Physics measures energy. Information theory measures information. Computer science measures computation. Neuroscience studies cognition. No widely accepted framework currently exists that compares adaptive intelligence across physical substrates according to energy efficiency — or, stated more carefully, no framework exists that is simultaneously rigorous about both the physical and the intelligence sides of such a comparison. This paper proposes Intelligence-Energy Density (IED) as a research program rather than a settled framework: a structured set of questions, candidate definitions, proposed measurements, and falsifiable predictions intended to make the comparison tractable rather than merely intuitive. The paper draws on the Landauer principle, Shannon information theory, the thermodynamics of computation, neuroscience's account of brain energy consumption, and the emerging literature on neuromorphic and photonic computing to assemble the conceptual components such a framework would require. It is explicit about three major difficulties: the definition of intelligence suitable for cross-substrate comparison is not settled; the Landauer limit is a theoretical minimum for irreversible computation, not a general intelligence efficiency floor; and the comparison between biological and artificial intelligence may involve category errors that no framework can fully eliminate. The paper is offered as a contribution to a research agenda the Foundation believes is consequential for the long-run governance of increasingly capable intelligence systems. It is not offered as a finished theory.
This paper is an independent technical contribution. It does not draw on or extend the EM-IAF assessment methodology, which operates at the behavioral rather than physical substrate level. The governance relevance of the IED research program is discussed in Section XII (Non-Adoption Scenario).
The comparison being proposed here is specific: can adaptive intelligence — the capacity of a physical system to receive information, update internal representations, and produce outputs that are reliably better-than-random with respect to some goal — be compared across physical substrates in terms of the energy required to produce it? This is not the question of whether artificial systems are intelligent. It is not the question of whether intelligence has a physical basis (it does — every intelligence we have empirical access to is instantiated in physical matter). It is the question of whether there is a principled, physics-grounded way to compare different physical implementations of intelligence with respect to their energy efficiency.
The honest answer is: we do not currently have such a framework. We have the Landauer principle, which sets a theoretical minimum energy cost per bit of irreversible computation. We have Shannon information theory, which provides a precise account of information content independent of physical substrate. We have neuroscience's increasingly detailed account of brain energy consumption and computational organization. And we have engineering's increasingly sophisticated account of silicon, neuromorphic, photonic, and other computing substrates. What we lack is a common currency — a unit in which the intelligence output of different substrates can be expressed and compared per unit of energy consumed.
The IED research program proposes to construct that common currency. It is a research program because the construction is not complete — the definition of intelligence suitable for cross-substrate comparison is not settled, the measurement methodology for intelligence output is contested, and the physical parameters relevant to the comparison differ across substrates in ways that complicate direct comparison. The paper makes these difficulties explicit in Section XII and does not resolve them. It proposes instead the research agenda that would be required to resolve them.
Three reasons make the IED research program consequential for the Foundation's governance agenda, quite apart from its scientific interest.
The first is sustainability. AI training and inference are already significant contributors to global energy consumption, and projected growth in AI capability and deployment will increase that consumption substantially unless efficiency improves commensurately.1 A framework for measuring intelligence per unit of energy would provide a principled metric for evaluating whether efficiency is improving, at what rate, and relative to what physical limits. Without such a metric, claims about AI efficiency improvements are not comparable across different architectures and substrates.
The second is hardware design. If intelligence-energy efficiency can be defined and measured, it becomes a design target rather than an emergent property. The neuromorphic computing research program — building hardware architectures that more closely resemble neural computation — is motivated in part by the observation that biological neural systems appear to be substantially more energy-efficient per unit of intelligent output than current silicon architectures.2,3 A precise IED framework would allow that efficiency gap to be quantified rather than merely asserted, and would provide research targets for hardware development.
The third is governance relevance. If advanced AI systems require orders of magnitude more energy than biological intelligence to produce comparable adaptive outputs, that inefficiency has distributional consequences: AI capability is accessible only to actors with access to large-scale energy infrastructure, which may be a smaller and less diverse set of actors than current AI development already involves. Conversely, if neuromorphic or photonic substrates can substantially close the biological-silicon efficiency gap, that has implications for the concentration of AI capability that governance frameworks need to anticipate. The IED research program is therefore not only a scientific question — it has direct relevance to the AI governance concerns the Foundation addresses through its assessment and accountability work.
The most important conceptual prerequisite for the IED framework is the distinction between computation and intelligence. They are related — all intelligence the Foundation is aware of involves computation — but they are not identical. Computation is the manipulation of symbols according to formal rules. Intelligence, as narrowly defined above, is the adaptive use of computation to produce outputs that are better-than-random with respect to a goal, where "better-than-random" requires that the system's outputs reflect information about the environment that was not present in its initial state.
This distinction matters for two reasons. First, it means that a system can perform large amounts of computation without producing much intelligence in the relevant sense — and vice versa, a system that performs small amounts of computation may produce intelligence efficiently if its architecture is well-matched to the information structure of its environment. The brain is the canonical case: it performs roughly 1015 synaptic operations per second at approximately 20 watts — an energy budget that would power a modest laptop — while demonstrating adaptive capabilities in perception, language, motor control, social interaction, and reasoning that no artificial system has matched in any domain other than specific narrow tasks.4
Second, the distinction means that measuring energy per computation (FLOP/Watt) is not the same as measuring energy per unit of intelligence. Current benchmarks for AI system efficiency — FLOP/Watt, tokens/Watt — measure computation efficiency, not intelligence efficiency. The IED framework requires a measure of intelligence output, not just computation throughput, in the numerator of the efficiency ratio. Section VII addresses how such a measure might be constructed.
The brain does not win because it computes differently. It wins, if it wins at all on any meaningful comparison, because it computes adaptively — matching computational cost to information value in ways that current architectures do not.
