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Improving Sparse Decomposition of Language Model Activations with Gated Sparse Autoencoders

Senthooran Rajamanoharan, Arthur Conmy, Lewis Smith, Tom Lieberum, Vikrant Varma, Janos Kramar, Rohin Shah, Neel Nanda

Recent work has found that sparse autoencoders (SAEs) are an effective technique for unsupervised discovery of interpretable features in language models' (LMs) activations, by finding sparse, linear reconstructions of those activations. We introduce the Gated Sparse Autoencoder (Gated SAE), which achieves a Pareto improvement over training with prevailing methods. In SAEs, the L1 penalty used to encourage sparsity introduces many undesirable biases, such as shrinkage -- systematic underestimation of feature activations. The key insight of Gated SAEs is to separate the functionality of (a) determining which directions to use and (b) estimating the magnitudes of those directions: this enables us to apply the L1 penalty only to the former, limiting the scope of undesirable side effects. Through training SAEs on LMs of up to 7B parameters we find that, in typical hyper-parameter ranges, Gated SAEs solve shrinkage, are similarly interpretable, and require half as many firing features to achieve comparable reconstruction fidelity.

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An Analysis of Tokenization: Transformers under Markov Data

Nived Rajaraman, Jiantao Jiao, Kannan Ramchandran

While there has been a large body of research attempting to circumvent tokenization for language modeling (Clark et al. 2022, Xue et al. 2022), the current consensus is that it is a necessary initial step for designing state-of-the-art performant language models. In this paper, we investigate tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. When trained on data drawn from certain simple $k^{\text{th}}$-order Markov processes for $k > 1$, transformers exhibit a surprising phenomenon - in the absence of tokenization, they empirically are incredibly slow or fail to learn the right distribution and predict characters according to a unigram model (Makkuva et al. 2024). With the addition of tokenization, however, we empirically observe that transformers break through this barrier and are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. With this observation as starting point, we study the end-to-end cross-entropy loss achieved by transformers with and without tokenization. With the appropriate tokenization, we show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from $k^{\text{th}}$-order Markov sources near optimally. Our analysis provides a justification for the use of tokenization in practice through studying the behavior of transformers on Markovian data.

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Algorithmic Capabilities of Random Transformers

Ziqian Zhong, Jacob Andreas

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To what extent do they depend on the supervisory signal provided to models, and to what extent are they attributable to behavior already present in models at the beginning of training? To investigate these questions, we investigate what functions can be learned by randomly initialized transformers in which only the embedding layers are optimized, so that the only input--output mappings learnable from data are those already implemented (up to a choice of encoding scheme) by the randomly initialized model. We find that these random transformers can perform a wide range of meaningful algorithmic tasks, including modular arithmetic, in-weights and in-context associative recall, decimal addition, parenthesis balancing, and even some aspects of natural language text generation. Our results indicate that some algorithmic capabilities are present in transformers (and accessible via appropriately structured inputs) even before these models are trained.

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Refusal in Language Models Is Mediated by a Single Direction

Andy Arditi, Oscar Balcells Obeso, Aaquib Syed, Daniel Paleka, Nina Rimsky, Wes Gurnee, Neel Nanda

Conversational large language models are fine-tuned for both instruction-following and safety, resulting in models that obey benign requests but refuse harmful ones. While this refusal behavior is widespread across chat models, its underlying mechanisms remain poorly understood. In this work, we show that refusal is mediated by a one-dimensional subspace, across 13 popular open-source chat models up to 72B parameters in size. Specifically, for each model, we find a single direction such that erasing this direction from the model's residual stream activations prevents it from refusing harmful instructions, while adding this direction elicits refusal on even harmless instructions. Leveraging this insight, we propose a novel white-box jailbreak method that surgically disables a model's ability to refuse, with minimal effect on other capabilities. This interpretable rank-one weight edit results in an effective jailbreak technique that is simpler and more efficient than fine-tuning. Finally, we mechanistically analyze how adversarial suffixes suppress propagation of the refusal-mediating direction. Our findings underscore the brittleness of current safety fine-tuning methods. More broadly, our work showcases how an understanding of model internals can be leveraged to develop practical methods for controlling model behavior.

