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If the brain were so simple: Information-based drivers of intelligence and their interaction through an n-body-inspired framework

Brett J. Kagan, Johnson Zhou, Forough Habibollahi, Valentina Baccetti

arXiv:2610.11142v1q-bio.NCcs.ITmath.ITnlin.AOphysics.bio-ph

TL;DR

The paper addresses limits in explaining why neural systems seek structured information and how simpler systems show adaptive behavior. It proposes information enthalpy as a complementary driver to the FEP and defines a metric for estimating structured information in signals; the reported examples show IEP sensitivity to structure in synthetic and stimulus-driven spiking data.

  • Problem

    The authors identify gaps in explaining why systems seek complex, structured input and how simple neural systems display adaptive behavior within FEP-based accounts.

    Source: §1.4 · p. 4

  • Method

    The paper proposes information enthalpy as an internal resource of structured predictive information and defines IEP using entropy-weighted redundancy and multiscale statistical complexity.

    Source: §3 · p. 18

  • Results

    IEP is sensitive to intrinsic multiscale structure in fractal-derived rasters and to subtler structure in realistic stimulus-driven spiking data.

    Source: §4.1 · p. 21, §4.2 · p. 22

  • Takeaways & Limitations

    The authors propose information enthalpy maximization as a complementary normative driver to FEP-based free-energy minimization.

    Source: §6 · pp. 28–29

    The authors note that FEP-based accounts relying on complex generative models may not explain adaptive behavior in simpler systems such as insects or in-vitro neural cultures.

    Source: §1.4 · p. 4

Abstract

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Theories of how the brain processes information and returns intelligent outputs are numerous and often difficult to conclusively test. Here, we consider an approach grounded in informatics and algorithmic thermodynamics for how neural systems respond to different patterns of information in different ways, with a focus on the relationship between the information entropy of a signal and a new proposed quantity we term information enthalpy, which represents the internal resource of structured information within a system available to be used for predictions and other forms of work. To evaluate the capacity of the external signals to increase information enthalpy in the system, we introduce the information enthalpy potential (IEP) as a defined metric. We propose and implement a method for quantifying the amount of potential information enthalpy - the IEP - in a given signal across a range of example signals. We offer a conjecture of how information enthalpy may be treated by neural systems within a biological framework before showing how it may integrate and offer falsifiability to existing approaches such as the Free Energy Principle. This framework is also positioned in light of the role of neural criticality. Finally, we postulate a testable and falsifiable framework where the distinct mechanisms within each driver interact through a described n-body-inspired model to govern the "motion" of a neural system through a high dimensional state-space. Through these processes, it is proposed that these features form the most fundamental basis of the neural drivers that give rise to the complexity of adaptive behaviors that are commonly called: intelligence.

1 Introduction

The introduction proposes an integrated, testable account of intelligence that links information processing to neural structure and function. It positions information enthalpy as a complement to the Free Energy Principle (FEP), addressing gaps the authors identify in explaining complex structured-input seeking and rudimentary adaptive behavior.

1 Introduction

  • The paper proposes a testable, falsifiable framework integrating information-processing drivers to connect neural structure and function.It aims to integrate, rather than discard, existing theories where evidence supports them.Source: §1 · p. 1

1.1 Information-based drivers of information processing and intelligence

  • The authors ask whether neural systems respond to broad structural properties of information, beyond fixed reactions to specific stimuli.They motivate a bottom-up account with information structure and complexity, rather than reward mechanisms alone, as potential drivers of adaptive responses.Source: §1.1 · p. 2

1.2 Active Inference and Markov Blankets as Processes

  • Active inference describes organisms as controlling action-perception loops and inferring hidden states through internal generative models, with Markov blankets separating internal from external states.The FEP is presented as the principal normative framework for these processes.Source: §1.2 · pp. 2–3

1.3 The Free Energy Principle as a normative principle

  • The FEP proposes that self-organizing systems minimize variational free energy, an upper bound on sensory surprise, through action or improved prediction.The introduction notes that FEP accounts often rely on ergodicity to connect ongoing sensory experience to long-term average surprise.Source: §1.3 · p. 3

1.4 Questions about FEP, information enthalpy, and neural criticality

  • The authors argue that FEP alone does not explain why systems seek complex input or how simpler systems exhibit adaptive behavior, and propose information enthalpy as a complementary driver.Information enthalpy is structured information available for future work; the proposal links structured environmental input to maintaining criticality and avoiding both noise and predictable stasis.Source: §1.4 · pp. 4–5

2 Information Enthalpy

This section formalizes information enthalpy as structured information acquired through system–environment interactions and available for prediction and self-regulation, alongside multiscale acquisition and predictive-information capacity. It describes how storage and throughput constraints, evolving statistical context, and proposed inflow and outflow mechanisms shape this resource over time.