Rolf Landauer's 1961 paper established that logically irreversible operations — specifically, the erasure of one bit of information — must dissipate at minimum kBT ln 2 of energy as heat, where kB is Boltzmann's constant and T is the temperature of the environment.5 At room temperature (T ≈ 300K), this is approximately 2.85 × 10-21 joules — roughly 1014 times smaller than the energy a modern transistor consumes switching state. The gap between the Landauer limit and current silicon performance represents the theoretical headroom for efficiency improvement in current computational architectures.
Charles Bennett extended the Landauer analysis by demonstrating that computation can in principle be made logically reversible — and therefore arbitrarily energy-efficient — if information is never erased.6 Reversible computing architectures exist experimentally, though they face engineering challenges that prevent them from approaching the theoretical limit in practice. The relevance of reversible computing to biological neural systems is an active research question: synaptic processes may involve significant reversible computation that current models do not fully characterize.7
Shannon's 1948 formalization of information as a measure of uncertainty reduction provides a substrate-independent account of information content.8 The Shannon entropy of a discrete probability distribution H(X) = -Σ pi log2 pi measures the average information content of outcomes drawn from that distribution in bits. This formalism is relevant to IED in two ways: it provides a principled definition of the information content of system outputs that is independent of the physical substrate producing them, and it connects to the Landauer principle through the thermodynamic interpretation of entropy — establishing that information processing has irreducible physical costs.
The limitation for IED purposes: Shannon information theory measures the statistical properties of outputs — how much information they contain — but not whether that information represents genuine adaptation to environmental structure. A system that produces high-entropy outputs is not necessarily more intelligent than one that produces low-entropy outputs; it may simply be less predictable. The IED framework needs a measure of adaptive information processing, not merely information production, which Shannon entropy alone does not provide.
The thermodynamics of computation, developed by Landauer, Bennett, and subsequently by Friston and others in the context of biological systems, establishes that any physical system that updates internal representations based on environmental inputs must pay a thermodynamic cost — and that this cost is bounded below by the Landauer limit per bit erased.5,6,9 Friston's free energy principle formalizes the claim that biological systems minimize surprise (in the information-theoretic sense) through predictive processing — a computational organization that may represent a particularly energy-efficient approach to adaptive information processing.9
The biological brain is the only physical substrate for which we have unambiguous evidence of broad adaptive intelligence — and it is therefore the natural benchmark for an IED comparison. But using the brain as a benchmark requires acknowledging several features of brain energy consumption that complicate the comparison.
The human brain consumes approximately 20 watts of continuous power, representing roughly 20% of the body's resting metabolic rate despite comprising only 2% of body mass by weight.4 This figure is well-established. What is not well-established is how that 20 watts is distributed across cognitive functions — what fraction of brain energy consumption is attributable to "intelligence" in the narrow adaptive sense versus baseline homeostatic maintenance, sensory processing, motor coordination, and other functions that do not require the kind of higher-order adaptive computation that IED is attempting to measure.
Estimates of the computationally relevant portion of brain energy consumption vary substantially in the literature. Synaptic transmission — the mechanism most directly analogous to the logical operations in silicon computing — accounts for roughly 50–80% of brain energy consumption, depending on methodology and brain region.10 But synaptic transmission includes both the "signal" (information-bearing activity) and substantial "noise" (spontaneous activity whose function is debated). The fraction attributable to adaptive intelligence is genuinely uncertain.
The brain's computational architecture offers a second feature relevant to IED: it is highly heterogeneous. Different brain regions perform qualitatively different computations — the visual cortex processes spatial and temporal patterns in ways that differ fundamentally from the prefrontal cortex's role in working memory and executive control — and the energy consumption of each region is matched to the specific computational demands of its function rather than to a uniform architecture. This heterogeneity is one of the features that neuromorphic computing research attempts to replicate, and it may be a significant source of the brain's energy efficiency advantage over uniform silicon architectures.
The five-component model establishes the conceptual chain the IED framework operates within. Matter is the physical substrate — silicon, biological neurons, photonic waveguides, molecular arrays — and constrains efficiency through its physical properties. Energy is the power budget that the substrate consumes during computation. Information is the Shannon-measurable content of system inputs and outputs. Structure is the architectural organization of the substrate — the wiring diagram, the connectivity pattern, the temporal dynamics — that determines how efficiently the substrate can process information. Adaptation is the goal-directed information processing that constitutes intelligence in the narrow sense used here.
IED is defined at the Adaptation level — the ratio of adaptive information processing output to energy consumed — but each lower level constrains what is achievable at the adaptation level. A substrate with high energy costs per information operation (low efficiency at the Energy level) cannot achieve high IED regardless of how well its architecture is organized. A substrate with high energy efficiency but poor architectural organization for the target task (high efficiency at Energy, low at Structure) may also fail to achieve high IED. The framework therefore requires analysis at all five levels, with IED as the integrating metric at the top.
The brain's apparent IED advantage over current silicon systems is not only an engineering observation. It is a biological fact that requires an explanation. Neural tissue is among the most metabolically expensive tissue in the body — consuming approximately 8 to 10 times more energy per unit mass than resting skeletal muscle.4,evo1 This metabolic cost is not incidental. It is a direct selection pressure: organisms that maintain large neural tissue at high metabolic cost must offset that cost with proportionally greater adaptive benefits. Those that do not are at a fitness disadvantage.
This argument, developed in the expensive tissue hypothesis by Aiello and Wheeler and extended in subsequent comparative neuroanatomy, suggests that evolutionary pressure has been operating on the brain's intelligence-energy ratio for hundreds of millions of years.evo2 Not intentionally — natural selection has no foresight and no concept of efficiency ratios — but consequentially: organisms whose neural architecture produced more adaptive behavior per unit of metabolic investment had higher fitness than those whose architecture produced less. Over geological time, this selection pressure has shaped neural architecture toward higher IED.
