Efficient Automated Circuit Discovery in Transformers using Contextual Decomposition

Thanks for the helpful comments and thoughtful feedback (and large time commitment). We sincerely appreciate your critique and address your concerns below. > I am unsure of the significance of the work due to the iterative nature of the process and the need for data to adequately stimulate different 'tasks' (or behavior modes, perhaps?) and therefore discover circuits in the model. This is to my eyes not clearly explained. Thank you for pointing this out! Regarding the need of data, this is really an indispensable part in circuit discovery in general for mechanistic interpretability. The definition of circuit discovery is to find a circuit that a model uses to perform a specific task, and a task has to be defined by a specified dataset and a corresponding task metric. In other words, circuit discovery itself cannot be meaningful without data. Regarding the concern about the iterative nature of CD-T, to our knowledge, if one wants to form a circuit through exact calculation (i.e. to avoid inducing estimation errors or manually crafting samples to train a model), all existing state-of-the-art methods available are iteration-based [4,5]. Among all existing iteration-based methods, CD-T is shown in the paper that is able to scale the best in an LLM (GPT2-small) by achieving the lowest runtime and the best performance. > Prior work is noted to have conducted circuit discovery on large language models, and I can't easily find the models used for circuit discovery here. That lack of clarity is concerning, especially when using the manually discovered circuits as a target and prior art as baselines. Sorry for the confusion! This information was actually included in Appendix A in our submission. We test our algorithm on GPT-2-small for the IOI and Greater-than tasks, and on a 4-layer attention-only transformer for the Docstring task. These choices of models are the same as what were used in their original papers [1-3] to be comparable. Section 3.3.1 (line 285-286) has also been adjusted to clarify. > I am also uncertain of scalability of this approach, considering that the network architectures under evaluation are not clear and that it has been restricted to attention heads rather than MLP layers. I am also uncertain of the effects of sequence length, autoregressive or non-autoregressive decoders. Section 5 does not make these things clear. Please see our response above regarding the model architectures. CD-T itself is a general method that can be used to calculate the effect of arbitrary constituent of the activations of an arbitrary node on the activations of another node (line 258-260). Hence the user can easily decide any compositions of nodes (e.g, any combinations of attention heads, MLPs, or even the layer norm modules) to look at using this tool. In the experiments, we chose to focus on examining circuits purely of attention heads to be comparable with prior work [1-3], because a lot of them didn’t include MLPs and only focused on explaining attention heads in the found circuits. We have modified line 293-294 in section 3.3.2 to clarify. We didn’t observe any impact on the resulting circuits due to a difference in the sequence length. A discussion on the difference between the two types of models is included in a separate response below. > I would suggest clearly presenting model architectures under evaluation and assumptions being made on input data for the approach - the mechanistic relevance metrics are ultimately calculated from the outputs derived from input data. Thank you for the suggestion! Please see our response above regarding the model architectures. To our knowledge, all existing circuit discovery methods, including our CD-T, don’t make any assumptions on the input data. In the circuit discovery setting, we only require users to specify a dataset that they are interested in interpreting a model’s behavior for, and a corresponding task metric to measure the performance. Section 3.3.1 (line 277-279) has been adjusted to make this fact clearer.

> How would this scale to large training datasets in LLMs? Is there a minimum dataset required? Can the authors comment on this? This is a great question! In all the three dataset we evaluated [1-3], the authors define a narrow task, and then construct a dataset where the correct behavior is clearly known to elicit the circuit needed to “perform the task”. As such, our method naturally can be performed on a single inference datapoint, but to answer the question of “what circuit performs the task in general”, it is better to perform it on the mean activations over 10-100 example points to reduce variance in the result. Details on how to handle sequence position information to align different examples are found in [1]. In our experiments, to be comparable, we used the same example counts as prior work [1-3] to obtain the circuits, with the exact numbers included in Appendix A. Typically we, alongside most prior work [1-3], find 10-100 datapoints is a sufficient range to obtain stable circuit discovery results in LLMs. More datapoints don’t necessarily yield better performance. Section 3.3.1 (line 282-285) has also been adjusted to make this clearer. > What is the effect of autoregressive models and sequence to sequence decoding on this approach? Is there a difference? I don't see a clear analysis in Section 5, and while that is not necessary it would be nice to have the authors comment on this in Section 6. Thank you for the suggestion! The difference in CD-T implementation for the two types of models is in enforcing different causal masks as mentioned in line 252. Although our CD-T code is designed and implemented to be run on both types of models, in the experiments shown in the paper, we only focused on generative models (GPT2-small and a 4-layer attention-only transformer) so we have prior work as a reference standard when quantifying our results. We couldn't find any prior work performing circuit discovery on encoder-based models, nor any work comparing the circuits distilled from the two kinds of models given the same task. With the flexibility of CD-T, this might be an interesting future direction to explore. Reference: [1] Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small. Wang et al. 2023. [2] How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model. Hanna et al. 2023. [3] A circuit for Python docstrings in a 4-layer attention-only transformer. Haimersheim & Janiak. 2023. [4] Towards automated circuit discovery for mechanistic interpretability. Conmy et al. 2023. [5] Attribution patching outperforms automated circuit discovery. Syed et al. 2023.