2 Information Enthalpy

  • The framework encodes joint past observations, internal states, and actions into a causal, pooled information-storage state rather than retaining the raw interaction history.The pool is a processed representation from which information relevant to future operation can be extracted.Source: §2 · p. 6
  • The retention timescale Tcap,t = 1/αt sets the historical depth a system can maintain, and bounds its predictive horizon.The text treats this as a state-dependent upper time bound; a zero retention window would sharply reduce predictive capability.Source: §2 · p. 8
  • Shannon entropy alone does not distinguish predictive information from redundancy or encoder-induced variability, and these categories are conceptual rather than additive entropy components.The framework identifies useful, redundant, and noise-related information as distinct factors underlying storage-state entropy.Source: §2 · p. 9

2.1 Information Enthalpy Acquisition

  • Information enthalpy is a resource for predicting future sensory inputs and selecting actions, as well as changing internal states to self-regulate.Its accumulation requires ongoing integration of historical sensory inputs and system states.Source: §2.1 · p. 9

2.1.1 Information throughput capacity.

  • Information inflow into each storage process cannot exceed throughput capacity, and its state entropy cannot exceed the actively maintainable storage capacity.These flow and storage limits define which information-storage processes are admissible.Source: §2.1.1 · p. 10

2.1.2 Scale Resolved Directed-Information Rate.

  • The scale-resolved directed-information subsection opens by referring to the baseline directed-information rate R(n).Source: §2.1.2 · p. 10
  • Multiscale structured-information throughput is bounded by system throughput capacity and by Γt, the signal-dependent fraction of capacity available for structured information.The scale-resolved rates are aggregated across macroscopic scales; Γt bounds the fraction that can be occupied, not the amount necessarily acquired.Source: §2.1.2 · p. 11

2.2 Predictive content of information-storage pool and information enthalpy

  • Predictive content is measured across weighted future horizons, conditioning on the planned actions to exclude future components predictable from those actions.The furthest horizon is bounded by the stored information’s maximal past temporal reach, Tcap,t.Source: §2.2 · pp. 11–12
  • The predictive-resource hypersurface defines upper predictive-information capacity under throughput, storage, and signal-structure constraints; it is non-decreasing in both capacities and concave in throughput.Information enthalpy scales that capacity by κ; κ is a dimensional factor, not a claim that predictive information becomes energy, and may be thermodynamic or biologically determined.Source: §2.2 · pp. 12–13

2.3 Biological Constraints on Information Enthalpy

  • Biological energetic and homeostatic constraints restrict attainable storage processes and information enthalpy, but do not directly dissipate information enthalpy.Homeostatic deviations beyond tolerance incur an energetic penalty; neural activity, plasticity, and action also draw on finite metabolic supply.Source: §2.3 · p. 14

2.4 Changes in Information Enthalpy

  • Information enthalpy may change with throughput and storage capacities, structured information in incoming signals, and energy available for biological processes.These constraints are collected into a generalized constraint vector.Source: §2.4 · pp. 14–15
  • Constraint-specific finite changes have conjugate predictive-resource forces, but coupled constraints require a specified path and cannot generally be summed independently.For throughput capacity, the force βt is non-increasing under the assumed concavity, indicating diminishing returns; no such general diminishing-returns assumption is made for storage capacity. The throughput-then-storage decomposition can yield different individual contributions if the order is reversed, though their sum remains the same.Source: §2.4 · pp. 15–16
  • The framework relates structured-information availability Γt to the IEP but specifies neither an explicit dependence of predictive capacity on Γt nor a law governing its changes.The value of the Γt-associated force may depend on processing capacities and energetic constraints; a time-resolved IEP is proposed as a possible future extension.Source: §2.4 · p. 16
  • Energy-budget effects are left system-dependent, while total predictive-capacity change separates evolving past–future statistics at fixed constraints from constraint changes at fixed statistics.The energy-budget dependence is not specified because it depends on the system’s metabolic properties; the framework notes that energetic efficiency could also be incorporated.Source: §2.4 · pp. 16–17