Three implications follow from the evolutionary argument for the IED framework:
Biological IED may be near a local optimum. If hundreds of millions of years of selection pressure have been operating on intelligence-per-metabolic-cost, the resulting architecture is unlikely to be dramatically suboptimal relative to the physical constraints it operates under. This does not mean biological IED is at the global physical maximum — it may be at a local optimum shaped by the specific constraints of carbon-based biochemistry, aqueous electrochemistry, and body-temperature operation. But it suggests the brain's IED is not merely historically contingent; it is at least locally well-optimized.
Cross-species comparison provides empirical IED data. If evolution has been optimizing toward higher IED under metabolic constraints, comparing IED across species provides independent empirical evidence about the IED landscape. The surprising intelligence of corvids relative to their small brain size, the complex cognition of cephalopods whose neurons are distributed across their arms rather than concentrated in a central brain, and the remarkable capabilities of bees relative to their approximately one milligram brain mass all constitute data points for the IED framework not available from artificial systems. They demonstrate that high IED is achievable across a wide range of architectural implementations.
Convergent evolution provides independent architectural evidence. Complex nervous systems evolved independently multiple times — in vertebrates, in cephalopod molluscs, in arthropods, and in other lineages. The convergent evolution of similar architectural features across these independent lineages — including layered processing, local inhibitory circuits, and spike-based signaling — is evidence that these features represent architectural solutions to the problem of high IED under metabolic constraints. Where independent evolutionary paths converge on similar architectures, those architectures likely represent stable attractors in the space of possible neural designs, and their common features are strong candidates for the structural correlates of high IED that Phase 2 of the research agenda would investigate.
The following table compares estimated IED-relevant parameters across species with documented intelligence. These estimates carry substantial uncertainty — the metabolic attribution problem identified in Section V applies to all species comparisons, and behavioral intelligence measures are not standardized across species. The table is presented as illustrative evidence for the IED research program, not as validated IED measurements.
| Species | Approx. Neurons | Est. Brain Energy (W) | Notable Adaptive Capabilities | IED-Relevant Observation |
|---|---|---|---|---|
| C. elegans (roundworm) | 302 (fully mapped)evo3 | <10⁻⁶ W | Chemotaxis, temperature sensing, simple learning | Complete connectome known; provides a ground-truth lower-bound case for IED research. High IED per neuron relative to computation, but limited total adaptive capacity. |
| Honeybee (Apis mellifera) | ~960,000 | ~10⁻³ W (estimated) | Navigation by sun compass; symbolic communication (waggle dance); abstract concept learning; numerical discriminationevo4 | High intelligence-per-watt relative to mass; complex social cognition at approximately 1 mg brain mass. Strong candidate for high IED relative to energy budget. |
| Common raven / corvids | ~1.5 billionevo5 | ~0.05–0.1 W (estimated) | Tool use; causal reasoning; future planning; deceptive behavior; mirror recognition in some species | Remarkable intelligence relative to brain mass and estimated energy. Lissencephalic cortex with different architecture from primate cortex achieving comparable adaptive outcomes — evidence for the Arrangement Hypothesis. |
| Octopus (O. vulgaris) | ~500 million (60% in arms)evo6 | ~0.1 W (estimated) | Tool use; problem-solving; individual recognition; distributed motor intelligence | Distributed neural architecture — most neurons outside the central brain — represents a fundamentally different structural solution to adaptive intelligence. Evidence that centralized architecture is not required for high IED. |
| Common dolphin | ~37 billion | ~3–5 W (estimated) | Complex social cognition; mirror self-recognition; cultural transmission; cooperative hunting | High absolute intelligence with brain-to-body mass ratio second only to humans among mammals. Consistent with the evolutionary IED optimization argument. |
| Human (H. sapiens) | ~86 billion4 | ~20 W | Language; cumulative culture; abstract reasoning; long-range planning; theory of mind; mathematics | Baseline biological benchmark for IED comparisons. Highest measured adaptive capability at highest documented metabolic cost among the species compared here. |
The five-component model treats Structure as an architectural property of a substrate at a given time — the connectivity pattern and temporal dynamics that determine how efficiently the substrate processes information. This is adequate for substrates with fixed architectures. It may be insufficient for substrates whose architecture changes in response to experience, and this insufficiency may matter for IED comparisons.
The concept proposed here is Structural Adaptability (SA): the capacity of a physical substrate to reconfigure its information-processing architecture in response to experience, rather than merely updating internal state parameters while holding architecture fixed. This is distinct from the Adaptation component of the five-component model. Adaptation describes what the system does with a given architecture. Structural Adaptability describes whether the architecture itself can be modified.
| Substrate | Architecture Fixed? | Structural Adaptability | Notes |
|---|---|---|---|
| Rock / Granite | Yes (effectively) | None | Atomic structure changes only under geological forces; no experience-driven reconfiguration |
| Transistor (fixed logic) | Yes | None | Logic gates execute fixed functions; architecture set at fabrication |
| FPGA | No — reconfigurable by design | Low-moderate | Can reconfigure routing between logic elements; reconfiguration is programmatic, not experience-driven |
| Artificial neural network | Partially — weights update, topology usually fixed | Low to moderate | Backpropagation updates weights; neural architecture search can modify topology; reconfiguration is not continuous or autonomous |
| Biological brain | No — continuously modified | High | Synaptic plasticity; long-term potentiation/depression; dendritic remodeling; neurogenesis in specific regions; operates across timescales from milliseconds to decades |
The biological brain is not merely adaptive in the parameter sense but structurally adaptive. Synaptic connections form, strengthen, weaken, and are pruned in response to experience. Dendritic arbors expand and contract. Myelination changes signal propagation speed. The architecture does not merely run adaptive algorithms — it continuously rewrites itself in response to what it encounters.
