Michael Timothy Bennett

Michael Timothy Bennett

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.

Michael Timothy Bennett

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.

Michael Timothy Bennett

If $A$ and $B$ are sets such that $A \subset B$, 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 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.

Michael Timothy Bennett

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.

Michael Timothy Bennett

Artificial general intelligence (AGI) may herald our extinction, according to AI safety research. Yet claims regarding AGI must rely upon mathematical formalisms -- theoretical agents we may analyse or attempt to build. AIXI appears to be the only such formalism supported by proof that its behaviour is optimal, a consequence of its use of compression as a proxy for intelligence. Unfortunately, AIXI is incomputable and claims regarding its behaviour highly subjective. We argue that this is because AIXI formalises cognition as taking place in isolation from the environment in which goals are pursued (Cartesian dualism). We propose an alternative, supported by proof and experiment, which overcomes these problems. Integrating research from cognitive science with AI, we formalise an enactive model of learning and reasoning to address the problem of subjectivity. This allows us to formulate a different proxy for intelligence, called weakness, which addresses the problem of incomputability. We prove optimal behaviour is attained when weakness is maximised. This proof is supplemented by experimental results comparing weakness and description length (the closest analogue to compression possible without reintroducing subjectivity). Weakness outperforms description length, suggesting it is a better proxy. Furthermore we show that, if cognition is enactive, then minimisation of description length is neither necessary nor sufficient to attain optimal performance, undermining the notion that compression is closely related to intelligence. However, there remain open questions regarding the implementation of scale-able AGI. In the short term, these results may be best utilised to improve the performance of existing systems. For example, our results explain why Deepmind's Apperception Engine is able to generalise effectively, and how to replicate that performance by maximising weakness.

Michael Timothy Bennett, Sean Welsh, Anna Ciaunica

We tackle the problem of consciousness by taking the naturally selected, embodied organism as our starting point. We provide a formalism describing how biological systems such as human bodies self-organize to hierarchically interpret unlabelled sensory information according to valence. The system is attracted and repelled at different spatial and temporal scales. This is a qualitative interpretation of an unlabelled physical state. We show how such interpretations imply behavioural policies which are differentiated from each other only by this qualitative aspect of information processing. Natural selection favours systems that actively intervene in the world to achieve homeostatic and reproductive goals. Put provocatively, death grounds meaning. This means that in living systems information processing is necessarily subjective, that is, it has quality embedded into its very core. Qualitative information processing involves interoceptive and exteroceptive classifiers, and determines priorities for self-survival. We formulate The Psychophysical Principle of Causality as a theorem, and prove generalisation optimal learning forces this valence first ontology. Qualitative good or bad processing necessarily comes \textit{before} quality neutral representations of properties (i.e. ``red'' is constructed from valence). Under selection pressures like sophisticated predation this produces a hierarchy of selves, of which reafference and reflective self awareness are a consequence. We discuss this in light of the seminal distinction between phenomenal and access consciousness. We claim that phenomenal consciousness without access is likely common, but the reverse is implausible. Our proposal lays the foundation of a formal science of consciousness, closer to human fact than zombie fiction.

Elija Perrier, Michael Timothy Bennett

Machine consciousness evaluations mostly see behavior. For language model agents that behavior is language and tool use. That lets an agent say the right things about itself even when the constraints that should make those statements matter are not jointly present at decision time. We apply Stack Theory's temporal gap to scaffold trajectories. This separates ingredient-wise occurrence within an evaluation window from co-instantiation at a single objective step. We then instantiate Stack Theory's Arpeggio and Chord postulates on grounded identity statements. This yields two persistence scores that can be computed from instrumented scaffold traces. We connect these scores to five operational identity metrics and map common scaffolds into an identity morphospace that exposes predictable tradeoffs. The result is a conservative toolkit for identity evaluation. It separates talking like a stable self from being organized like one.

