Awarded “Best Student Paper” and published in Proceedings of The 16th International Conference on Artificial General Intelligence, Stockholm, 2023.To make accurate inferences in an interactive setting, an agent must not confuse passive observation of events with having intervened to cause them. 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 a do operator, an intervention can be represented by a variable. We then argue that variables are abstractions, and that need to explicitly represent interventions in advance arises only because we presuppose these sorts of 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 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.

Awarded "Best Student Paper" at the 17th Conference on Artificial General Intelligence, 2024The concept of intelligent software is flawed. The behaviour of software is determined by the hardware that "interprets" it. This undermines claims regarding the behaviour of theorised, software superintelligence. Here we characterise this problem as "computational dualism", where instead of mental and physical substance, we have software and hardware. We argue that to make objective claims regarding performance we must avoid computational dualism. We propose a pancomputational alternative wherein every aspect of the environment is a relation between irreducible states. We formalise systems as behaviour (inputs and outputs), and cognition as embodied, embedded, extended and enactive. The result is cognition formalised as a part of the environment, rather than as a disembodied policy interacting with the environment through an interpreter. This allows us to make objective claims regarding intelligence, which we argue is the ability to "generalise", identify causes and adapt. We then establish objective upper bounds for intelligent behaviour. This suggests AGI will be safer, but more limited, than theorised.

Is a biological self-organising system more `intelligent' than an artificial intelligence? If so, why? We explore this question from a theoretical point of view. We characterise intelligence as sample efficiency in adaptation, and build upon a mathematical formalism of enactive causal learning. We extend it to formalise the distributed, multiscale computational architecture of biological self-organisation, and then show that such an architecture allows for more efficient adaptation than the static interpreters used in computers. To put it provocatively, biology is more intelligent because cells adapt to provide a helpful inductive bias, and static interpreters do not. We call this multiscale causal learning (MCL). However MCL inherits the flaws of biological self-organisation too, such as cancer. It has been shown that cells abandon their higher level `collective' policy and revert to primitive transcriptional behaviour when isolated from the collective's informational structure. We show that, in the context of our formalism, failure states like cancer occur when systems are over-constrained. This suggests control should be distributed (bottom-up rather than top-down) to ensure graceful degradation. We speculate about what MCL may imply for systems in general, from machine learning hardware to human organisational systems. We suggest MCL may inform the design of more resilient, adaptive systems.

We tackle the hard problem of consciousness taking the naturally selected, self-organising, embodied organism as our starting point. We provide a mathematical formalism describing how biological systems self-organise to hierarchically interpret unlabelled sensory information according to valence and specific needs. Such interpretations imply behavioural policies which can only be differentiated from each other by the qualitative aspect of information processing. Selection pressures favour systems that can intervene in the world to achieve homeostatic and reproductive goals. Quality is a property arising in such systems to link cause to affect to motivate real world interventions. This produces a range of qualitative classifiers (interoceptive and exteroceptive) that motivate specific actions and determine priorities and preferences. Building upon the seminal distinction between access and phenomenal consciousness, our radical claim here is that phenomenal consciousness without access consciousness is likely very common, but the reverse is implausible. To put it provocatively: death grounds meaning, and Nature does not like zombies. We formally describe the multilayered architecture of self-organisation from rocks to Einstein, illustrating how our argument applies in the real world. We claim that access consciousness at the human level is impossible without the ability to hierarchically model i) the self, ii) the world/others and iii) the self as modelled by others. Phenomenal consciousness is therefore required for human-level functionality. Our proposal lays the foundations of a formal science of consciousness, deeply connected with natural selection rather than abstract thinking, closer to human fact than zombie fiction.

Accepted for full oral presentation at the 16th Conference on Artificial General Intelligence, taking place in Stockholm, 2023. We integrate foundational theories of meaning with a mathematical formalism of artificial general intelligence (AGI) to offer a comprehensive mechanistic explanation of meaning, communication, and symbol emergence. This synthesis holds significance for both AGI and broader debates concerning the nature of language, as it unifies pragmatics, logical truth conditional semantics, Peircean semiotics, and a computable model of enactive cognition, addressing phenomena that have traditionally evaded mechanistic explanation. By examining the conditions under which a machine can generate meaningful utterances or comprehend human meaning, we establish that the current generation of language models do not possess the same understanding of meaning as humans nor intend any meaning that we might attribute to their responses. To address this, we propose simulating human feelings and optimising models to construct weak representations. Our findings shed light on the relationship between meaning and intelligence, and how we can build machines that comprehend and intend meaning.

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.

Simplicity is held by many to be the key to general intelligence. Simpler models tend to “generalise”, identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and generalisation extend far beyond computer science, addressing questions of physics and even biology. Yet simplicity is a property of form, while generalisation is of function. In interactive settings, any correlation between the two depends on interpretation. In theory there could be no correlation and yet in practice, there is. Previous theoretical work showed generalisation to be a consequence of “weak” constraints implied by function, not form. Experiments demonstrated choosing weak constraints over simple forms yielded a 110-500% improvement in generalisation rate. Here we show that all constraints can take equally simple forms, regardless of weakness. However if forms are spatially extended, then function is represented using a finite subset of forms. If function is represented using a finite subset of forms, then we can force a correlation between simplicity and generalisation by making weak constraints take simple forms. If function is determined by a goal directed process that favours versatility (e.g. natural selection), then efficiency demands weak constraints take simple forms. Complexity has no causal influence on generalisation, but appears to due to confounding.In Press: Accepted for publication in the Proceedings of The 17th Conference on Artificial General Intelligence, 2024

An artificial general intelligence (AGI), by one definition, is an agent that requires less information than any other to make an accurate prediction. It is arguable that the general reinforcement learning agent AIXI not only met this definition, but was the only mathematical formalism to do so. Though a significant result, AIXI was incomputable and its performance subjective. This paper proposes an alternative formalism of AGI which overcomes both problems. Formal proof of its performance is given, along with a simple implementation and experimental results that support these claims.