Two reasons the hypothesis that SA contributes independently to IED is plausible: First, a substrate that can reshape its information-processing topology to match new environmental structure may require substantially less energy per unit of adaptive output than one constrained to solve every problem with its initial architecture — because topology itself can encode environmental information, reducing the energy required for explicit computation. Second, Structural Adaptability may enable a form of compression unavailable to fixed architectures: rather than storing environmental regularities in parameter values within a fixed network, a structurally adaptive system can encode regularities in topology itself, potentially requiring fewer total parameters to represent the same environmental structure.
If SA contributes independently to IED, comparing biological and artificial systems without accounting for it may systematically misattribute the source of the biological efficiency advantage. Separating SA contributions from fixed-architecture efficiency contributions is part of the Phase 2 research agenda in Section IX.
Consider three physical objects of approximately equal mass:
| Object | Mass | Organizational Complexity | Adaptive Intelligence |
|---|---|---|---|
| Granite block | ~3 kg | Crystalline atomic lattice; minimal hierarchy above atomic scale | None detectable |
| Silicon chip array | ~3 kg | Engineered transistor logic; billions of logic gates in organized computational hierarchy | Moderate — capable of executing complex algorithms |
| Human brain | ~1.4 kg (brain) / ~3 kg (brain + immediate support) | Self-organizing biological network; ~86 billion neurons; ~10¹⁵ synaptic connections; continuous structural modification | High — by every available behavioral measure |
The three objects are composed primarily of the same elements — silicon, oxygen, carbon, hydrogen, trace metals — in broadly similar proportions by mass. The intelligence they support differs by many orders of magnitude. The composition is similar; the organization is radically different.
The Arrangement Hypothesis, as proposed here, is that adaptive intelligence is determined more strongly by the organizational structure of a physical substrate than by its material composition — that it is the arrangement of matter, more than its material nature, that gives rise to intelligent behavior. This observation is not new in philosophy of mind: functionalism holds that mind is a property of functional organization rather than specific biological materials.new3 What the IED framework adds is the question of whether this organizational dependency can be characterized in physically precise, measurable terms.
Three implications for the IED research program: Material substitutability. If intelligence is an organizational property, specific material substrates matter primarily to the extent that they enable or constrain the relevant organizational structures. Biological neurons are not special because they are biological; they are special insofar as they enable organizational structures that silicon cannot currently replicate. The neuromorphic research program implicitly tests this hypothesis. Emergence and complexity. The intelligence difference between granite and a brain is not accountable by any simple additive combination of material properties. Anderson's "More is Different" argument established that new organizational levels give rise to genuinely new physical phenomena not predictable from lower-level descriptions alone.new4 Whether intelligence is emergent in this strong sense — not merely complex but producing qualitatively new causal powers — is an open question the Arrangement Hypothesis motivates. Hierarchical organization. Biological neural architecture is organized at multiple scales simultaneously — from molecular mechanisms at the synapse, to local circuit dynamics, to large-scale network dynamics, to system-level coordination. This multi-scale hierarchy may be a key contributor to the brain's IED advantage, enabling efficient processing at each scale matched to the information structure of inputs at that scale.
The IED framework requires three definitional components: a measure of intelligence output I(s); a measure of energy consumption E(s); and a definition of the ratio IED(s) = I(s) / E(s) for a given substrate s operating on a given task T. Each component faces significant definitional challenges that the paper identifies but does not fully resolve.
The most fundamental challenge for the IED framework is defining I(s) — the intelligence output of a system in a form that is comparable across substrates. For a specific task T with well-defined inputs and outputs (e.g., classifying images, predicting the next token in a text sequence), I(s) can be approximated by a task performance metric — accuracy, perplexity, F1 score — normalized to some baseline. But this approach has three problems: it is task-specific (a system that achieves high I(s) on image classification may achieve very different I(s) on language reasoning); it depends on the task difficulty calibration (accuracy on a trivial task is not comparable to accuracy on a hard task); and it does not straightforwardly extend to general adaptive intelligence (where there is no single well-defined task).
The paper proposes, without claiming to resolve, a definition of I(s) as the information-theoretic mutual information between a system's outputs and the environmental states relevant to its task — normalized by the maximum achievable mutual information given the information available in the inputs. This captures the extent to which a system's outputs actually reflect the environmental structure relevant to its goal, rather than merely its computational activity. The mutual information formulation is both more principled than task-accuracy metrics and harder to measure in practice — particularly for complex real-world tasks where the relevant environmental states are not precisely defined.
The following candidate equations are proposed as research targets, not derivations. They are formalized versions of intuitive claims about intelligence-energy relationships that the IED research program would need to evaluate empirically.
This formulation has the virtue of using only measurable quantities — accuracy and power consumption are both well-defined in principle. It has the limitation that H_task (task difficulty) is not straightforwardly measured and that accuracy is task-specific in ways that complicate cross-domain comparison.
This formulation is more principled — mutual information is a substrate-independent measure of how much the system's outputs reflect the relevant environmental structure — but harder to measure in practice, because Y* (relevant environmental states) must be precisely defined for each task.
This formulation is the most physically principled but requires measuring N_ops — the number of irreversible logical operations — which is straightforward for digital silicon but non-trivial for biological neural systems and for neuromorphic architectures that blur the distinction between logical and physical reversibility.
The IED metric — adaptive intelligence output per unit of energy — addresses one dimension of the efficiency question. A complementary metric deserves consideration: Intelligence Density (ID), which measures adaptive intelligence per unit of mass or volume rather than per unit of energy. The two metrics are related but distinct, and their relationship may itself be informative.
