Source-linked AI summary
Cognitive Cells: A Compositional Framework for Populations of Small Language Models
Silvan Ferreira
TL;DR
The paper addresses the lack of a shared unit and predictive laws for composing multi-agent artificial cognition. It proposes frozen cognitive cells and measures populations by varying composition variables while holding the cell fixed. Initial measurements show benefits depend on error correlation, interactive protocols do not beat matched-cost voting in this setting, and relay ability predicts performance on distributed-memory tasks.
Problem
Multi-agent systems lack a shared unit of analysis and predictive laws for understanding how artificial cognition should be decomposed, measured, and composed.
Method
The paper defines a cognitive cell, characterizes it with a datasheet, and studies replicated populations while varying size, topology, bandwidth, and coordination protocol under the fixed-cell principle.
Results
Adding cells helps only when errors are not too correlated; open-ended voting can exceed the correct/incorrect null, while debate, blackboard, and chain revision do not beat matched-cost voting in this setting.
Takeaways & Limitations
Cell datasheet quantities can organize measurable composition laws, including whether a population can solve tasks whose evidence exceeds any single cell’s memory.
Abstract
from arXiv · showhide
Recent work on large language models and agentic systems raises a basic question that current practice leaves open: how should artificial cognition be decomposed, measured, and composed? We propose studying multi-agent systems from a fixed unit we call a cognitive cell: a small, frozen language model with bounded memory and a message interface. The methodological commitment, the fixed-cell principle, is to hold this unit constant and vary only the population size, the communication topology, the message bandwidth, and the coordination protocol, so that collective behavior becomes a measurable property of a known device rather than an artifact of per-study engineering. We characterize a single cell by a compact datasheet of measurable parameters, and we ask when replicating and connecting cells improves performance: first we measure how one cell behaves alone, then we replicate it and test when voting, communication, and topology help. Instantiating the framework with small frozen models (1.5 and 3 billion parameters), we report a first round of measurements. Adding cells helps only when their errors are not too correlated. A simple correct/incorrect voting model is a useful but conservative null: real open-ended voting can exceed it, because errors are dispersed across many wrong answers rather than concentrated on one. Popular interactive protocols, namely debate, a shared blackboard, and chain revision, do not beat a matched-cost voting baseline in our setting. Finally, a cell's ability to relay several facts, itself a datasheet quantity, predicts whether a population can solve tasks whose evidence exceeds any single cell's memory. We present these as initial measurements within a broader program on scalable artificial cognition, in which multi-agent architectures appear as the special case of cells autonomous enough to be treated as agents.
1 Introduction
The paper introduces cognitive cells as a fixed unit for measuring how multi-agent populations compose, addressing the absence of shared units and predictive laws. It distinguishes aggregation from genuinely interaction-created capability and proposes initial measurements of composition.
- Motivation: Multi-agent research lacks a shared unit of analysis and predictive laws comparable to neural scaling laws for monolithic models.
- Measurements: The program characterizes cells with a datasheet and tests composition through voting, communication, topology, and candidate laws across parallel, serial, and consensual regimes.
- Framework: The framework adapts cellular-automata methodology by studying globally collective behavior generated from a fixed unit replicated over a topology.
- Framework: A cognitive cell is a minimal, frozen unit whose replicated copies vary in population size, topology, communication budget, and coordination protocol.
- Measurements: Initial measurements report that adding cells helps when errors are not too correlated, while interaction value remains the central open measurement problem.
- Emergence: Because cognitive cells are individually competent, collective capability must be separated into aggregation from single-cell competence and capability created through interaction.
3 The Cognitive Cell
The cognitive cell is a minimal, versioned, frozen, bounded-memory stochastic policy with explicit interfaces. The fixed-cell principle holds its specification constant while varying composition variables, making population behavior measurable and falsifiable.
- Definition: A cognitive cell is a minimal, versioned, frozen unit of cognition with explicit interfaces for perception, memory, reasoning, action, goals, and communication.
- Interfaces: Perception encodes observations into events, memory stores bounded state, reasoning uses a frozen stochastic policy, and action produces task-level outputs.