2.5 Changes in predictive-information resource hI

  • Predictive-information inflow is illustrated as proportional to structured-information rate, but conversion efficiency may vary with intrinsic mechanisms and available metabolic resources, and the dependence may be nonlinear.The conversion fraction ηt lies between 0 and 1; insufficient energy can lower it.Source: §2.5 · p. 17
  • The proposed phenomenological balance law accounts for predictive-information change through acquisition and four forms of loss, while requiring their net contribution to recover the defined change.The losses are passive degradation, loss through use, maintenance loss under insufficient metabolic resources, and contextual loss when environmental structure changes. The balance law is a decomposition, not an independent definition of the resource.Source: §2.5 · p. 17

3 Information Enthalpy Potential

The Information Enthalpy Potential (IEP) is proposed as a dimensionless measure of structured information in an input signal that could contribute to predictive resources. It combines entropy-weighted redundancy with statistical complexity across scales.

3 Information Enthalpy Potential

  • The method converts a signal into a symbolic sequence, weighting symbols by permutation statistical complexity to accentuate organized regimes before calculating IEP.For raster data, patches are pooled, thresholded, and flattened into symbols; the weighting preserves chronological order.Source: §3 · pp. 18–19

3.1 Entropy-Weighted Shuffled Lempel-Ziv Complexity and Redundancy Score

  • The entropy-weighted redundancy score compares Lempel-Ziv phrase counts in the sequence and shuffled surrogates, then uses token entropy to down-weight trivial, low-variety structure.The shuffled sequence preserves the token histogram while destroying temporal dependence.Source: §3.1 · p. 19

3.2 Multi-scale statistical complexity

  • Multiscale complexity measures structural persistence by shuffling contiguous blocks at different sizes and integrating scale-conditional redundancy across a logarithmic scale grid.Small blocks disrupt local structure, while large blocks preserve local structure but scramble larger-scale order.Source: §3.2 · p. 20

3.3 Information Enthalpy Potential

  • IEP combines entropy-weighted redundancy and multiscale statistical complexity to quantify structured information a system might acquire from a signal.The mixing weight β balances these components.Source: §3.3 · p. 20

Hyperparameter roles and interactions

  • IEP hyperparameters jointly shape tokenization, symbol weighting, and the balance between local redundancy and multiscale organization.Changing tokenization or PSC parameters alters the sequence on which both component scores are computed.Source: Hyperparameter roles and interactions · p. 21

4 Assessment of IEP as a metric of Spatiotemporal Complexity

The authors assess IEP on synthetic fractal rasters and speech-driven spike rasters, comparing originals with controls that disrupt structure while preserving selected marginal statistics. Originals generally score above controls, though some simpler synthetic sequences show comparable scores.

4 Assessment of IEP as a metric of Spatiotemporal Complexity

  • The assessment uses fractal-derived and biologically realistic spiking data, with surrogate controls that progressively disrupt structure while preserving different marginal statistics.Controls include within-channel time permutations, global-rate Bernoulli rasters, and full permutations.Source: §4 · p. 21

4.1 Fractal-driven spike rasters from synthetic geometries

  • Original fractal rasters usually score higher than surrogate controls, while some simpler or more homogeneous hand-crafted sequences have comparable scores.The results are interpreted as sensitivity to intrinsic organization rather than firing-rate statistics alone.Source: §4.1 · pp. 21–22

4.2 Auditory-driven spike rasters from the Spiking Speech Commands (SSC) dataset

  • Across words, original speech-driven rasters show consistently elevated IEP relative to surrogate groups, demonstrating sensitivity to subtler structure in high-dimensional auditory data.The signals come from 700-channel Spiking Speech Commands representations.Source: §4.2 · p. 22
  • Permute-time controls occasionally retain non-negligible IEP when preserved channel firing rates retain spatial heterogeneity; global Bernoulli and full-permutation controls yield effectively zero.This occurs particularly in fractal-driven rasters.Source: §4.2 · p. 22

5 How do different drivers of intelligence interact?

The section frames neural intelligence as emerging from interacting physical subsystems, timescales, and information-based drivers. It proposes that entropy, information enthalpy, and criticality jointly shape neural dynamics.