Thanks for the helpful comments and thoughtful feedback (and large time commitment). We sincerely appreciate your critique and address your concerns below. > The description of the algorithm can be improved. In particular, the algorithm description is relatively informal and could benefit from more details and formalism. For “Prune nodes from S for which doing so increases the task metric”, how is increasing the task metric evaluated? In addition, what’s the computational complexity of the algorithm in terms of the input parameter? Thank you for the suggestion! We’ve revised Algorithm1 to make it more precise, which also includes details on how exactly we pruned the nodes. Text in section 3.3.1 has been also adjusted to include more details to support the algorithm. In short, if removing a node in a circuit results in an improvement (usually means a “greater” score in the maximization setting, which is true in all the 3 tasks we evaluated) in the score measured using the task metric compared to the original circuit before the removal, we deem this head to be unnecessary and remove it. The computational complexity of the algorithm scales linearly in the number of examples. We’ve also added in a detailed discussion on heuristics used and a complete complexity analysis in Appendix B. > How does pruning affect the mechanistic interpretability of the model? In our paper, pruning refers to removing nodes from a candidate circuit, and not to the model as a whole. In general, our method only finds circuits and does not attempt to perform the interpretation of the circuits, which is still a task left to the user. Some of the papers we use as our baselines have performed much of this interpretation analysis [1-3] to characterize functionality of attention head groups in a circuit. After finding a circuit with high performance, the user can then use the existing techniques to find an interpretation of the resulting circuit as well as to interpret the contribution of the pruned node. There is no reason in principle that the resulting pruned circuit cannot be interpreted in the usual way. Reference: [1] Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small. Wang et al. 2023. [2] How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model. Hanna et al. 2023. [3] A circuit for Python docstrings in a 4-layer attention-only transformer. Haimersheim & Janiak. 2023.

Thanks for the helpful comments and thoughtful feedback (and large time commitment). We sincerely appreciate your critique and address your concerns below. > Manual circuits are not fully explained (definition, how they are computed, cost of computation, etc.) - manual circuits are used as reference during evaluation (line 405), and it is necessary to provide these details regarding them. Sorry for the confusion! Details of the evaluated manual circuits were actually included in Appendix A. During this revision, we have additionally put in sentences in the main text to explain the manual circuits (line 58-59, line 119-121). To answer your question in full, the “manual” circuits we evaluated precede the existence of any “automated” circuit discovery algorithm, and the term “manual circuits” reflects that a substantial amount of direct human effort went into isolating the circuits that the papers [1-3] produce. All of our “manual circuits” baselines are found by either manually examining the attention patterns of different attention heads or conducting ad-hoc task-specific analyses to decide the connectivity of a circuit. As such, there is no clear notion of runtime. Unlike the focus of our paper, optimizing for a more efficient algorithm to obtain a circuit, those papers tried to answer different questions, through manual efforts, 1. Whether it is possible to find a circuit to explain a model’s behavior performing a given task and 2. Interpreting each attention heads’ functionality in the circuit. > It is unclear how CD-T works for inference - is there a distinct circuit discovered for each inference datapoint, or is the circuit found on a broader scale, so as to tradeoff size vs. performance for a larger test set? Apologies! In all the three dataset we evaluated [1-3], the authors define a narrow task, and then construct a dataset where the correct behavior is clearly known to elicit the circuit needed to “perform the task”. As such, our method naturally can be performed on a single inference datapoint, but to answer the question of “what circuit performs the task in general”, it is better to perform it on the mean activations over 10-100 example points to reduce variance in the result. Details on how to handle sequence position information to align different examples are found in [1]. In our experiments, to be comparable, we used the same example counts as prior work [1-3] to obtain the circuits, and the exact numbers were included in Appendix A. Section 3.3.1 (line 282-285) has also been adjusted to make this clearer. > The authors are encouraged to discuss the practical utility of CD-T. Once their method yields a circuit, could additional analyses, such as on attention heads, be conducted? For instance, are there heads that consistently produce positive or negative outputs across all data points, or do the importance of attention heads vary based on input data characteristics? Thank you for the suggestion! Some of the papers we use as our baselines have performed much of this interpretation analysis [1-3] to characterize functionality of attention head groups in a circuit. Since we are attempting to evaluate the same model on the same task, the question of whether specific nodes help or hurt task performance will necessarily be the same. Instead, our paper’s focus is on efficiently finding the circuit which emulates the original model’s performance, at which point known techniques can be used to interpret the found circuits. Section 3.3.1 (line 286-288) has been updated to make the nature of our contribution clearer. > What transformer architecture is used for the experimental results? Sorry for the confusion! This information was actually included in Appendix A in our submission. We test our algorithm on GPT-2-small for the IOI and Greater-than tasks, and on a 4-layer attention-only transformer for the Docstring task. These choices of models are the same as what were used in their original papers [1-3] to be comparable. Section 3.3.1 (line 285-286) has also been adjusted to clarify. > Line 20: "CD-T is the first ---?" there seems to be a missing word here Thank you for pointing out! This sentence has now been fixed. Reference: [1] Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small. Wang et al. 2023. [2] How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model. Hanna et al. 2023. [3] A circuit for Python docstrings in a 4-layer attention-only transformer. Haimersheim & Janiak. 2023.