Vincent Wang-Maścianica

Vincent Wang-Maścianica, Nikhil Khatri

Architecture diagrams are ubiquitous in deep learning, but they are usually only representational: the tensor-program identities they suggest are still proved by prose and tensor-axis manipulation. We introduce a formal graphical calculus for the structural fragment of tensor programming underlying einops, making such diagrams proof-enabling. Our calculus represents tensor axes as nested graded tubes around a base type. The tube boundary recovers the undirected tensor-network view of axes, while the directed interior retains the operational reading of computation graphs. The key rewrite is grade-naturality: sliding spectacles over tubes. Standard equivariance proofs become short diagrammatic derivations. We additionally demonstrate how our rewrite system may be applied to convert attention masks into pre-processing operations, recovering efficient implementations of sparse attention blocks.

Muhammad Hamza Waseem, Jonathon Liu, Vincent Wang-Maścianica et al.

DisCoCirc is a newly proposed framework for representing the grammar and semantics of texts using compositional, generative circuits. While it constitutes a development of the Categorical Distributional Compositional (DisCoCat) framework, it exposes radically new features. In particular, [14] suggested that DisCoCirc goes some way toward eliminating grammatical differences between languages. In this paper we provide a sketch that this is indeed the case for restricted fragments of English and Urdu. We first develop DisCoCirc for a fragment of Urdu, as it was done for English in [14]. There is a simple translation from English grammar to Urdu grammar, and vice versa. We then show that differences in grammatical structure between English and Urdu - primarily relating to the ordering of words and phrases - vanish when passing to DisCoCirc circuits.

Philipp Koralus, Vincent Wang-Maścianica

Increase in computational scale and fine-tuning has seen a dramatic improvement in the quality of outputs of large language models (LLMs) like GPT. Given that both GPT-3 and GPT-4 were trained on large quantities of human-generated text, we might ask to what extent their outputs reflect patterns of human thinking, both for correct and incorrect cases. The Erotetic Theory of Reason (ETR) provides a symbolic generative model of both human success and failure in thinking, across propositional, quantified, and probabilistic reasoning, as well as decision-making. We presented GPT-3, GPT-3.5, and GPT-4 with 61 central inference and judgment problems from a recent book-length presentation of ETR, consisting of experimentally verified data-points on human judgment and extrapolated data-points predicted by ETR, with correct inference patterns as well as fallacies and framing effects (the ETR61 benchmark). ETR61 includes classics like Wason's card task, illusory inferences, the decoy effect, and opportunity-cost neglect, among others. GPT-3 showed evidence of ETR-predicted outputs for 59% of these examples, rising to 77% in GPT-3.5 and 75% in GPT-4. Remarkably, the production of human-like fallacious judgments increased from 18% in GPT-3 to 33% in GPT-3.5 and 34% in GPT-4. This suggests that larger and more advanced LLMs may develop a tendency toward more human-like mistakes, as relevant thought patterns are inherent in human-produced training data. According to ETR, the same fundamental patterns are involved both in successful and unsuccessful ordinary reasoning, so that the "bad" cases could paradoxically be learned from the "good" cases. We further present preliminary evidence that ETR-inspired prompt engineering could reduce instances of these mistakes.

Nikhil Khatri, Tuomas Laakkonen, Jonathon Liu et al.

We introduce a category-theoretic diagrammatic formalism in order to systematically relate and reason about machine learning models. Our diagrams present architectures intuitively but without loss of essential detail, where natural relationships between models are captured by graphical transformations, and important differences and similarities can be identified at a glance. In this paper, we focus on attention mechanisms: translating folklore into mathematical derivations, and constructing a taxonomy of attention variants in the literature. As a first example of an empirical investigation underpinned by our formalism, we identify recurring anatomical components of attention, which we exhaustively recombine to explore a space of variations on the attention mechanism.