- Interfaces: Goals are loaded as declarative data at episode start, leaving the cell architecture unchanged while conditioning behavior on different objectives.
- Qualification: A qualifying cell jointly requires goal conditioning, bounded persistent state, a stochastic policy over actions and messages, and a bounded versioned interface.
- Qualification: The definition excludes stateless functions, fixed-rule routers, and modules with unbounded peer activation exchange, while admitting bounded verifiers, proposers, and learned routers.
- Fixed-cell principle: Under the fixed-cell principle, population size, topology, bandwidth, protocol, and task distribution vary while the cell remains published, versioned, and constant.
4 Composition
Composition models a population as identical cells connected through an explicit graph and protocol. Performance and cost are measured across population, topology, bandwidth, and coordination choices under controlled operating conditions.
- Population model: A population is a directed graph G = (V, E) containing N cells that receive messages from in-neighbors and emit actions and messages.
- Population model: All cells share the same parameters, while heterogeneity can arise through differences in their memory states.
- Performance and cost: Collective performance Ψ and total cost K are evaluated over task rollouts using inference and message costs across rounds.
- Protocols: A coordination protocol specifies scheduling, role assignment, output aggregation, and termination, with parallel, serial, and consensual regimes anchoring the analysis.
- Scope: Protocols are imposed exogenously so that task decomposition, work assignment, and self-generated coordination remain outside the framework’s controlled operating conditions.
5 Quantifying Cognitive Capacity
The framework quantifies individual cells with task-indexed datasheets and collective capacity with voting and interaction-based null models. It links collective gains to error diversity and tests whether communication creates capability unavailable to isolated cells.
- Individual capacity: the datasheet: A cell’s task-family-indexed datasheet is a low-dimensional vector of measurable parameters intended to predict collective behavior without exposing internal architecture.The datasheet is not universal across tasks and is measured from inexpensive pilot runs.
- Individual capacity: the datasheet: Error correlation ρ is the load-bearing datasheet parameter because shared model parameters create a common component that replication cannot remove.Replication mainly cancels stochastic trajectory noise while preserving shared bias.
- Individuation: how identical cells differ: Identical cells become behaviorally distinct through stochastic sampling, different contexts and messages, and divergent memory histories.The framework treats memory divergence as a candidate mechanism for specialization.
- Collective capacity and the effective-population law: Equation 6 is a conservative aggregation null because open-ended voting can benefit when wrong answers disperse across alternatives.The framework therefore treats error diversity D, not only error rate, as relevant to open-ended aggregation.
- The value of interaction, and a test for emergence: The value of communication is defined as observed performance minus matched-cost aggregation-null performance, ΔΨcomm = Ψobserved − Pmaj.Positive values indicate added information, while negative values indicate interaction-related loss.
- The value of interaction, and a test for emergence: When single-cell competence is structurally null, p ≈ 0, any measured Ψ > 0 constitutes strong emergence relative to the aggregation null.Candidate mechanisms include distributed working memory, interleaved restoration, and generate-and-verify asymmetry.
6 Composition Laws and Operating Regimes
The framework organizes populations into parallel, serial, and consensual regimes with distinct scaling patterns and failure modes. It also defines a cost-matched frontier for comparing cell populations with monolithic models across task structure.
- Operating regimes: The three protocol regimes exhibit saturation from correlated errors, error accumulation in chains, and unreliable consensus, respectively.These failure modes motivate separate composition laws for parallel, serial, and consensual systems.
- Parallel regime: logistic growth and decomposability: For decomposable tasks, collective performance is expected to grow logistically with population size, with midpoint N0 and steepness k determined by datasheet properties and decomposition width.Voting saturation depends on error correlation, while verification-based aggregation depends on verification fidelity φ.
- Serial regime: cascades, error accumulation, and restoration: Serial chains compound per-stage errors multiplicatively, making early-stage quality especially important.The proposed response is preferential early verification or interleaved verifier cells stronger than the proposers they check.
- Serial regime: cascades, error accumulation, and restoration: Interleaving a restoring stage every k steps can bound end-to-end error for arbitrary chain length when verifier error is below the segment error it corrects, at overhead O(r/k).Each restoring stage checks the partial result and applies local majority correction.