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Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Space

Core Francisco Park, Maya Okawa, Andrew Lee, Ekdeep Singh Lubana, Hidenori Tanaka

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model’s learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model’s learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

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Optimal ablation for interpretability

Maximilian Li, Lucas Janson

Interpretability studies often involve tracing the flow of information through machine learning models to identify specific model components that perform relevant computations for tasks of interest. Prior work quantifies the importance of a model component on a particular task by measuring the impact of performing ablation on that component, or simulating model inference with the component disabled. We propose a new method, optimal ablation (OA), and show that OA-based component importance has theoretical and empirical advantages over measuring importance via other ablation methods. We also show that OA-based component importance can benefit several downstream interpretability tasks, including circuit discovery, localization of factual recall, and latent prediction.

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Measuring Per-Unit Interpretability at Scale Without Humans

Roland S. Zimmermann, David Klindt, Wieland Brendel

In today’s era, whatever we can measure at scale, we can optimize. So far, measuring the interpretability of units in deep neural networks (DNNs) for computer vision still requires direct human evaluation and is not scalable. As a result, the inner workings of DNNs remain a mystery despite the remarkable progress we have seen in their applications. In this work, we introduce the first scalable method to measure the per-unit interpretability in vision DNNs. This method does not require any human evaluations, yet its prediction correlates well with existing human interpretability measurements. We validate its predictive power through an interventional human psychophysics study. We demonstrate the usefulness of this measure by performing previously infeasible experiments: (1) A large-scale interpretability analysis across more than 70 million units from 835 computer vision models, and (2) an extensive analysis of how units transform during training. We find an anticorrelation between a model's downstream classification performance and per-unit interpretability, which is also observable during model training. Furthermore, we see that a layer's location and width influence its interpretability.

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InversionView: A General-Purpose Method for Reading Information from Neural Activations

Xinting Huang, Madhur Panwar, Navin Goyal, Michael Hahn

The inner workings of neural networks can be better understood if we can fully decipher the information encoded in neural activations. In this paper, we argue that this information is embodied by the subset of inputs that give rise to similar activations. We propose InversionView, which allows us to practically inspect this subset by sampling from a trained decoder model conditioned on activations. This helps uncover the information content of activation vectors, and facilitates understanding of the algorithms implemented by transformer models. We present four case studies where we investigate models ranging from small transformers to GPT-2. In these studies, we show that InversionView can reveal clear information contained in activations, including basic information about tokens appearing in the context, as well as more complex information, such as the count of certain tokens, their relative positions, and abstract knowledge about the subject. We also provide causally verified circuits to confirm the decoded information.

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B-cosification: Transforming Deep Neural Networks to be Inherently Interpretable

Shreyash Arya, Sukrut Rao, Moritz Böhle, Bernt Schiele

B-cos Networks have been shown to be effective for obtaining highly human interpretable explanations of model decisions by architecturally enforcing stronger alignment between inputs and weight. B-cos variants of convolutional networks (CNNs) and vision transformers (ViTs), which primarily replace linear layers with B-cos transformations, perform competitively to their respective standard variants while also yielding explanations that are faithful by design. However, it has so far been necessary to train these models from scratch, which is increasingly infeasible in the era of large, pre-trained foundation models. In this work, inspired by the architectural similarities in standard DNNs and B-cos networks, we propose ‘B-cosification’, a novel approach to transform existing pre-trained models to become inherently interpretable. We perform a thorough study of design choices to perform this conversion, both for convolutional neural networks and vision transformers. We find that B-cosification can yield models that are on par with B-cos models trained from scratch in terms of interpretability, while often outperforming them in terms of classification performance at a fraction of the training cost. Subsequently, we apply B-cosification to a pretrained CLIP model, and show that, even with limited data and compute cost, we obtain a B-cosified version that is highly interpretable and competitive on zero shot performance across a variety of datasets. We release our code and pre-trained model weights at https://github.com/shrebox/B-cosification.