The concept has analogues in physics. Energy density measures energy per unit volume (J/m³). Information density measures bits per unit volume. Computational density measures FLOPS per unit volume. Each captures a different dimension of what a physical system can do within a given material footprint. Intelligence Density would measure adaptive intelligence output per unit mass or volume of the physical substrate:
Three observations motivate treating ID as a potentially independent metric. First, the brain achieves its estimated IED advantage partly through architectural features that depend on the specific spatial organization of approximately 86 billion neurons within a roughly 1.3-liter volume.4 Whether this spatial density is achievable in artificial substrates is a hardware question; whether it matters for intelligence independent of energy efficiency is an ID question distinct from the IED question. Second, current large-scale AI architectures scale intelligence by scaling physical size — more chips, more floor space. If intelligence could be concentrated spatially (high ID) rather than spread across large physical infrastructure, governance implications for capability concentration would be substantially different. Third, IED and ID are not necessarily correlated: a high IED, low energy substrate may be physically large (low ID); a miniaturized, energy-inefficient substrate might achieve high ID despite poor IED. The two metrics capture different efficiency dimensions relevant to different governance and design questions.
The most significant challenge for ID as a rigorous metric is the boundary problem: the brain's volume does not include the metabolic infrastructure sustaining it; a GPU cluster's volume does not include the cooling infrastructure operating it. Whether a consistent, physically principled boundary can be defined that makes ID comparable across substrates is an open methodological question and a prerequisite for ID to function as more than a suggestive analogy.
~20W continuous; ~10¹⁰ neurons, ~10¹⁴⁻¹⁵ synapses. Heterogeneous architecture; spike-based computation; massive parallelism; significant reversible computation. Benchmark substrate for IED comparison. Limitation: energy attribution to adaptive vs. non-adaptive processes remains uncertain.
Leading AI training: 10s to 100s of kilowatts. FLOP/Watt improving ~2× per 2–3 years. Highly optimized for matrix multiplication (the dominant operation in current deep learning). Architecturally uniform. Gap from Landauer limit: ~10 orders of magnitude.
Intel Loihi 2, IBM TrueNorth, SpiNNaker. Spike-based; event-driven; asynchronous. Demonstrated 1,000× energy efficiency improvement over GPU on specific tasks. Early-stage; limited generality. Closest architectural analog to biological neural computation currently implemented in silicon.
Photonic: speed-of-light propagation; potentially high bandwidth-per-watt; limited by photodetection energy costs. Quantum: exponential state space; error correction overhead currently prevents energy efficiency. Both are research-stage for intelligent computation.
Current AI performance benchmarks reward computation: FLOP/Watt, tokens per second, operations per joule. These are well-defined, reproducible, and useful metrics within a single architectural paradigm. They are not measures of intelligence density. The conflation of computation density with intelligence density is the most practically consequential error the IED framework is designed to correct.
| System | Computation Density | Intelligence Density (est.) | Why They Diverge |
|---|---|---|---|
| Calculator | Very high per watt for arithmetic | Near zero | Executes fixed rules; no environmental model; no adaptation; no generalization beyond programmed operations |
| GPU cluster | High — optimized for matrix multiplication | Low to moderate, task-dependent | High throughput; adaptation only through gradient descent on fixed objectives; generalization limited to training distribution |
| Large Language Model | High during inference | Moderate, contested | Apparent cross-domain generalization; limited model updating at inference time; energy cost per adaptive output high relative to biological baseline |
| Biological brain | Low per conventional measure | High by all available behavioral benchmarks | Continuous model updating; structural adaptability; massively parallel heterogeneous processing; energy matched to information content at the individual synapse |
The divergence arises from four features of adaptive intelligence that raw computation metrics do not capture:
Prediction. Adaptive intelligence, as described in Friston's free energy principle, operates by minimizing prediction error — maintaining internal models of the environment and updating them when predictions fail.9 A system computing large volumes of operations to minimize training loss is performing computation; a system maintaining and updating a predictive model of its environment in real time is performing something categorically more relevant to adaptive intelligence. Energy required per unit of prediction error reduction is not the same metric as energy per FLOP.
Compression. Efficient intelligence compresses environmental regularities into compact internal representations.new1 High computation density is consistent with low compression efficiency: a system using many operations to represent a simple regularity is not energy-efficient in the intelligence sense regardless of throughput. The brain's sparse coding literature suggests biological systems achieve substantially higher compression efficiency than current deep learning architectures on equivalent inputs.new2
Adaptation from minimal experience. Few-shot generalization — acquiring new predictive models from very few examples — is a hallmark of intelligent behavior that computation density metrics systematically underweight. A system requiring millions of training examples to learn what a biological system learns from tens is not energy-efficient in the intelligence sense regardless of how efficiently it processes those examples.
Model updating at inference time. Current large-scale AI architectures learn during training and execute during inference; they do not substantially update their world models in real time during deployment. The brain updates continuously. This architectural difference is invisible to computation density metrics but central to the kind of energy efficiency IED attempts to capture.
The research agenda required to make the IED framework empirically useful has three phases. Phase 1 addresses definitional and measurement prerequisites: developing a precise, operationally measurable definition of I(s); establishing a brain energy baseline with appropriate attribution of energy to adaptive versus non-adaptive processes; developing a methodology for task difficulty measurement (H_task); and building the measurement toolkit required to apply the candidate equations to real systems. Phase 1 alone is a multi-year research program at the intersection of neuroscience, information theory, and computer science — and the EM Foundation does not have the laboratory infrastructure to conduct it independently. The Foundation's role is to articulate the research agenda and its governance relevance, not to be the primary executor of the experimental work.
Phase 2 applies the tools developed in Phase 1 to measure IED across physical substrates, test the candidate equations against measured data, identify the architectural features that are strongest predictors of high IED, and validate the falsifiable predictions in Section X. Phase 3 applies the validated framework to hardware design targets, governance metrics for AI sustainability and access, and longitudinal tracking of whether the biological-silicon efficiency gap is narrowing over time.
A framework that makes no falsifiable predictions is not a scientific contribution — it is a taxonomy. The IED framework proposes five falsifiable predictions. These are not claims the Foundation asserts to be true; they are claims that the IED framework implies and that empirical research could confirm or refute. If the predictions fail, the framework requires revision; if they hold, the framework gains evidential support.