- Consensual regime: Gossip-based consensus can drift toward confident but unsupported conclusions when sampling noise overwhelms intrinsic biases or task evidence.The framework distinguishes this memetic-drift regime from selection, where sufficiently strong evidence reliably amplifies the correct option.
- The cost frontier and the crossover with monolithic scale: At matched inference cost, populations are expected to favor tasks with wide decomposition, diverse hypothesis generation, or interaction-created capability, whereas monoliths favor long serial dependencies without checkable intermediate states.The proposed crossover is parameterized initially by decomposition width and serial depth.
7 The Compilation Problem
The compilation problem treats system construction as budget-constrained optimization over cell populations, communication graphs, and protocols. Its goal is to map task structure and cell datasheets to predictive, executable circuits of cells.
- Optimization: Given task structure, a cell datasheet, and budget B, the framework chooses population size, topology, and protocol to maximize predicted performance.Task structure includes decomposition width, serial depth, and verification cost.
- Compilation: The predictive model combines the composition laws and empirical refinements, turning task-to-system mapping into a hardware-like compilation problem.The practical deliverable is an open-source runtime that spawns, connects, and schedules cell populations.
8 Learning to Compose
The current framework keeps the shared cell parameters frozen, while proposing collective training as future work. The extension would test whether training can reduce error correlation, improve communication fidelity, and generalize across population sizes.
- Future work: The present program treats θ as frozen rather than training cells against a collective reward.The proposed future extension trains one shared model to be a good collaborator rather than only a good soloist.
- Future work: Future collective training would examine whether it lowers error correlation ρ, raises communication fidelity φ under bandwidth β, and transfers from small to larger populations.Parameter sharing is proposed to keep training within modest compute.
9 Research Agenda: Hypotheses and Experimental Program
The paper proposes seven falsifiable hypotheses about how fixed cognitive cells compose, then outlines an inference-only experimental program to test them across population sizes, topologies, bandwidths, protocols, and task families.
- Falsifiable hypotheses: Seven hypotheses separate composition laws, which predict collective behavior from device parameters, from emergence hypotheses, which posit capabilities absent from individual cells.H1, H2, H3, and H5 concern composition laws; H4, H6, and H7 concern emergence.
- Falsifiable hypotheses: Above a competence–diversity threshold, aggregation gains should follow a correct/incorrect voting lower bound, saturate near N ≈1/ρ, and increase with error diversity in open-ended voting.Below the threshold, aggregation alone is predicted to yield no gains, especially when p ≈0.
- Falsifiable hypotheses: The datasheet hypothesis predicts Ψ(N, G, P) from six cell parameters, while task decomposability predicts logistic, cascade-decay, or phase-transition-like functional forms across parallel, serial, and consensual protocols.The hypotheses also predict stable role structure, matched-budget cost crossovers, and collective-training effects on ρ and ∆Ψcomm.
- Falsifiable hypotheses: Strong emergence is predicted when single-cell competence is structurally null because required state exceeds Hmax or inferential depth exceeds single-trajectory reliability, yet interacting populations achieve Ψ substantially above zero.The hypothesis further predicts threshold-like onset as interaction resources such as bandwidth β or restoration density 1/k cross critical values.
- Experimental program: The program instantiates frozen 1.5-billion- and 3-billion-parameter cells with bounded scratchpad memory, a JSON-schema interface, and a minimal perception–reason–act loop.Cell versions are published and versioned; silent modifications are prohibited.
- Experimental program: Experiments sweep N ∈{1, 2, 4, . . . , 1024}, chain, star, random, and small-world topologies, bandwidth β, and task families, using resampling-and-voting, matched-budget larger-model, and published-framework baselines.Population experiments are inference-only over replicas of a small frozen model, while collective training uses a single parameter-sharing model.
10 Illustrative Measurements
The measurements show how frozen cells behave individually and in populations, testing voting, communication, and distributed memory under controlled conditions. Gains depend on error correlation, open-ended voting exceeds its conservative binary null, and relay fidelity predicts distributed-task limits.
