Decomposing The Dark Matter of Sparse Autoencoders

Sparse autoencoders (SAEs) are a promising technique for decomposing language model activations into interpretable linear features. However, current SAEs fall short of completely explaining model performance, resulting in "dark matter": unexplained variance in activations. This work investigates dark matter as an object of study in its own right. Surprisingly, we find that much of SAE dark matter--about half of the error vector itself and >90% of its norm--can be linearly predicted from the initial activation vector. Additionally, we find that the scaling behavior of SAE error norms at a per token level is remarkably predictable: larger SAEs mostly struggle to reconstruct the same contexts as smaller SAEs. We build on the linear representation hypothesis to propose models of activations that might lead to these observations, including postulating a new type of "introduced error"; these insights imply that the part of the SAE error vector that cannot be linearly predicted ("nonlinear" error) might be fundamentally different from the linearly predictable component. To validate this hypothesis, we empirically analyze nonlinear SAE error and show that 1) it contains fewer not yet learned features, 2) SAEs trained on it are quantitatively worse, 3) it helps predict SAE per-token scaling behavior, and 4) it is responsible for a proportional amount of the downstream increase in cross entropy loss when SAE activations are inserted into the model. Finally, we examine two methods to reduce nonlinear SAE error at a fixed sparsity: inference time gradient pursuit, which leads to a very slight decrease in nonlinear error, and linear transformations from earlier layer SAE outputs, which leads to a larger reduction.

Efficient Dictionary Learning with Switch Sparse Autoencoders

Sparse autoencoders (SAEs) are a recent technique for decomposing neural network activations into human-interpretable features. However, in order for SAEs to identify all features represented in frontier models, it will be necessary to scale them up to very high width, posing a computational challenge. In this work, we introduce Switch Sparse Autoencoders, a novel SAE architecture aimed at reducing the compute cost of training SAEs. Inspired by sparse mixture of experts models, Switch SAEs route activation vectors between smaller "expert" SAEs, enabling SAEs to efficiently scale to many more features. We present experiments comparing Switch SAEs with other SAE architectures, and find that Switch SAEs deliver a substantial Pareto improvement in the reconstruction vs. sparsity frontier for a given fixed training compute budget. We also study the geometry of features across experts, analyze features duplicated across experts, and verify that Switch SAE features are as interpretable as features found by other SAE architectures.

Not All Language Model Features Are Linear

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

Approximate Nearest Neighbor Search with Window Filters

We define and investigate the problem of $\textit{c-approximate window search}$: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a $75\times$ speedup over existing solutions at the same level of recall.

PECANN: Parallel Efficient Clustering with Graph-Based Approximate Nearest Neighbor Search

This paper studies density-based clustering of point sets. These methods use dense regions of points to detect clusters of arbitrary shapes. In particular, we study variants of density peaks clustering, a popular type of algorithm that has been shown to work well in practice. Our goal is to cluster large high-dimensional datasets, which are prevalent in practice. Prior solutions are either sequential, and cannot scale to large data, or are specialized for low-dimensional data. This paper unifies the different variants of density peaks clustering into a single framework, PECANN, by abstracting out several key steps common to this class of algorithms. One such key step is to find nearest neighbors that satisfy a predicate function, and one of the main contributions of this paper is an efficient way to do this predicate search using graph-based approximate nearest neighbor search (ANNS). To provide ample parallelism, we propose a doubling search technique that enables points to find an approximate nearest neighbor satisfying the predicate in a small number of rounds. Our technique can be applied to many existing graph-based ANNS algorithms, which can all be plugged into PECANN. We implement five clustering algorithms with PECANN and evaluate them on synthetic and real-world datasets with up to 1.28 million points and up to 1024 dimensions on a 30-core machine with two-way hyper-threading. Compared to the state-of-the-art FASTDP algorithm for high-dimensional density peaks clustering, which is sequential, our best algorithm is 45x-734x faster while achieving competitive ARI scores. Compared to the state-of-the-art parallel DPC-based algorithm, which is optimized for low dimensions, we show that PECANN is two orders of magnitude faster. As far as we know, our work is the first to evaluate DPC variants on large high-dimensional real-world image and text embedding datasets.

BOLT: An Automated Deep Learning Framework for Training and Deploying Large-Scale Neural Networks on Commodity CPU Hardware

Efficient large-scale neural network training and inference on commodity CPU hardware is of immense practical significance in democratizing deep learning (DL) capabilities. Presently, the process of training massive models consisting of hundreds of millions to billions of parameters requires the extensive use of specialized hardware accelerators, such as GPUs, which are only accessible to a limited number of institutions with considerable financial resources. Moreover, there is often an alarming carbon footprint associated with training and deploying these models. In this paper, we address these challenges by introducing BOLT, a sparse deep learning library for training massive neural network models on standard CPU hardware. BOLT provides a flexible, high-level API for constructing models that will be familiar to users of existing popular DL frameworks. By automatically tuning specialized hyperparameters, BOLT also abstracts away the algorithmic details of sparse network training. We evaluate BOLT on a number of machine learning tasks drawn from recommendations, search, natural language processing, and personalization. We find that our proposed system achieves competitive performance with state-of-the-art techniques at a fraction of the cost and energy consumption and an order-of-magnitude faster inference time. BOLT has also been successfully deployed by multiple businesses to address critical problems, and we highlight one customer deployment case study in the field of e-commerce.