Compact Proofs of Model Performance via Mechanistic Interpretability

In this work, we propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving lower bounds on the accuracy of 151 small transformers trained on a Max-of-$K$ task. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless noise as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.

Provable Guarantees for Model Performance via Mechanistic Interpretability

In this work, we propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving lower bounds on the accuracy of 151 small transformers trained on a Max-of-$K$ task. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless noise as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.

Successor Heads: Recurring, Interpretable Attention Heads In The Wild

In this work we present successor heads: attention heads that increment tokens with a natural ordering, such as numbers, months, and days. For example, successor heads increment 'Monday' into 'Tuesday'. We explain the successor head behavior with an approach rooted in mechanistic interpretability, the field that aims to explain how models complete tasks in human-understandable terms. Existing research in this area has found interpretable language model components in small toy models. However, results in toy models have not yet led to insights that explain the internals of frontier models and little is currently understood about the internal operations of large language models. In this paper, we analyze the behavior of successor heads in large language models (LLMs) and find that they implement abstract representations that are common to different architectures. They form in LLMs with as few as 31 million parameters, and at least as many as 12 billion parameters, such as GPT-2, Pythia, and Llama-2. We find a set of 'mod-10 features' that underlie how successor heads increment in LLMs across different architectures and sizes. We perform vector arithmetic with these features to edit head behavior and provide insights into numeric representations within LLMs. Additionally, we study the behavior of successor heads on natural language data, identifying interpretable polysemanticity in a Pythia successor head.

Image Hijacks: Adversarial Images can Control Generative Models at Runtime

Are foundation models secure from malicious actors? In this work, we focus on the image input to a vision-language model (VLM). We discover image hijacks, adversarial images that control generative models at runtime. We introduce Behaviour Matching, a general method for creating image hijacks, and we use it to explore three types of attacks. Specific string attacks generate arbitrary output of the adversary's choice. Leak context attacks leak information from the context window into the output. Jailbreak attacks circumvent a model's safety training. We study these attacks against LLaVA, a state-of-the-art VLM based on CLIP and LLaMA-2, and find that all our attack types have above a 90% success rate. Moreover, our attacks are automated and require only small image perturbations. These findings raise serious concerns about the security of foundation models. If image hijacks are as difficult to defend against as adversarial examples in CIFAR-10, then it might be many years before a solution is found -- if it even exists.

Learnable Commutative Monoids for Graph Neural Networks

Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their $O(V)$ depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of $O(\log V)$ depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.