- Experimental setup: The study measures frozen language models using procedurally generated, mechanically checkable tasks and a datasheet of competence, correlation, diversity, fidelity, and persuadability.Cell v0.1 is a frozen 1.5B model; Cell v0.2 is a distinct frozen 3B model under the same interface.
- Datasheet measurements: ρ = 1.00 at temperature zero, while the larger cell reaches ρ = 0.85–0.94 and D as low as 0.05 bits, versus ρ ≈0.6 and D ≈1.3 bits for the smaller cell.The measurements expose a capability–diversity tension: greater confidence can reduce diversity, increase shared error, and accelerate voting saturation.
- Voting: As temperature rises from 0.3 to 1.3, ρ falls from ρ ≈0.82 to ρ ≈0.37 and voting saturates progressively later, approximately as N ≈1/ρ.Measured vote accuracy remains above the correct/incorrect prediction, with the gap widening as output diversity increases.
- Voting: At temperature 1.3, voting reaches accuracy 0.63 despite single-cell competence p = 0.47, because errors are dispersed across many wrong answers.This makes the binary correct/incorrect model a conservative lower bound for open-ended voting rather than a complete prediction.
- Communication: At matched token cost, debate, a shared blackboard, and chain revision do not beat voting; each has paired difference −0.02 with a 95% interval of [−0.10, +0.07].Against spending the same budget on additional independent votes, all three protocols are worse by about 0.09.
- Distributed capacity: Multi-fact fidelity φ(j) falls below one-half at j ≈3 for Cell v0.1 but stays above one-half through j = 10 for Cell v0.2, predicting distributed-memory ceilings.The small cell fails the distributed task once k exceeds about three, consistent with its measured relay fidelity.
11 Discussion and Limitations
The discussion frames the framework as an empirical device theory rather than a claim of equivalence with brains, electronics, or cellular automata. It identifies scope boundaries involving coordination, extrapolation, task dependence, and exchangeability.
- Scope: The framework claims a repeated frozen unit whose replication supports scaling, but makes no mechanistic commitment about brains or equivalence with transistors and cellular automata.Its fixed-cell principle favors compositional validity over per-task benchmark optimization.
- Failure modes: Known pathologies—including error-correlation collapse, non-monotonic returns, cascade amplification, coordination overhead, and drift-dominated consensus—are treated as measurable regimes.Each pathology is associated with named control parameters and possible mechanism studies.
- Distributed capacity: Multi-fact fidelity predicts relay capacity, but robust distributed capability also requires clean multi-round coordination, which small frozen cells lack.The larger cell does not cross the distributed-capability onset cleanly end-to-end in the reported runs.
- Threats to validity: Datasheet parameters may be task-family-dependent, small-cell results may not extrapolate to more capable units, and the exchangeable null fails on structured topologies.The proposed responses are family-indexed datasheets, versioned-device comparisons, and graph-based correlated-jury generalizations.
12 Conclusion
The conclusion presents cognitive cells and datasheets as a device abstraction for compositional artificial cognition. Initial measurements support the framework while identifying error correlation, error dispersion, matched-cost comparisons, and multi-fact fidelity as central quantities.
- Conclusion: The paper proposes a minimal, frozen, versioned cognitive cell with explicit interfaces and organizes a program around datasheets, composition laws, and task-to-population mapping.The framework adapts cellular-automata methodology and treats multi-agent architectures as autonomous-cell special cases.
- Conclusion: Initial measurements show that adding cells helps only when error correlation is low, open-ended voting exceeds the conservative binary null, and interactive protocols do not beat matched-cost voting.Multi-fact fidelity predicts the prerequisite for distributed capability beyond a single cell’s memory.
Disclosure of AI Assistance
The author reports using Claude Fable 5 to assist with literature survey, drafting, and LaTeX preparation while retaining responsibility for the paper’s content.
- Disclosure: Claude Fable 5 assisted with literature survey, drafting, and LaTeX preparation; the author reviewed and verified the final content.The disclosure assigns the core concept, research direction, content decisions, and responsibility to the author.