Michael Timothy Bennett

Are biological self-organising systems more `intelligent' than artificial intelligence? If so, why? We frame intelligence as adaptability, and explore this question using a mathematical formalism of causal learning. We compare systems by how they delegate control, illustrating how this applies with examples of computational, biological, human organisational and economic systems. We formally show the scale-free, dynamic, bottom-up architecture of biological self-organisation allows for more efficient adaptation than the static top-down architecture typical of computers, because adaptation can take place at lower levels of abstraction. Artificial intelligence rests on a static, human-engineered `stack'. It only adapts at high levels of abstraction. To put it provocatively, a static computational stack is like an inflexible bureaucracy. Biology is more `intelligent' because it delegates adaptation down the stack. We call this multilayer-causal-learning. It inherits a flaw of biological systems. Cells become cancerous when isolated from the collective informational structure, reverting to primitive transcriptional behaviour. We show states analogous to cancer occur when collectives are too tightly constrained. To adapt to adverse conditions control should be delegated to the greatest extent, like the doctrine of mission-command. Our result shows how to design more robust systems and lays a mathematical foundation for future empirical research.

Michael Timothy Bennett

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.

Elija Perrier, Michael Timothy Bennett

Language Model Agents (LMAs) are increasingly treated as capable of autonomously navigating interactions with humans and tools. Their design and deployment tends to presume they are normal agents capable of sustaining coherent goals, adapting across contexts and acting with a measure of intentionality. These assumptions are critical to prospective use cases in industrial, social and governmental settings. But LMAs are not normal agents. They inherit the structural problems of the large language models (LLMs) around which they are built: hallucinations, jailbreaking, misalignment and unpredictability. In this Position paper we argue LMAs should not be treated as normal agents, because doing so leads to problems that undermine their utility and trustworthiness. We enumerate pathologies of agency intrinsic to LMAs. Despite scaffolding such as external memory and tools, they remain ontologically stateless, stochastic, semantically sensitive, and linguistically intermediated. These pathologies destabilise the ontological properties of LMAs including identifiability, continuity, persistence and and consistency, problematising their claim to agency. In response, we argue LMA ontological properties should be measured before, during and after deployment so that the negative effects of pathologies can be mitigated.

Ricard Solé, Luis F Seoane, Jordi Pla-Mauri et al.

Cognitive processes are realized across an extraordinary range of natural, artificial, and hybrid systems, yet there is no unified framework for comparing their forms, limits, and unrealized possibilities. Here, we propose a cognition space approach that replaces narrow, substrate-dependent definitions with a comparative representation based on organizational and informational dimensions. Within this framework, cognition is treated as a graded capacity to sense, process, and act upon information, allowing systems as diverse as cells, brains, artificial agents, and human-AI collectives to be analyzed within a common conceptual landscape. We introduce and examine three cognition spaces -- basal aneural, neural, and human-AI hybrid -- and show that their occupation is highly uneven, with clusters of realized systems separated by large unoccupied regions. We argue that these voids are not accidental but reflect evolutionary contingencies, physical constraints, and design limitations. By focusing on the structure of cognition spaces rather than on categorical definitions, this approach clarifies the diversity of existing cognitive systems and highlights hybrid cognition as a promising frontier for exploring novel forms of complexity beyond those produced by biological evolution.

Michael Timothy Bennett

Artificial general intelligence (AGI) is an established field of research. Yet some have questioned if the term still has meaning. AGI has been subject to so much hype and speculation it has become something of a Rorschach test. Melanie Mitchell argues the debate will only be settled through long term, scientific investigation. To that end here is a short, accessible and provocative overview of AGI. I compare definitions of intelligence, settling on intelligence in terms of adaptation and AGI as an artificial scientist. Taking my cue from Sutton's Bitter Lesson I describe two foundational tools used to build adaptive systems: search and approximation. I compare pros, cons, hybrids and architectures like o3, AlphaGo, AERA, NARS and Hyperon. I then discuss overall meta-approaches to making systems behave more intelligently. I divide them into scale-maxing, simp-maxing, w-maxing based on the Bitter Lesson, Ockham's and Bennett's Razors. These maximise resources, simplicity of form, and the weakness of constraints on functionality. I discuss examples including AIXI, the free energy principle and The Embiggening of language models. I conclude that though scale-maxed approximation dominates, AGI will be a fusion of tools and meta-approaches. The Embiggening was enabled by improvements in hardware. Now the bottlenecks are sample and energy efficiency.

