arXiv subjects

Michael Timothy Bennett

Publications and source records attributed to Michael Timothy Bennett.

At least 19 recordsLinked to original sources

arXiv2026

Why the Third Axis Is Freedom

In generative training, a model produces an output and is penalised for its difference from an example. With one output per comparison, a model that produces one common answer can outperform a model retaining a broader repertoire. Explorative Modeling (XM) produces $K$ outputs per comparison and updates on the closest, claiming exploration as a "third pretraining axis" associated with generative expressivity. Here I show the third axis is actually freedom, meaning the weakness of the constraint implied by a model's behaviour. Previous work showed freedom is a property of function rather than form. Parameters, architecture, minimum-description-length (MDL), and data can vary while the behavioural constraint remains unchanged. It was formally proved that weakest models are likeliest to generalise, and freedom selection beat MDL by 110-500\% in induction experiments. I prove average XM loss depends on the chance a candidate misses an acceptable region, with exploration raising miss probability to power $K$. For $K>1$, match probability rises with freedom. I then demonstrate empirically that XM optimises for freedom. In a Forward XM experiment, larger $K$ increased or saturated measured freedom, and increased freedom at every tested value under context-dependent targets. I trained XM candidate pools and compared validation selection with a freedom selector that read unlabelled parent contexts. Freedom won in 29 of 30 cases. Generative expressivity is a mode-count proxy for freedom, that discards the extension structure that gives freedom its generalisation significance. XM is a means, freedom an end, and selecting for freedom improved XM under distribution shift.

cs.LG↗

arXiv2026

Are Flat Minima an Illusion?

Flat minima are an account of why deep networks generalise. However flatness is a matter of form (parameters), while generalisation is of function. The same function can be a result of many different parameterisations. I demonstrate this by rescaling ReLU networks, changing raw Hessian trace by up to $99$ times while every prediction remains fixed. Raw curvature cannot identify a function-level explanation. Previous theoretical work traced generalisation to the weakness of constraints implied by function, meaning the freedom a model retains within the bounds of what it has learned to be correct. A policy is weaker when more future commitments remain compatible with what it has learned, allowing more freedom to adapt. To measure this for neural networks, I freeze the last hidden representation and ask whether each of 512 sampled label bundles can be met by a replacement affine classifier. The resulting joint completion score is invariant under invertible linear mixing and translation of feature coordinates. Across two predeclared cohorts of 100 networks, it predicts held-out accuracy with rank correlations $0.29$ and $0.47$. Raw Hessian trace and relative flatness have no multiplicity-corrected association. To put it provocatively, freedom is correlated with adaptability, while flatness is a matter of description.

cs.LG↗

arXiv2026

Time, Identity and Consciousness in Language Model Agents

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.

cs.AI↗

arXiv2026

Cognition spaces: natural, artificial, and hybrid

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.

q-bio.NC↗

arXiv2026

A Mind Cannot Be Smeared Across Time

Whether machines can be conscious depends not only on what they compute, but \emph{when} they compute it. Most deployed artificial systems realise their functions via sequential or time-multiplexed updates, yet a moment of conscious experience feels unified and simultaneous. I prove that this difference matters. I augment Stack Theory with algebraic laws relating within time-window constraint satisfaction to conjunction. I introduce a temporal semantics over windowed trajectories $\tau_{\Delta}$ and prove that existential temporal realisation $\Diamond_{\Delta}$ does not preserve conjunction. A system can realise all the ingredients of experience across time without ever instantiating the experienced conjunction itself. I then distinguish two postulates, Chord and Arpeggio. Chord is the position that conscious unity requires \textit{objective co-instantiation} of the grounded conjunction within the window, like a musical chord. Arpeggio only needs the ingredients to \textit{occur} within window, like a melody. I formalise concurrency-capacity to measure what is needed to satisfy co-instantiation. Finally, I review neurophysiological evidence suggesting that consciousness depends on phase synchrony and effective connectivity, and that loss of consciousness is associated with its breakdown. Under Chord, software consciousness on strictly sequential substrates is impossible for contents whose grounding requires two or more simultaneous contributors. The hardware matters.

cs.AI↗

arXiv2025

Agent Identity Evals: Measuring Agentic Identity

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.

cs.AI↗

arXiv2025

Quantum AGI: Ontological Foundations

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.

quant-ph↗

arXiv2025

What the F*ck Is Artificial General Intelligence?

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.

cs.AI↗

arXiv2025

Position: Stop Acting Like Language Model Agents Are Normal Agents

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.

cs.AI↗

arXiv2024

Why Is Anything Conscious?

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.

cs.AI↗

arXiv2024

Are Biological Systems More Intelligent Than Artificial Intelligence?

Are biological self-organising systems more ``intelligent'' than artificial intelligence (AI)? If so, why? I address this question using a mathematical framework that defines intelligence in terms of adaptability. Systems are modelled as stacks of abstraction layers (\emph{Stack Theory}) and compared by how effectively they delegate agentic control down their stacks. I illustrate this using computational, biological, military, governmental, and economic systems. Contemporary AI typically relies on static, human-engineered stacks whose lower layers are fixed during deployment. Put provocatively, such systems resemble inflexible bureaucracies that adapt only top-down. Biological systems are more intelligent because they delegate adaptation. Formally, I prove a theorem (\emph{The Law of the Stack}) showing that adaptability at higher layers is bottlenecked by adaptability at lower layers. I further show that, under standard viability assumptions, maximising adaptability is equivalent to minimising variational free energy, implying that delegation is necessary for free-energy minimisation. Generalising bioelectric accounts of cancer as isolation from collective informational structures, I analyse cancer-like failure modes in non-biological systems when delegation is inadequate. This yields design principles for building robust systems via delegated control, and reframes hybrid agents (e.g. organoids or human--AI systems) as weak boundary-condition design problems in which constraints shape low-level policy spaces while preserving collective identity.

cs.AI↗

arXiv2024

Is Complexity an Illusion?

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.

cs.AI↗

arXiv2023

On the Computation of Meaning, Language Models and Incomprehensible Horrors

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.

cs.AI↗

arXiv2023

Emergent Causality and the Foundation of Consciousness

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.

cs.AI↗

arXiv2023

Computational Dualism and Objective Superintelligence

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.

cs.AI↗

arXiv2023

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

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.

cs.AI↗

arXiv2022

Computable Artificial General Intelligence

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.

cs.AI↗

arXiv2021

Compression, The Fermi Paradox and Artificial Super-Intelligence

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.

cs.AI↗