Vincent Wang-Maścianica

Vincent Wang-Mascianica, Jonathon Liu, Bob Coecke

This paper concerns the structure of meanings within natural language. Earlier, a framework named DisCoCirc was sketched that (1) is compositional and distributional (a.k.a. vectorial); (2) applies to general text; (3) captures linguistic `connections' between meanings (cf. grammar) (4) updates word meanings as text progresses; (5) structures sentence types; (6) accommodates ambiguity. Here, we realise DisCoCirc for a substantial fragment of English. When passing to DisCoCirc's text circuits, some `grammatical bureaucracy' is eliminated, that is, DisCoCirc displays a significant degree of (7) inter- and intra-language independence. That is, e.g., independence from word-order conventions that differ across languages, and independence from choices like many short sentences vs. few long sentences. This inter-language independence means our text circuits should carry over to other languages, unlike the language-specific typings of categorial grammars. Hence, text circuits are a lean structure for the `actual substance of text', that is, the inner-workings of meanings within text across several layers of expressiveness (cf. words, sentences, text), and may capture that what is truly universal beneath grammar. The elimination of grammatical bureaucracy also explains why DisCoCirc: (8) applies beyond language, e.g. to spatial, visual and other cognitive modes. While humans could not verbally communicate in terms of text circuits, machines can. We first define a `hybrid grammar' for a fragment of English, i.e. a purpose-built, minimal grammatical formalism needed to obtain text circuits. We then detail a translation process such that all text generated by this grammar yields a text circuit. Conversely, for any text circuit obtained by freely composing the generators, there exists a text (with hybrid grammar) that gives rise to it. Hence: (9) text circuits are generative for text.

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.

Joe Edelman, Tan Zhi-Xuan, Ryan Lowe et al.

Beneficial societal outcomes cannot be guaranteed by aligning individual AI systems with the intentions of their operators or users. Even an AI system that is perfectly aligned to the intentions of its operating organization can lead to bad outcomes if the goals of that organization are misaligned with those of other institutions and individuals. For this reason, we need full-stack alignment, the concurrent alignment of AI systems and the institutions that shape them with what people value. This can be done without imposing a particular vision of individual or collective flourishing. We argue that current approaches for representing values, such as utility functions, preference orderings, or unstructured text, struggle to address these and other issues effectively. They struggle to distinguish values from other signals, to support principled normative reasoning, and to model collective goods. We propose thick models of value will be needed. These structure the way values and norms are represented, enabling systems to distinguish enduring values from fleeting preferences, to model the social embedding of individual choices, and to reason normatively, applying values in new domains. We demonstrate this approach in five areas: AI value stewardship, normatively competent agents, win-win negotiation systems, meaning-preserving economic mechanisms, and democratic regulatory institutions.

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.

Benjamin Rodatz, Ian Fan, Tuomas Laakkonen et al.

We formalise the essential data of objective functions as equality constraints on composites of learners. We call these constraints "tasks", and we investigate the idealised view that such tasks determine model behaviours. We develop a flowchart-like graphical mathematics for tasks that allows us to; (1) offer a unified perspective of approaches in machine learning across domains; (2) design and optimise desired behaviours model-agnostically; and (3) import insights from theoretical computer science into practical machine learning. As a proof-of-concept of the potential practical impact of our theoretical framework, we exhibit and implement a novel "manipulator" task that minimally edits input data to have a desired attribute. Our model-agnostic approach achieves this end-to-end, and without the need for custom architectures, adversarial training, random sampling, or interventions on the data, hence enabling capable, small-scale, and training-stable models.

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.

Andrew Keenan Richardson, Ryan Othniel Kearns, Sean Moss et al.

We study logical reasoning in language models by asking whether their errors follow established human fallacy patterns. Using the Erotetic Theory of Reasoning (ETR) and its open-source implementation, PyETR, we programmatically generate 383 formally specified reasoning problems and evaluate 38 models. For each response, we judge logical correctness and, when incorrect, whether it matches an ETR-predicted fallacy. Two results stand out: (i) as a capability proxy (Chatbot Arena Elo) increases, a larger share of a model's incorrect answers are ETR-predicted fallacies $(ρ=0.360, p=0.0265)$, while overall correctness on this dataset shows no correlation with capability; (ii) reversing premise order significantly reduces fallacy production for many models, mirroring human order effects. Methodologically, PyETR provides an open-source pipeline for unbounded, synthetic, contamination-resistant reasoning tests linked to a cognitive theory, enabling analyses that focus on error composition rather than error rate.

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.

Vincent Wang-Mascianica, Bob Coecke

This paper concerns the intersection of natural language and the physical space around us in which we live, that we observe and/or imagine things within. Many important features of language have spatial connotations, for example, many prepositions (like in, next to, after, on, etc.) are fundamentally spatial. Space is also a key factor of the meanings of many words/phrases/sentences/text, and space is a, if not the key, context for referencing (e.g. pointing) and embodiment. We propose a mechanism for how space and linguistic structure can be made to interact in a matching compositional fashion. Examples include Cartesian space, subway stations, chesspieces on a chess-board, and Penrose's staircase. The starting point for our construction is the DisCoCat model of compositional natural language meaning, which we relax to accommodate physical space. We address the issue of having multiple agents/objects in a space, including the case that each agent has different capabilities with respect to that space, e.g., the specific moves each chesspiece can make, or the different velocities one may be able to reach. Once our model is in place, we show how inferences drawing from the structure of physical space can be made. We also how how linguistic model of space can interact with other such models related to our senses and/or embodiment, such as the conceptual spaces of colour, taste and smell, resulting in a rich compositional model of meaning that is close to human experience and embodiment in the world.