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Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models

Adam Karvonen, Benjamin Wright, Can Rager, Rico Angell, Jannik Brinkmann, Logan Riggs Smith, Claudio Mayrink Verdun, David Bau, Samuel Marks

What latent features are encoded in language model (LM) representations? Recent work on training sparse autoencoders (SAEs) to disentangle interpretable features in LM representations has shown significant promise. However, evaluating the quality of these SAEs is difficult because we lack a ground-truth collection of interpretable features which we expect good SAEs to identify. We thus propose to measure progress in interpretable dictionary learning by working in the setting of LMs trained on Chess and Othello transcripts. These settings carry natural collections of interpretable features—for example, “there is a knight on F3”—which we leverage into metrics for SAE quality. To guide progress in interpretable dictionary learning, we introduce a new SAE training technique, $p$-annealing, which demonstrates improved performance on our metric.

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InterpBench: Semi-Synthetic Transformers for Evaluating Mechanistic Interpretability Techniques

Rohan Gupta, Iván Arcuschin, Thomas Kwa, Adrià Garriga-Alonso

Mechanistic interpretability methods aim to identify the algorithm a neural network implements, but it is difficult to validate such methods when the true algorithm is unknown. This work presents InterpBench, a collection of semi-synthetic yet realistic transformers with known circuits for evaluating these techniques. We train simple neural networks using a stricter version of Interchange Intervention Training (IIT) which we call Strict IIT (SIIT). Like the original, SIIT trains neural networks by aligning their internal computation with a desired high-level causal model, but it also prevents non-circuit nodes from affecting the model's output. We evaluate SIIT on sparse transformers produced by the Tracr tool and find that SIIT models maintain Tracr's original circuit while being more realistic. SIIT can also train transformers with larger circuits, like Indirect Object Identification (IOI). Finally, we use our benchmark to evaluate existing circuit discovery techniques.

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CoSy: Evaluating Textual Explanations of Neurons

Laura Kopf, Philine Lou Bommer, Anna Hedström, Sebastian Lapuschkin, Marina MC Höhne, Kirill Bykov

A crucial aspect of understanding the complex nature of Deep Neural Networks (DNNs) is the ability to explain learned concepts within their latent representations. While methods exist to connect neurons to human-understandable textual descriptions, evaluating the quality of these explanations is challenging due to the lack of a unified quantitative approach. We introduce CoSy (Concept Synthesis), a novel, architecture-agnostic framework for evaluating textual explanations of latent neurons. Given textual explanations, our proposed framework uses a generative model conditioned on textual input to create data points representing the explanations. By comparing the neuron's response to these generated data points and control data points, we can estimate the quality of the explanation. We validate our framework through sanity checks and benchmark various neuron description methods for Computer Vision tasks, revealing significant differences in quality.

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Iteration Head: A Mechanistic Study of Chain-of-Thought

Vivien Cabannes, Charles Arnal, Wassim Bouaziz, Xingyu Alice Yang, Francois Charton, Julia Kempe

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities remains limited. This paper helps fill this gap by demonstrating how CoT reasoning emerges in transformers in a controlled and interpretable setting. In particular, we observe the appearance of a specialized attention mechanism dedicated to iterative reasoning, which we coined "iteration heads". We track both the emergence and the precise working of these iteration heads down to the attention level, and measure the transferability of the CoT skills to which they give rise between tasks.