Section X presents falsifiable predictions — claims the IED framework implies that experiment could confirm. This section does something different and equally necessary: it states explicitly the conditions under which the Foundation would conclude the IED framework is not merely unconfirmed but wrong, and should be abandoned or fundamentally revised. A research program that cannot specify what would falsify it is not a scientific research program. The following conditions are organized by the framework component they would falsify. Each specifies what would need to be measured, what result constitutes falsification, and what the falsification would imply.
Measurement required: IED using Candidate Equations 1 and 2 applied to matched pairs of systems with well-documented performance differences on identical tasks.
Falsification result: If measured IED consistently fails to rank systems in the same order as independent behavioral assessments of adaptive intelligence across matched tasks — if the IED metric places the lower-performing system higher on efficiency — the metric is not measuring what it claims. This is the most severe possible falsification result.
Implication: The definitional framework for I(s) requires fundamental revision. The IED research program, as specified, must be substantially redesigned.
Measurement required: IED₂ (mutual information formulation) computed for the same substrate on qualitatively different task domains with matched difficulty.
Falsification result: If IED₂ for the same substrate varies by more than two orders of magnitude across domains, this falsifies the claim that mutual information IED captures a substrate-level property rather than a task-specific one. A substrate with genuinely high intelligence-energy density should exhibit consistently elevated IED across domains.
Implication: Candidate Equation 2 requires revision or replacement. Candidate Equation 1 (task accuracy) may be more appropriate despite lower theoretical elegance.
Measurement required: Systematic comparison of IED across artificial architectures differing in organizational complexity — connectivity graph entropy, hierarchical depth, Structural Adaptability SA — while holding material substrate and energy budget constant.
Falsification result: If organizational complexity measures are not positively correlated with IED across architectures within the same substrate class — if randomly organized networks achieve equivalent IED to hierarchically organized ones of the same size and energy budget — the Arrangement Hypothesis is falsified.
Implication: The brain's IED advantage may be attributable to material properties of biological neurons rather than their organizational structure, requiring a fundamentally different theoretical framing for the IED research program.
Measurement required: IED comparison between two systems matched on architecture and energy budget but differing in Structural Adaptability — a static network versus an equivalent network with dynamic connectivity that reconfigures in response to experience.
Falsification result: If systems with high SA do not demonstrate systematically higher IED on tasks requiring adaptation to novel environmental structure — if the energy cost of structural reconfiguration is not offset by efficiency gains in adaptive performance — SA does not contribute independently to IED.
Implication: Structural Adaptability should not be treated as a distinct variable in the framework. The five-component model should not be extended to include it as a sixth variable.
Measurement required: Brain energy consumption with full embodiment costs included (metabolic infrastructure; developmental energy amortized over lifespan) compared to silicon systems with equivalent embodiment costs (cooling infrastructure; fabrication energy; training energy amortized over deployment lifetime), using a consistent and principled accounting methodology.
Falsification result: If the biological-silicon IED gap narrows to less than one order of magnitude under comprehensive embodiment accounting, the apparent IED advantage of biological systems is largely an artifact of selective accounting rather than genuine substrate efficiency.
Implication: All comparative IED estimates in this paper require revision. The framework is not falsified conceptually, but every specific comparative claim must be revised to reflect the full lifecycle accounting methodology.
Measurement required: The relationship between IED and model scale for current silicon architectures, tracking whether IED improves as model size increases while holding architecture constant.
Falsification result: If IED for silicon transformer architectures scales positively with model size at a rate projecting to biological IED levels within two to three orders of magnitude of scale increase — without architectural change — this falsifies the prediction that achieving biological IED requires architectural innovation rather than scale.
Implication: The IED gap is primarily a scale gap, not an architecture gap. The Arrangement Hypothesis's emphasis on heterogeneity and hierarchy is misplaced. This would substantially revise the framework's implications for hardware design and the research agenda in Section IX.
The following criticisms represent the strongest objections to the IED framework as proposed. They are presented not to be dismissed but to be engaged — because a framework that cannot withstand the strongest version of these criticisms does not warrant the research investment the roadmap proposes.
The most fundamental criticism of the IED framework is that comparing biological intelligence and artificial intelligence on an efficiency metric may be a category error — that "intelligence" as instantiated in biological neural systems and "intelligence" as instantiated in transformer architectures are not the same kind of thing, and that measuring both against the same metric is like measuring the efficiency of a bicycle and a boat in terms of speed on water. A bicycle appears inefficient on a metric designed for boats, but this tells us nothing about bicycle design.
The Foundation takes this criticism seriously. The response is not that the category error objection is wrong — it may well be correct — but that answering the question of whether it is correct requires precisely the kind of rigorous cross-substrate comparison the IED framework proposes. The category error objection is itself a falsifiable claim: if biological and artificial intelligence produce comparable adaptive outputs (measured by mutual information or task performance) using radically different energy budgets, this is at minimum evidence that they are solving the same problem differently, and at most evidence that they are solving categorically different problems that happen to produce similar outputs. The IED framework is designed to distinguish these possibilities.
Shannon information theory was developed to characterize communication channels, not intelligent systems. The mutual information formulation of I(s) — measuring the mutual information between system outputs and environmental states — may capture statistical regularity without capturing the aspects of intelligence that matter most: understanding, reasoning, creativity, moral judgment. A system that produces outputs highly correlated with environmental states through brute-force pattern matching is not, intuitively, as intelligent as a system that produces the same outputs through principled reasoning.
This criticism identifies a genuine limitation. The Foundation's response: the IED framework does not claim to measure intelligence in all its dimensions — it claims to measure one specific, precisely defined, physically grounded aspect of intelligence (adaptive information processing efficiency). The framework is useful for the governance and hardware design purposes identified in Section II even if it captures only this one dimension. If a richer theory of intelligence emerges that allows more dimensions to be compared across substrates, the IED framework should be extended to incorporate it.
