# Mapping the Hidden Geometry of Sparse Autoencoders: A Graph-Based Approach > Coverage of lessw-blog **Published:** March 27, 2026 **Author:** PSEEDR Editorial **Category:** platforms **Tags:** AI Interpretability, Sparse Autoencoders, Machine Learning, Large Language Models, Feature Geometry **Canonical URL:** https://pseedr.com/platforms/mapping-the-hidden-geometry-of-sparse-autoencoders-a-graph-based-approach --- A recent post from lessw-blog introduces a novel methodology for constructing sparse conditional dependence graphs from Sparse Autoencoder (SAE) features, offering a rigorous new lens for AI interpretability. In a recent post, lessw-blog discusses preliminary results on building graphs from Sparse Autoencoder (SAE) features. As the artificial intelligence community pushes for greater transparency in foundation models, understanding the internal representations of these complex systems has become a paramount challenge. Sparse Autoencoders (SAEs) are increasingly utilized to disentangle the dense, opaque activations of Large Language Models (LLMs) into interpretable, sparse features. However, mapping the relationships between these extracted features remains notoriously difficult. Historically, researchers have relied on simple activation correlations or cosine similarity to understand SAE feature geometry. While useful, these baseline metrics often fail to capture the true conditional dependence between features. This leaves phenomena like feature splitting, absorption, and duplication-where redundant features represent overlapping concepts-poorly understood. Furthermore, navigating the superposition hypothesis, which posits that neural networks represent more features than they have dimensions by packing them into nearly orthogonal spaces, requires far more sophisticated geometric modeling than simple pairwise comparisons can provide. lessw-blog's analysis addresses this critical gap by introducing Nodewise LASSO to the interpretability toolkit. This statistical technique is used to build approximate sparse conditional dependence graphs over SAE features. Nodewise LASSO operates by performing L1-regularized regression for each feature against all others, effectively isolating direct dependencies while zeroing out indirect correlations. By utilizing resampling and null controls, the author ensures that the resulting graphs reflect genuine structural relationships rather than statistical noise. The initial experiments yield highly promising results. The methodology successfully identifies small, stable, standalone modules within the feature graphs. Crucially, these modules frequently align with coherent linguistic features and exhibit only a weak correlation with traditional cosine similarity metrics. This divergence indicates that conditional dependence captures a distinct, highly relevant structural layer of SAEs that prior models entirely missed. For practitioners working on foundation models, this means a better toolkit for diagnosing model behavior, auditing for biases, and mapping the intricate circuits that drive specific outputs. Presented as a proof-of-concept with ongoing methodological refinement, this research marks a significant step forward for circuits-type approaches in AI interpretability. By mapping the true dependency structure and redundancy within SAE features, this methodology paves the way for more robust, transparent, and aligned AI systems. [Read the full post](https://www.lesswrong.com/posts/vrHwxuoizHcrRQzed/preliminary-results-on-building-graphs-from-saes) ### Key Takeaways * Nodewise LASSO is utilized to construct approximate sparse conditional dependence graphs for SAE features, isolating direct relationships. * The methodology successfully identifies small, stable modules within the graphs that align with coherent linguistic concepts. * These newly mapped conditional dependencies show weak correlation with traditional cosine similarity, revealing previously hidden structural insights. * The approach addresses critical gaps in understanding feature redundancy, such as feature splitting, absorption, and duplication. * This proof-of-concept advances LLM interpretability, offering a more rigorous framework for analyzing the superposition hypothesis and internal model circuits. [Read the original post at lessw-blog](https://www.lesswrong.com/posts/vrHwxuoizHcrRQzed/preliminary-results-on-building-graphs-from-saes) --- ## Sources - https://www.lesswrong.com/posts/vrHwxuoizHcrRQzed/preliminary-results-on-building-graphs-from-saes