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Talking Heads: Understanding Inter-Layer Communication in Transformer Language Models

Jack Merullo, Carsten Eickhoff, Ellie Pavlick

Although it is known that transformer language models (LMs) pass features from early layers to later layers, it is not well understood how this information is represented and routed by the model. We analyze a mechanism used in two LMs to selectively inhibit items in a context in one task, and find that it underlies a commonly used abstraction across many context-retrieval behaviors. Specifically, we find that models write into low-rank subspaces of the residual stream to represent features which are then read out by later layers, forming low-rank *communication channels* (Elhage et al., 2021) between layers. A particular 3D subspace in model activations in GPT-2 can be traversed to positionally index items in lists, and we show that this mechanism can explain an otherwise arbitrary-seeming sensitivity of the model to the order of items in the prompt. That is, the model has trouble copying the correct information from context when many items ``crowd" this limited space. By decomposing attention heads with the Singular Value Decomposition (SVD), we find that previously described interactions between heads separated by one or more layers can be predicted via analysis of their weight matrices alone. We show that it is possible to manipulate the internal model representations as well as edit model weights based on the mechanism we discover in order to significantly improve performance on our synthetic Laundry List task, which requires recall from a list, often improving task accuracy by over 20\%. Our analysis reveals a surprisingly intricate interpretable structure learned from language model pretraining, and helps us understand why sophisticated LMs sometimes fail in simple domains, facilitating future analysis of more complex behaviors.

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Partial observation can induce mechanistic mismatches in data-constrained models of neural dynamics

William Qian, Jacob A Zavatone-Veth, Benjamin Samuel Ruben, Cengiz Pehlevan

One of the central goals of neuroscience is to gain a mechanistic understanding of how the dynamics of neural circuits give rise to their observed function. A popular approach towards this end is to train recurrent neural networks (RNNs) to reproduce experimental recordings of neural activity. These trained RNNs are then treated as surrogate models of biological neural circuits, whose properties can be dissected via dynamical systems analysis. How reliable are the mechanistic insights derived from this procedure? While recent advances in population-level recording technologies have allowed simultaneous recording of up to tens of thousands of neurons, this represents only a tiny fraction of most cortical circuits. Here we show that observing only a subset of neurons in a circuit can create mechanistic mismatches between a simulated teacher network and a data-constrained student, even when the two networks have matching single-unit dynamics. In particular, we show that partial observation of models of low-dimensional cortical dynamics based on functionally feedforward or low-rank connectivity can lead to surrogate models with spurious attractor structure. In total, our results illustrate the challenges inherent in accurately uncovering neural mechanisms from single-trial data, and suggest the need for new methods of validating data-constrained models for neural dynamics.

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What Makes and Breaks Safety Fine-tuning? A Mechanistic Study

Samyak Jain, Ekdeep Singh Lubana, Kemal Oksuz, Tom Joy, Philip Torr, Amartya Sanyal, Puneet K. Dokania

Safety fine-tuning helps align Large Language Models (LLMs) with human preferences for their safe deployment. To better understand the underlying factors that make models safe via safety fine-tuning, we design a synthetic data generation framework that captures salient aspects of an unsafe input by modeling the interaction between the task the model is asked to perform (e.g., “design”) versus the specific concepts the task is asked to be performed upon (e.g., a “cycle” vs. a “bomb”). Using this, we investigate three well-known safety fine-tuning methods—supervised safety fine-tuning, direct preference optimization, and unlearning—and provide significant evidence demonstrating that these methods minimally transform MLP weights to specifically align unsafe inputs into its weights’ null space. This yields a clustering of inputs based on whether the model deems them safe or not. Correspondingly, when an adversarial input (e.g., a jailbreak) is provided, its activations are closer to safer samples, leading to the model processing such an input as if it were safe. Code is available at https://github.com/fiveai/understanding_safety_finetuning.

