Computable Artificial General Intelligence

2023

Preprint

Self Cite

We bring together foundational theories of meaning and a mathematical formalism of artificial general intelligence to provide a mechanistic explanation of meaning, communication and symbol emergence. We establish circumstances under which a machine might mean what we think it means by what it says, or comprehend what we mean by what we say. We conclude that a language model such as ChatGPT does not comprehend or engage in meaningful communication with humans, though it may exhibit complex behaviours such as theory of mind.

Section: A Foundational Theory Of Foundational Theoriesmentioning

confidence: 99%

On the Computation of Meaning, Language Models and Incomprehensible Horrors

2023

Preprint

Self Cite

“…To do so, we employ a formalism of enactive cognition [10,11] in which sets of declarative programs are related to one another in such a way as to form a lattice. This unusual representation is necessary to ensure that both the weakness and description length of a hypothesis are well defined 4 .…”

Section: Background Definitionsmentioning

confidence: 99%

“…This assigns a probability to every statement l ∈ L v given an implementable language. It is a probability distribution in the sense that the probability of mutually exclusive statements sums to one 11 . This prior may be considered universal in the very limited sense that it assigns a probability to every conceivable hypothesis (where what is conceivable depends upon the implementable language) absent any parameters or specific assumptions about the task as with AIXI's intelligence order relation [9, def.…”

Section: Proofsmentioning

confidence: 99%

The Optimal Choice of Hypothesis Is the Weakest, Not the Shortest

2023

Preprint

If A and B are sets such that A is a subset of B, generalisation may be understood as the inference from A of a hypothesis sufficient to construct B. One might infer any number of hypotheses from A, yet only some of those may generalise to B. How can one know which are likely to generalise? One strategy is to choose the shortest, equating the ability to compress information with the ability to generalise (a ``proxy for intelligence”). We examine this in the context of a mathematical formalism of enactive cognition. We show that compression is neither necessary nor sufficient to maximise performance (measured in terms of the probability of a hypothesis generalising). We formulate a proxy unrelated to length or simplicity, called weakness. We show that if tasks are uniformly distributed, then there is no choice of proxy that performs at least as well as weakness maximisation in all tasks while performing strictly better in at least one. In other words, weakness is the pareto optimal choice of proxy. In experiments comparing maximum weakness and minimum description length in the context of binary arithmetic, the former generalised at between 1.1 and 5 times the rate of the latter. We argue this demonstrates that weakness is a far better proxy, and explains why Deepmind's Apperception Engine is able to generalise effectively.

“…We would suggest his argument extends to our formalism, and in any case if qualia are a mechanistic phenomenon then they are already represented by the vocabulary of the implementable language. What is novel in our formalism is not just that it points out that causal inference must construct identity and awareness, but that it does so with a formulation that also addresses enactive cognition, symbol emergence and empathy [21,15,25,26,27,17].…”

Section: Consciousnessmentioning

confidence: 99%

Emergent Causality & the Foundation of Consciousness

2023

Preprint

To make accurate inferences in an interactive setting, an agent must not confuse passive observation of events with having intervened to cause those events. The do' operator formalises interventions so that we may reason about their effect. Yet there exist pareto optimal mathematical formalisms of general intelligence in an interactive setting which, presupposing no explicit representation of intervention, make maximally accurate inferences. We examine one such formalism. We show that in the absence of an operator, an intervention can still be represented by a variable. Furthermore, the need to explicitly represent interventions in advance arises only because we presuppose abstractions. The aforementioned formalism avoids this and so, initial conditions permitting, representations of relevant causal interventions will emerge through induction. These emergent abstractions function as representations of one’s self and of any other object, inasmuch as the interventions of those objects impact the satisfaction of goals. We argue (with reference to theory of mind) that this explains how one might reason about one's own identity and intent, those of others, of one's own as perceived by others and so on. In a narrow sense this describes what it is to be aware, and is a mechanistic explanation of aspects of consciousness.