5 How do different drivers of intelligence interact?

  • Original fractal-derived and auditory spike rasters tend to score higher IEP than surrogate controls, consistent with sensitivity to multiscale and spectrotemporal structure.The controls include per-channel temporal shuffling, global-rate Bernoulli spikes, and full shuffling.Source: Figure 5 · p. 23, Figure 6 · p. 24

5.1 The brain consists of multiple interrelated interacting physical structures that operate across timescales.

  • Neural intelligence spans nested dendritic, somatic, and network systems with distinct dynamics and timescales, so anatomical hierarchy alone is insufficient.The section argues that interactions across physical levels and temporal scales must be considered together.Source: §5.1 · pp. 25–26

5.2 The interaction of systems across timescales supports adopting n-body-inspired system modeling

  • Three proposed drivers—information-enthalpy maximization, free-energy minimization, and criticality maintenance—interact across neural systems to shape their states.The framework treats these influences as a nonlinear, n-body-inspired interplay rather than a sum of independent drivers.Source: §5 · p. 22, §5.2 · p. 26

5.3 Relationship between Information Entropy, Information Enthalpy and Neural Criticality

  • Information entropy represents input uncertainty and prediction-related surprise, while information enthalpy is the system’s predictive-information resource capacity, balancing information quality and quantity.The authors hypothesize that useful, nonredundant information supports predictive capacity, whereas redundant information can consume resources without adding predictive utility.Source: §5.3 · pp. 26–27
  • Critical dynamics combine variability with long-range organization, and the authors hypothesize that sufficiently high, high-quality information enthalpy supports dynamics near criticality.They distinguish depleted capacity and abundant low-quality information as regimes that may not sustain critical-like dynamics.Source: §5.3 · p. 27
  • The authors hypothesize that high-IEP structured input can move neural dynamics toward a near-critical regime, while spontaneous dynamics explore a landscape of distinct regimes.The proposed landscape includes subcriticality, supercriticality, hypersynchrony, decoupled noise, and an unstable near-critical regime.Source: §5.3 · p. 27

6 Discussion

The discussion presents the framework as a conceptual stepping stone toward explaining intelligence, with testable predictions and proposed extensions to free-energy accounts. It emphasizes that other drivers may exist and that detailed biophysical interactions remain beyond this paper’s scope.

6 Discussion

  • The paper does not fully answer how intelligence arises, but presents a conceptual framework with four falsifiable implications.The proposed tests concern input IEP and criticality, sensitivity near the order–disorder boundary, throughput capacity, and the n-body formulation.Source: §6 · pp. 27–28
  • Information enthalpy is proposed as a complementary, interacting normative principle to free-energy minimization in active inference.The authors suggest this may simplify FEP accounts that require complex generative models to explain behavior.Source: §6 · pp. 28–29
  • The framework allows for additional drivers, proposing information-enthalpy maximization and free-energy minimization as primary and criticality maintenance as secondary.The authors describe exact biophysical interactions as beyond this paper’s scope, while proposing that drivers can be measured and manipulated under controlled conditions.Source: §6 · p. 29

Declarations

The authors disclose industry ties involving Cortical Labs and state that data and code will be made publicly available after peer-review.

Declarations

  • Four authors are Cortical Labs employees and may hold shares or another interest in the company, which works in a related space and holds related patents.The authors report no specific incentive for any author’s contribution.Source: Declarations · p. 29

Data and Code Availability

A.1 Information-storage dynamics and historical capacity depth

The proposed storage model treats information retention as a changing historical capacity, with a minimum retrospective window and a prospective horizon bounded by retained history. A ceiling on storage is also used to define effective throughput capacity.

