datasets with abstract content or short texts (GoEmotions, PoemSum)—shows that MTMs either match or exceed standard and neural baselines for coherence and diversity. Notably, the feature-based approach is consistently preferred by the LLM topic judge in datasets with abstract or stylistic content.

Standard metrics (feature intruder tests and diversity) confirm that MTMs capture both commonalities and novel, previously unmodeled themes, particularly stylistic and affective phenomena.

6. Applications and Broader Implications

The major advantages of MTMs (Zheng et al., 31 Jul 2025) include:

• Semantic abstraction: Topics capture complex concepts exceeding surface-cooccurrence, including subtle stylistic and affective distinctions.
• Interpretability: Feature descriptions and the explicit mapping from features to topics facilitate direct human understanding and model introspection.
• Controllability: Mechanistic interventions via steering vectors provide unparalleled control over LLM generation, a unique capability among topic models.
• Generalization: Feature-based topics demonstrate superior generality in short and abstract text domains, often where classical models underperform.

A plausible implication is that interpretability tools (such as SAEs) are now transitioning from passive explanation to foundational roles in the construction of new model classes—here, as the substrate for generative and analytical tasks, including controlled text generation.

7. Outlook and Future Directions

Mechanistic Topic Models mark a convergence of interpretability and generative modeling. While current models leverage SAE-extracted features from LLMs, future research may refine the extraction of activation directions, integrate cross-modal features, and develop more efficient mechanisms for automatic textual description of high-dimensional features. The topic judge framework also opens new perspectives for LLM-augmented evaluation of abstract topic models, complementing traditional statistical measures.

Open questions include the representation of topics in multimodal contexts, the role of steerability in downstream tasks, and systematic comparison with recent advances in semantic and graph-based topic models. The capacity of MTMs to model "non-word-like" semantics is a notable departure from the constraints of co-occurrence statistics, establishing a new axis of exploration in unsupervised language understanding.