The estimates of brain energy consumption used in Section V are themselves contested. The ~20 watt figure is well-established for total brain energy consumption. The attribution of this consumption to specific cognitive functions — and specifically to the "adaptive intelligence" component relevant to IED — is not well-established, and estimates in the literature vary by orders of magnitude depending on methodology, brain region, and the definition of "cognitive work." Comparisons of brain and silicon efficiency that use total brain energy as the denominator may systematically understate the brain's effective efficiency on specific tasks, or overstate it depending on how cognitive overhead is attributed.
The Foundation acknowledges this limitation explicitly. It is the primary reason Phase 1 of the research roadmap requires establishing a brain baseline with appropriate energy attribution before cross-substrate comparisons can be made meaningfully. The estimates in Figure 2 should be treated as order-of-magnitude orientation, not as precise measurements — and the IED framework's usefulness is contingent on Phase 1 producing better measurements.
A reasonable critic would argue: the governance relevance of the IED framework is contingent on the framework being validated — and the roadmap proposes that validation requires a multi-year multi-institution research program that the Foundation is not positioned to lead. An unvalidated framework with governance pretensions but no empirical support does not advance governance; it provides the rhetorical form of scientific support without the substance.
This is the strongest criticism and the one the Foundation finds hardest to fully answer in this paper. The response: the IED framework has governance relevance even at the pre-validation stage as a structuring device for questions that governance frameworks need to ask. The question of whether AI efficiency is converging on biological efficiency, whether the biological-silicon gap is closing, and what architectural features explain efficiency differences are governance-relevant questions regardless of whether the IED metric is ultimately the right one to measure. The framework provides a vocabulary for asking these questions more precisely; the validation determines whether that vocabulary is also correct.
Four specific governance applications become tractable if the IED framework is validated — worth articulating even now so that governance frameworks can be designed to accommodate them when validation occurs:
Sustainability assessments. Current AI energy consumption is assessed in absolute terms. A validated IED metric would allow energy consumption to be assessed relative to intelligence output — enabling sustainability assessments that ask not only how much energy an AI system consumes but how efficiently that energy is converted into adaptive intelligence. This allows governance frameworks to distinguish energy-intensive systems that are genuinely more capable from those that are computationally wasteful, and to incentivize efficiency improvement as a governance objective alongside absolute consumption reduction.
AI deployment policy. Deployment policies requiring a sufficient benefit-to-cost ratio need a metric for "benefit" beyond task-performance benchmarks. IED applied at the deployment level could provide a principled efficiency metric for comparing the adaptive value delivered against energy cost — enabling policies that favor high-IED systems over low-IED systems consuming equivalent energy for equivalent tasks.
Infrastructure planning and capability concentration analysis. If advanced AI capability requires high energy consumption because current architectures have low IED, the geography and economics of energy infrastructure directly shapes the geography of AI capability. A validated IED trajectory — tracking whether the biological-silicon gap is closing — would allow governance frameworks to anticipate when energy infrastructure constraints on AI capability are likely to change. A world where neuromorphic substrates close most of the IED gap is a world where capable AI becomes accessible to actors without data center infrastructure — with significant implications for capability concentration governance.
Connection to the Foundation's governance architecture. The EM Foundation's AI Assessment Index evaluates systems on behavioral governance dimensions defined in the EM-IAF: accuracy, hallucination resistance, fairness, manipulation resistance. IED operates at a different level — the physical substrate beneath behavior. Behavioral governance determines whether outputs are trustworthy; physical governance determines the energy and infrastructure requirements of the systems producing them. A complete AI governance framework eventually requires both levels. The IED research program is the Foundation's contribution to establishing the physical substrate layer.
This section makes no claims. It asks a question the IED research program exists to make investigable.
Physics has found that several phenomena previously treated as descriptive — heat, entropy, information — are precisely measurable physical properties subject to universal laws. Thermodynamics is not a description of specific heat engines; it is a universal theory of energy transformation. Information theory is not a description of specific communication systems; it is a universal theory of uncertainty reduction. Each field began with practical measurement problems and ended with fundamental physical theories.
The question this paper raises — but explicitly does not answer — is whether intelligence might eventually become a measurable physical property in the same sense. Not intelligence as a psychological concept or engineering performance metric, but intelligence as a physical property: a quantifiable feature of physical systems constrained by universal laws, comparable across substrates, subject to theoretical unification.
What would be required scientifically? At minimum, four conditions:
A substrate-independent definition of intelligence. The mutual information formulation proposed here is a candidate. Whether this narrow definition can be broadened to capture dimensions of intelligence that matter most without losing measurability is the foundational question.
A conserved or bounded physical quantity. Physical laws typically describe conserved quantities (energy, momentum) or bounded ones (entropy in closed systems). Whether there is a conserved or bounded quantity governing intelligence — an "intelligence budget" analogous to an energy budget — is not established but implied by the thermodynamic arguments in Section IV.
Universal applicability across substrates. A physics of intelligence would need to apply to biological neural systems, silicon architectures, and any future substrate — just as thermodynamics applies to steam engines, refrigerators, and black holes. The IED framework's substrate-independence is a prerequisite for this applicability, not yet an achievement of it.
Falsifiable predictions derivable from first principles. The test of a physical theory is predictions confirmable or refutable by experiment. The five falsifiable predictions in Section X are a first step; a physics of intelligence would need to derive them from physical principles rather than proposing them as empirical regularities to be tested.
The IED research program is not a physics of intelligence. It is, at best, a preliminary program for determining whether the conditions for such a physics could be met. The Foundation presents this framing not to overstate the program's current status but to be explicit about the intellectual ambition motivating it. A framework that could make intelligence a measurable physical property would be among the most consequential scientific contributions of the century. That is a reason for scientific humility about what the IED framework currently achieves — and a reason the research agenda it proposes is worth pursuing rigorously.