Michael Timothy Bennett

Neural networks that land in flat regions of the loss landscape tend to generalise better than those in sharp regions. Sharpness-Aware Minimisation exploits this to improve generalisation. But function-preserving reparameterisation can inflate the Hessian of any minimum by two orders of magnitude without changing a single prediction. If the geometry of weight space can be manufactured from nothing, it cannot be the cause of anything. In other words, flat is simple and simplicity depends on encoding. Here I show that the actual driver is weakness, the volume of completions compatible with the learned function in the learner's embodied language. Weakness is reparameterisation-invariant because it is defined over what the network \emph{does}, not how it is parameterised. I prove weakness is minimax-optimal under exchangeable demands, and that PAC-Bayes bounds work because they correlate with it. On MNIST, the large-batch generalisation advantage \emph{vanishes} as training data grows, from $+1.6\%$ at $n = 2{,}000$ to $+0.02\%$ at $n = 60{,}000$. A quantity whose predictive power depends on how much data you have is not a cause but a confounder. I run head-to-heads on 100 networks with identical architecture and training. For MNIST weakness predicts generalisation ($ρ= +0.374$, $p = 0.00012$), sharpness anticorrelates ($ρ= -0.226$) and simplicity predicts nothing ($p = 0.848$). For Fashion-MNIST ($ρ= +0.384$, $p = 8.15 \times 10^{-5}$), though simplicity is at least somewhat predictive there. Simplicity is dataset dependent, whereas weakness is invariant. Flat minima were never the answer.

Elija Perrier, Michael Timothy Bennett

Central to agentic capability and trustworthiness of language model agents (LMAs) is the extent they maintain stable, reliable, identity over time. However, LMAs inherit pathologies from large language models (LLMs) (statelessness, stochasticity, sensitivity to prompts and linguistically-intermediation) which can undermine their identifiability, continuity, persistence and consistency. This attrition of identity can erode their reliability, trustworthiness and utility by interfering with their agentic capabilities such as reasoning, planning and action. To address these challenges, we introduce \textit{agent identity evals} (AIE), a rigorous, statistically-driven, empirical framework for measuring the degree to which an LMA system exhibit and maintain their agentic identity over time, including their capabilities, properties and ability to recover from state perturbations. AIE comprises a set of novel metrics which can integrate with other measures of performance, capability and agentic robustness to assist in the design of optimal LMA infrastructure and scaffolding such as memory and tools. We set out formal definitions and methods that can be applied at each stage of the LMA life-cycle, and worked examples of how to apply them.

Elija Perrier, Michael Timothy Bennett

We examine the implications of quantum foundations for AGI, focusing on how seminal results such as Bell's theorems (non-locality), the Kochen-Specker theorem (contextuality) and no-cloning theorem problematise practical implementation of AGI in quantum settings. We introduce a novel information-theoretic taxonomy distinguishing between classical AGI and quantum AGI and show how quantum mechanics affects fundamental features of agency. We show how quantum ontology may change AGI capabilities, both via affording computational advantages and via imposing novel constraints.

Michael Timothy Bennett

The following briefly discusses possible difficulties in communication with and control of an AGI (artificial general intelligence), building upon an explanation of The Fermi Paradox and preceding work on symbol emergence and artificial general intelligence. The latter suggests that to infer what someone means, an agent constructs a rationale for the observed behaviour of others. Communication then requires two agents labour under similar compulsions and have similar experiences (construct similar solutions to similar tasks). Any non-human intelligence may construct solutions such that any rationale for their behaviour (and thus the meaning of their signals) is outside the scope of what a human is inclined to notice or comprehend. Further, the more compressed a signal, the closer it will appear to random noise. Another intelligence may possess the ability to compress information to the extent that, to us, their signals would appear indistinguishable from noise (an explanation for The Fermi Paradox). To facilitate predictive accuracy an AGI would tend to more compressed representations of the world, making any rationale for their behaviour more difficult to comprehend for the same reason. Communication with and control of an AGI may subsequently necessitate not only human-like compulsions and experiences, but imposed cognitive impairment.

