Grokking Group Multiplication with Cosets

We use the group Fourier transform over the symmetric group $S_n$ to reverse engineer a 1-layer feedforward network that has "grokked" the multiplication of $S_5$ and $S_6$. Each model discovers the true subgroup structure of the full group and converges on circuits that decompose the group multiplication into the multiplication of the group's conjugate subgroups. We demonstrate the value of using the symmetries of the data and models to understand their mechanisms and hold up the ``coset circuit'' that the model uses as a fascinating example of the way neural networks implement computations. We also draw attention to current challenges in conducting mechanistic interpretability research by comparing our work to Chughtai et al. [6] which alleges to find a different algorithm for this same problem.

Characterizing Mechanisms for Factual Recall in Language Models

Language Models (LMs) often must integrate facts they memorized in pretraining with new information that appears in a given context. These two sources can disagree, causing competition within the model, and it is unclear how an LM will resolve the conflict. On a dataset that queries for knowledge of world capitals, we investigate both distributional and mechanistic determinants of LM behavior in such situations. Specifically, we measure the proportion of the time an LM will use a counterfactual prefix (e.g., "The capital of Poland is London") to overwrite what it learned in pretraining ("Warsaw"). On Pythia and GPT2, the training frequency of both the query country ("Poland") and the in-context city ("London") highly affect the models' likelihood of using the counterfactual. We then use head attribution to identify individual attention heads that either promote the memorized answer or the in-context answer in the logits. By scaling up or down the value vector of these heads, we can control the likelihood of using the in-context answer on new data. This method can increase the rate of generating the in-context answer to 88\% of the time simply by scaling a single head at runtime. Our work contributes to a body of evidence showing that we can often localize model behaviors to specific components and provides a proof of concept for how future methods might control model behavior dynamically at runtime.

Are Language Models Worse than Humans at Following Prompts? It's Complicated

Prompts have been the center of progress in advancing language models' zero-shot and few-shot performance. However, recent work finds that models can perform surprisingly well when given intentionally irrelevant or misleading prompts. Such results may be interpreted as evidence that model behavior is not "human like". In this study, we challenge a central assumption in such work: that humans would perform badly when given pathological instructions. We find that humans are able to reliably ignore irrelevant instructions and thus, like models, perform well on the underlying task despite an apparent lack of signal regarding the task they are being asked to do. However, when given deliberately misleading instructions, humans follow the instructions faithfully, whereas models do not. Thus, our conclusion is mixed with respect to prior work. We argue against the earlier claim that high performance with irrelevant prompts constitutes evidence against models' instruction understanding, but we reinforce the claim that models' failure to follow misleading instructions raises concerns. More broadly, we caution that future research should not idealize human behaviors as a monolith and should not train or evaluate models to mimic assumptions about these behaviors without first validating humans' behaviors empirically.

Does CLIP Bind Concepts? Probing Compositionality in Large Image Models

Large-scale models combining text and images have made incredible progress in recent years. However, they can still fail at tasks requiring compositional knowledge, such as correctly picking out a red cube from a picture of multiple shapes. We examine the ability of CLIP (Radford et al., 2021), to caption images requiring compositional knowledge. We implement five compositional language models to probe the kinds of structure that CLIP may be using, and develop a novel training algorithm, Compositional Skipgram for Images (CoSI), to train these models. We look at performance in attribute-based tasks, requiring the identification of a particular combination of attribute and object (such as "red cube"), and in relational settings, where the spatial relation between two shapes (such as "cube behind sphere") must be identified. We find that in some conditions, CLIP is able to learn attribute-object labellings, and to generalize to unseen attribute-object combinations. However, we also see evidence that CLIP is not able to bind features together reliably. Moreover, CLIP is not able to reliably learn relations between objects, whereas some compositional models are able to learn these perfectly. Of the five models we developed, none were able to generalize to unseen relations.