If no principled cross-substrate intelligence-efficiency framework is developed, the governance and hardware design communities will continue to work with efficiency metrics that measure computation rather than intelligence — FLOP/Watt, tokens/Watt — that are internally consistent within architectures but not comparable across substrates. This means that claims about the efficiency of neuromorphic versus silicon architectures, or about the sustainability of AI energy consumption relative to biological alternatives, will continue to be made without a common metric that would allow them to be evaluated.
More significantly for the Foundation's governance agenda: the question of whether advanced AI systems are converging on the energy efficiency of biological intelligence — and therefore whether the energy constraints that currently limit AI capability will become less binding — is one of the most consequential questions for the long-run governance of AI. An AI development trajectory in which energy efficiency improves by several orders of magnitude has radically different governance implications than one in which current efficiency levels persist. Without the IED framework or an equivalent, this question will be answered — if at all — by hardware developers with commercial interests in the answer rather than by independent research with governance interests in the question.
The Foundation does not claim that IED is the only or necessarily the best framework for addressing these questions. It claims that the questions are consequential for governance and that the absence of any principled cross-substrate efficiency framework for intelligence represents a gap in the research infrastructure that governance depends on.
This paper does not claim that Intelligence-Energy Density is a validated scientific theory. IED is a research program, a set of candidate definitions and equations, and a framework for asking questions more precisely. It is not a law, an established measurement, or a validated theory. Every equation in Section VII is labeled as a candidate, not a derivation.
This paper does not claim that biological intelligence is superior to artificial intelligence on any dimension other than the specific energy efficiency comparison proposed. The brain is used as a benchmark because it is the only substrate for which we have unambiguous evidence of broad adaptive intelligence at low energy cost. This is not a normative claim about the superiority of biological systems.
This paper does not claim that the Landauer limit is a realistic target for intelligent systems. The Landauer limit is the theoretical minimum energy per bit of irreversible computation. It is used in the paper as a reference point for comparing substrate efficiencies, not as a realistic engineering target.
This paper does not claim that the category error objection to IED is wrong. The comparison between biological and artificial intelligence may involve category errors that the IED framework cannot eliminate. This objection is taken seriously in Section XII and is not resolved.
This paper does not claim that current AI systems are comparable to biological intelligence on any dimension. The comparison proposed is directional — can biological and artificial intelligence be compared on energy efficiency? — not evaluative — which is more intelligent? The paper explicitly brackets questions of consciousness, moral status, and general intelligence that are discussed in the Trust Infrastructure essay and other Foundation documents.
The following questions represent the deepest unresolved issues for the IED research program. They differ from the Open Questions above — which address specific methodological challenges — in that they concern the conceptual foundations on which any answer to those methodological questions ultimately depends. They are offered not as admissions of failure but as the honest accounting of what a genuinely foundational research agenda requires.
The framework is pre-empirical. No measurements using the proposed IED metrics exist. The framework is a proposal for how such measurements might be made, not a report of measurements already conducted. All figures and comparisons in this paper are estimates or conceptual illustrations, not data.
The brain baseline is uncertain. The energy attribution problem identified in Section V — how much of the brain's 20 watts is attributable to adaptive intelligence versus non-adaptive processes — is unresolved. This uncertainty propagates into all comparisons between biological and artificial systems and substantially limits the precision of any cross-substrate efficiency claim.
The operational definition of intelligence is narrow and contestable. The adaptive information processing definition used throughout this paper is chosen for measurability, not for completeness. It excludes dimensions of intelligence — understanding, reasoning, creativity — that many researchers consider central. The Foundation's choice to focus on measurable dimensions reflects the constraints of the IED framework, not a claim that unmeasurable dimensions are unimportant.
The governance relevance is indirect. The IED framework's governance implications depend on the framework being validated and on the validated results being meaningful for governance decisions. An unvalidated framework's governance implications are, strictly speaking, speculative — the Foundation acknowledges this and presents the governance argument as motivation for the research agenda rather than as a conclusion from it.
Physics sets limits on what intelligence can cost. Information theory provides a substrate-independent language for describing what intelligence produces. The gap between these two disciplines — the absence of a principled, empirically grounded framework for comparing adaptive intelligence across physical substrates in terms of energy efficiency — is real, and it matters.
It matters for hardware design: if the features of biological neural architecture that produce high intelligence-energy density can be identified and replicated in artificial substrates, the energy constraints that currently limit AI capability may become substantially less binding. It matters for sustainability: a principled metric for intelligence-per-watt would allow the efficiency trajectory of AI systems to be tracked against a meaningful physical reference point rather than against shifting benchmarks within a single architectural paradigm. And it matters for governance: the question of whether capable AI is converging on biological energy efficiency levels — and therefore who can afford to develop and deploy it — is a governance question that current efficiency metrics are not designed to answer.
The IED framework proposed here does not resolve these questions. It proposes a conceptual structure within which they can be asked more precisely, a set of candidate equations that operationalize the comparison, five falsifiable predictions that distinguish this framework from untestable speculation, and an explicit account of the criticisms and limitations that a rigorous development of the framework would need to address. It is offered as a starting point for a research agenda, not as an endpoint of one.
The central question of this research program is not which material computes most efficiently. The deeper question is whether intelligence itself possesses measurable physical properties independent of the substrate in which it is instantiated. If so, future science may discover that intelligence is not merely a psychological phenomenon or an engineering outcome, but a physical phenomenon — constrained by energy, information, structure, and adaptation in ways that obey discoverable regularities. The purpose of the IED framework is not to answer that question. It is to provide a path by which it might eventually be investigated rigorously, transparently, and with the scientific humility a question of this magnitude requires.
The honest conclusion is also the appropriate one for a framework at this stage of development: the Foundation believes the IED research agenda is consequential and that the questions it addresses cannot be responsibly avoided as AI capability and energy consumption both continue to grow. It does not claim to have answered those questions.