A.1 Information-storage dynamics and historical capacity depth

  • The system’s cache is modeled as fading memory, using a linear time-varying difference equation.The proposed analogies are a leaky reservoir, varying capacity, and an RC circuit with varying resistance.Source: §A.1 · p. 38
  • Capacity build, pruning, and passive decay rates govern storage dynamics, while a minimum retrospective window prevents a zero-horizon state as Cst,t approaches zero.The window is described as a baseline for bootstrapping predictive generative models and for active-inference policy selection.Source: §A.1 · p. 38
  • Prospective policy depth is constrained by retained history, with the prospective horizon H bounded by retrospective capacity Tcap,t.The authors describe this as a path-dependent conditional optimization.Source: §A.1 · p. 38
  • A fixed storage ceiling modifies the capacity dynamics, and retention depth is then calculated using effective capacity in place of Cr,t.The text introduces effective throughput capacity in this capped-storage setting.Source: §A.1 · p. 38

A.2 Information rate

This subsection defines the long-term average rate of directed information as a limit, when the limit exists, and notes how it is evaluated under a finite temporal bound.

A.2 Information rate

  • The long-term average rate of directed information is defined as a limit, whenever that limit exists.Source: §A.2 · p. 38
  • In practice, evaluation is bounded by the system's finite temporal limit Tcap(t).Source: §A.2 · p. 38
  • At time t, the long-term average rate is evaluated with T approaching Tcap,t.Source: §A.2 · p. 38

A.3 Homeostatic penalty

The section gives a homeostatic penalty example that remains negligible within a tolerance radius and increases smoothly as deviations exceed it.

A.3 Homeostatic penalty

  • The penalty remains negligible while homeostatic deviation ht is below tolerance radius htol.Source: §A.3 · p. 39
  • Beyond htol, growth exponent p sets how steeply the penalty increases, while γ sets its gain.Source: §A.3 · p. 39
  • A softplus function provides a smooth, increasing penalty, with σ controlling smoothness.Source: §A.3 · p. 39

A.4 Setup and symbolization

The signal is represented as a binary channel-by-time raster, then converted into a scale-dependent sequence of tokens through patching and occupancy pooling. Patch overlap and token granularity can be adjusted to capture structure at different scales.

A.4 Setup and symbolization

  • The method represents a signal of any dimensionality, but demonstrates IEP using a 2D binary raster of channels by time, suitable for patterned stimulation.Source: §A.4 · p. 39
  • Patch dimensions Cp × Tp set the observation scale, while strides sc and st determine patch start positions along channel and time coordinates.Source: §A.4 · p. 39, Figure 8 · p. 39
  • Choosing patch dimensions at least as large as the strides creates overlap, preserving spatial and temporal correlations across patches.Source: §A.4 · p. 39
  • Each patch is block-pooled using sizes pc and pt and threshold θ; pooled bits form a binary token for that patch.Source: §A.4 · pp. 39–40
  • The pooled grid is flattened into binary tokens, which are aggregated into sequence S and define an alphabet of unique tokens.Source: §A.4 · p. 40
  • Alphabet size M depends on the signal and chosen scale, making pooling and tokenization granularity important to assessing structure across scales.Source: §A.4 · p. 40

IEP demonstration - Hyperparameter settings by dataset

Hyperparameters are adapted to the distinct organization of synthetic fractal and SSC rasters, with longer temporal patches and localized settings for SSC. The analysis retains PSC weighting for fractals but disables it for SSC.

IEP demonstration - Hyperparameter settings by dataset

  • SSC uses longer temporal patches (Tp = 256 versus 64), smaller spatial patches (Cp = 4 versus 8), non-overlapping channel coverage, and a lower occupancy threshold (θ = 0.4 versus 0.5).These settings accommodate temporally extended, concentrated auditory activity; fractal rasters have structure distributed across spatial and temporal scales.Source: IEP demonstration - Hyperparameter… · p. 40, Table S1 · p. 41
  • SSC uses lower α (0.3 versus 0.5) and β (0.6 versus 0.7), emphasizing local entropy-weighted redundancy, while its compact block scales focus on shorter and intermediate token scales.Fractal analysis uses larger block sizes to capture broader multiscale organization.Source: IEP demonstration - Hyperparameter… · p. 40
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