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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: 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.

As the focus of quantum science shifts from basic research to development and implementation of applied quantum technology, calls for a robust, diverse quantum workforce have increased. However, little research has been done on the design and impact on participants of workforce preparation efforts outside of R1 contexts. In order to begin to answer the question of how program design can or should attend to the needs and interests of diverse groups of students, we performed interviews with students from two Colorado-based quantum education/workforce development programs, one in an undergraduate R1 setting and one in a distributed community setting and serving students largely from two-year colleges. Through analysis of these interviews, we were able to highlight differences between the student populations in the two programs in terms of participation goals, prior and general awareness of quantum science, and career interest and framing of career trajectories. While both groups of students reported benefits from program participation, we highlight the ways in which students' different needs and contexts have informed divergent development of the two programs, framing contextual design of quantum education and workforce efforts as an issue of equity and representation for the burgeoning quantum workforce., Comment: 15 pages, 1 figure, 1 table

Biological intelligence is more sample-efficient than artificial intelligence (AI), learning from fewer examples. Here we answer why. Given data, there can be many policies which seem "correct" because they perfectly fit the data. However, only one correct policy could have actually caused the data. Sample-efficiency requires a means of discerning which. Previous work showed sample efficiency is maximised by weak-policy-optimisation (WPO); preferring policies that more weakly constrain what is considered to be correct, given finite resources. Biology's sample-efficiency demonstrates it is better at WPO. To understand how, we formalise the "multiscale-competency-architecture" (MCA) observed in biological systems, as a sequence of nested "agentic-abstraction-layers". We show that WPO at low levels enables synthesis of weaker policies at high. We call this "multiscale-causal-learning", and argue this is how we might construct more scale-able, sample-efficient and reliable AI. Furthermore, a sufficiently weak policy at low levels is a precondition of collective policy at higher levels. The higher level "identity" of the collective is lost if lower levels use an insufficiently weak policy (e.g. cells may become isolated from the collective informational structure and revert to primitive behaviour). This has implications for biology, machine learning, AI-safety, and philosophy., Comment: Definitions shared with arXiv:2404.07227, arXiv:2302.00843

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., Comment: Accepted for publication in the Proceedings of the 17th Conference on Artificial General Intelligence, 2024. Definitions shared with arXiv:2302.00843

We show how to effectively solve 5-term $S$-unit equations when the set of primes $S$ has cardinality at most 3, and use this to provide an explicit answer to an old question of D.J. Newman on representations of integers as sums of $S$-units.

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., Comment: Published (and accepted for full oral presentation) at the 16th 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., Comment: Published (and won "Best Student Paper") at the 16th Conference on Artificial General Intelligence, Stockholm, 2023

We answer a number of questions of Erd\H{o}s on the existence of arithmetic progressions in $k$-full numbers (i.e. integers with the property that every prime divisor necessarily occurs to at least the $k$-th power). Further, we deduce a variety of arithmetic constraints upon such progressions, under the assumption of the $abc$-conjecture of Masser and Oesterl\'e.

The 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., Comment: Accepted for publication in the Proceedings of the 17th Conference on Artificial General Intelligence, 2024