Michael Timothy Bennett, Yoshihiro Maruyama

We attempt to define what is necessary to construct an Artificial Scientist, explore and evaluate several approaches to artificial general intelligence (AGI) which may facilitate this, conclude that a unified or hybrid approach is necessary and explore two theories that satisfy this requirement to some degree.

Michael Timothy Bennett

The following defines intent, an arbitrary task and its solutions, and then argues that an agent which always constructs what is called an Intensional Solution would qualify as artificial general intelligence. We then explain how natural language may emerge and be acquired by such an agent, conferring the ability to model the intent of other individuals labouring under similar compulsions, because an abstract symbol system and the solution to a task are one and the same.

Michael Timothy Bennett, Yoshihiro Maruyama

In order to construct an ethical artificial intelligence (AI) two complex problems must be overcome. Firstly, humans do not consistently agree on what is or is not ethical. Second, contemporary AI and machine learning methods tend to be blunt instruments which either search for solutions within the bounds of predefined rules, or mimic behaviour. An ethical AI must be capable of inferring unspoken rules, interpreting nuance and context, possess and be able to infer intent, and explain not just its actions but its intent. Using enactivism, semiotics, perceptual symbol systems and symbol emergence, we specify an agent that learns not just arbitrary relations between signs but their meaning in terms of the perceptual states of its sensorimotor system. Subsequently it can learn what is meant by a sentence and infer the intent of others in terms of its own experiences. It has malleable intent because the meaning of symbols changes as it learns, and its intent is represented symbolically as a goal. As such it may learn a concept of what is most likely to be considered ethical by the majority within a population of humans, which may then be used as a goal. The meaning of abstract symbols is expressed using perceptual symbols of raw sensorimotor stimuli as the weakest (consistent with Ockham's Razor) necessary and sufficient concept, an intensional definition learned from an ostensive definition, from which the extensional definition or category of all ethical decisions may be obtained. Because these abstract symbols are the same for both situation and response, the same symbol is used when either performing or observing an action. This is akin to mirror neurons in the human brain. Mirror symbols may allow the agent to empathise, because its own experiences are associated with the symbol, which is also associated with the observation of another agent experiencing something that symbol represents.

Michael Timothy Bennett, Yoshihiro Maruyama

We argue that an explainable artificial intelligence must possess a rationale for its decisions, be able to infer the purpose of observed behaviour, and be able to explain its decisions in the context of what its audience understands and intends. To address these issues we present four novel contributions. Firstly, we define an arbitrary task in terms of perceptual states, and discuss two extremes of a domain of possible solutions. Secondly, we define the intensional solution. Optimal by some definitions of intelligence, it describes the purpose of a task. An agent possessed of it has a rationale for its decisions in terms of that purpose, expressed in a perceptual symbol system grounded in hardware. Thirdly, to communicate that rationale requires natural language, a means of encoding and decoding perceptual states. We propose a theory of meaning in which, to acquire language, an agent should model the world a language describes rather than the language itself. If the utterances of humans are of predictive value to the agent's goals, then the agent will imbue those utterances with meaning in terms of its own goals and perceptual states. In the context of Peircean semiotics, a community of agents must share rough approximations of signs, referents and interpretants in order to communicate. Meaning exists only in the context of intent, so to communicate with humans an agent must have comparable experiences and goals. An agent that learns intensional solutions, compelled by objective functions somewhat analogous to human motivators such as hunger and pain, may be capable of explaining its rationale not just in terms of its own intent, but in terms of what its audience understands and intends. It forms some approximation of the perceptual states of humans.