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Transcoders find interpretable LLM feature circuits

Jacob Dunefsky, Philippe Chlenski, Neel Nanda

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features—such as those found by sparse autoencoders (SAEs)—are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior. To address this we explore **transcoders**, which seek to faithfully approximate a densely activating MLP layer with a wider, sparsely-activating MLP layer. We introduce a novel method for using transcoders to perform weights-based circuit analysis through MLP sublayers. The resulting circuits neatly factorize into input-dependent and input-invariant terms. We then successfully train transcoders on language models with 120M, 410M, and 1.4B parameters, and find them to perform at least on par with SAEs in terms of sparsity, faithfulness, and human-interpretability. Finally, we apply transcoders to reverse-engineer unknown circuits in the model, and we obtain novel insights regarding the "greater-than circuit" in GPT2-small. Our results suggest that transcoders can prove effective in decomposing model computations involving MLPs into interpretable circuits. Code is available at https://github.com/jacobdunefsky/transcoder_circuits/

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Grokking of Implicit Reasoning in Transformers: A Mechanistic Journey to the Edge of Generalization

Boshi Wang, Xiang Yue, Yu Su, Huan Sun

We study whether transformers can learn to *implicitly* reason over parametric knowledge, a skill that even the most capable language models struggle with. Focusing on two representative reasoning types, composition and comparison, we consistently find that transformers *can* learn implicit reasoning, but only through *grokking*, i.e., extended training far beyond overfitting. The levels of generalization also vary across reasoning types: when faced with out-of-distribution examples, transformers fail to systematically generalize for composition but succeed for comparison. We delve into the model's internals throughout training, conducting analytical experiments that reveal: 1) the mechanism behind grokking, such as the formation of the generalizing circuit and its relation to the relative efficiency of generalizing and memorizing circuits, and 2) the connection between systematicity and the configuration of the generalizing circuit. Our findings guide data and training setup to better induce implicit reasoning and suggest potential improvements to the transformer architecture, such as encouraging cross-layer knowledge sharing. Furthermore, we demonstrate that for a challenging reasoning task with a large search space, GPT-4-Turbo and Gemini-1.5-Pro based on non-parametric memory fail badly regardless of prompting styles or retrieval augmentation, while a fully grokked transformer can achieve near-perfect accuracy, showcasing the power of parametric memory for complex reasoning.

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Linking In-context Learning in Transformers to Human Episodic Memory

Li Ji-An, Corey Yishan Zhou, Marcus K. Benna, Marcelo G Mattar

Understanding connections between artificial and biological intelligent systems can reveal fundamental principles of general intelligence. While many artificial intelligence models have a neuroscience counterpart, such connections are largely missing in Transformer models and the self-attention mechanism. Here, we examine the relationship between interacting attention heads and human episodic memory. We focus on induction heads, which contribute to in-context learning in Transformer-based large language models (LLMs). We demonstrate that induction heads are behaviorally, functionally, and mechanistically similar to the contextual maintenance and retrieval (CMR) model of human episodic memory. Our analyses of LLMs pre-trained on extensive text data show that CMR-like heads often emerge in the intermediate and late layers, qualitatively mirroring human memory biases. The ablation of CMR-like heads suggests their causal role in in-context learning. Our findings uncover a parallel between the computational mechanisms of LLMs and human memory, offering valuable insights into both research fields.

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Evidence of Learned Look-Ahead in a Chess-Playing Neural Network

Erik Jenner, Shreyas Kapur, Vasil Georgiev, Cameron Allen, Scott Emmons, Stuart Russell

Do neural networks learn to implement algorithms such as look-ahead or search "in the wild"? Or do they rely purely on collections of simple heuristics? We present evidence of *learned look-ahead* in the policy and value network of Leela Chess Zero, the currently strongest deep neural chess engine. We find that Leela internally represents future optimal moves and that these representations are crucial for its final output in certain board states. Concretely, we exploit the fact that Leela is a transformer that treats every chessboard square like a token in language models, and give three lines of evidence: (1) activations on certain squares of future moves are unusually important causally; (2) we find attention heads that move important information "forward and backward in time," e.g., from squares of future moves to squares of earlier ones; and (3) we train a simple probe that can predict the optimal move 2 turns ahead with 92% accuracy (in board states where Leela finds a single best line). These findings are clear evidence of learned look-ahead in neural networks and might be a step towards a better understanding of their capabilities.

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