A memory-based active inference model of DishBrain-like adaptive behaviour

Aswin Paul; Moein Khajehnejad; Forough Habibollahi; Brett J. Kagan; Adeel Razi

cs.AIAug 9, 2025

A memory-based active inference model of DishBrain-like adaptive behaviour

Authors: Aswin Paul, Moein Khajehnejad, Forough Habibollahi, Brett J. Kagan, Adeel Razi

Organizations: Turner Institute for Brain and Mental Health, School of Psychological Sciences, Monash University, Clayton 3800, Australia · VERSES, Los Angeles, California, USA · Cortical Labs Pty Ltd, Melbourne 3056, Australia · CIFAR Azrieli Global Scholars Program, CIFAR, Toronto, Canada

Abstract

Recent and rapid advances in artificial intelligence (AI) make it increasingly important to understand the foundations of adaptive behaviour in autonomous agents, especially for building safe and efficient systems. While artificial neural networks have dominated the development of AI, recent work has begun to explore living biological neuronal networks as an alternative substrate for computation. These systems promise remarkable data and sample efficiency and rich dynamics, and may also inspire explainable and biologically plausible models. Here, we develop an experiment-informed active inference framework to model decision-making in closed-loop agents that mirror experimental setups using biological neurons. Using a generative model whose dimensions are matched to an experiment protocol, we systematically compare three decision-making schemes within this common generative model. Under matched episode counts (i.e. total data available for learning) to the in-vitro experiment, our simulations show that agents with short memory horizons reach a level of performance close to that of mouse and human cortical cultures (DishBrain platform), whereas longer memory horizons depart from it substantially. Increasing the planning horizon, by contrast, confers no comparable benefit. Because all model parameters are explicit, we can also track the quantities in our generative model that accompany this improvement, such as the risk term and the entropy of the transition and state-action mappings. Together, these results illustrate how active inference offers a formal language for comparing decision-making schemes in similar closed-loop control environments.

Figures & tables

Models and methods		Experimental groups
AI	Artificial intelligence	MCC	Mouse cortical cells
ANN	Artificial neural network	HCC	Human cortical cells
BNN	Biological neuronal network	CTL	Media-only control
SBI	Synthetic biological intelligence	RST	Rest session (spontaneous activity), no feedback
RL	Reinforcement learning	IS	In-silico control, random paddle
POMDP	Partially observable Markov decision process

Table 1: Abbreviations used in this paper. Experimental group labels follow the original DishBrain study Kagan et al. (2022) .

Figure 1: Memory horizon influences performance in CFL agents and comparison with MCC and HCC groups. Relative improvement in key performance metrics for in-silico CFL agents and in-vitro MCC and HCC cultures. Performance is evaluated by comparing the first 5 minutes (open boxes) and last 15 minutes (filled boxes) of each trial. Points on the box plots show individual sessions (in vitro) or trials (in silico); in c, g and h, where the boxes summarise per-minute (c) or per-episode (g, h) values, the points are session or trial means. Metrics include average rally length, percentage of aces (Aces are episodes with score-zero (i.e. immediate miss), lower the better), and percentage of long rallies (

\geq 3

hits). a–c: CFL-

T

performance across discrete trial windows. d–f: Linear-regression analysis of continuous-time performance. g: Evolution of the NTE of the

\mathbb{CL}

vector. h: Evolution of the average risk term

\Gamma_{t}

. i–j: Continuous-time evolution of NTE and risk. k: Relative improvement of CFL agents across memory horizons. l: Relative improvement of the experimental baseline groups. Group abbreviations: MCC, mouse cortical cells; HCC, human cortical cells; CTL, media-only control; RST, rest session, in which an active culture drove the paddle but received no sensory input; IS, in-silico control, in which the paddle was driven by random noise Kagan et al. (2022) . CFL-

T

denotes a counterfactual learning agent with a finite state-action update window of length

T

; NTE denotes normalised total entropy. All abbreviations are collected in Table 1 .

Agent	Culture	$\Delta$ rally	95% CI	Hedges’ $g$	$p_{\mathrm{adj}}$	Outcome
CFL-1	MCC	+0.169	[0.039, 0.336]	+0.33	0.013	agent higher
CFL-1	HCC	+0.139	[0.000, 0.312]	+0.28	0.060	not distinguishable
CFL-2	MCC	+0.161	[0.057, 0.268]	+0.45	0.005	agent higher
CFL-2	HCC	+0.131	[0.017, 0.247]	+0.37	0.032	agent higher
CFL-3	MCC	+0.588	[0.401, 0.790]	+0.86	$<$ 0.001	agent higher
CFL-3	HCC	+0.558	[0.366, 0.765]	+0.86	$<$ 0.001	agent higher

Table 2: Average rally length reached in the second window (6-20 min) by each in-silico agent, compared with the mouse (MCC) and human (HCC) cortical cultures. Differences and intervals come from a bootstrap that resamples whole replicates;

p

-values are Benjamini-Hochberg corrected across all 18 contrasts.

Figure 2: Performance of AIF-1 compared to MCC and HCC. Relative improvement in average rally length, percentage of aces, and percentage of long rallies, evaluated over the first 5 minutes (open boxes) and last 15 minutes (filled boxes). Points on the box plots show individual sessions (in vitro) or trials (in silico); in c, g and h, where the boxes summarise per-minute (c) or per-episode (g, h) values, the points are session or trial means. a–c: Discrete-window performance. d–f: Continuous-time regression. g–h: Evolution of NTE for transition dynamics and prior preferences. i–j: Continuous-time NTE evolution. k: Relative improvement of AIF-1. l: Experimental baselines. AIF-1 denotes the active inference agent with one-step planning; NTE denotes normalised total entropy. Group abbreviations: MCC, mouse cortical cells; HCC, human cortical cells; CTL, media-only control; RST, rest session, in which an active culture drove the paddle but received no sensory input; IS, in-silico control, in which the paddle was driven by random noise Kagan et al. (2022) . See Table 1 .

Figure 3: Performance of DPEFE agents compared to MCC and HCC. Structure and metric layout follow Fig. 2 . Points on the box plots show individual sessions (in vitro) or trials (in silico); in c, g and h, where the boxes summarise per-minute (c) or per-episode (g, h) values, the points are session or trial means. a–c: DP-

T

performance. d–f: Continuous-time regression. g–h: NTE evolution for transition and preference distributions. i–j: Continuous-time NTE evolution. k: Relative improvement of DP-

T

agents. l: Experimental baselines. DP-

T

denotes a dynamic-programming expected-free-energy agent with planning horizon

T

; NTE denotes normalised total entropy. Group abbreviations: MCC, mouse cortical cells; HCC, human cortical cells; CTL, media-only control; RST, rest session, in which an active culture drove the paddle but received no sensory input; IS, in-silico control, in which the paddle was driven by random noise Kagan et al. (2022) . See Table 1 .

Figure 4: Experiment-informed generative model shared by all agents. a: The Pong court to scale (

600\times 600

px, paddle

250

px). Each state factor discretises one game variable: ‘ball-x’ into 38 bins of 16 px, communicated to DishBrain as a rate code (

4

–

41

Hz); ‘ball-y’ into 8 bins of 86 px, place-coded over 8 stimulation electrodes; and ‘paddle-y’, the paddle centre, into the same 8 bins. Filled cells mark the bins of the example ball and paddle; hatched cells lie beyond the court edge. b: The generative model over one time step. Each factor has its own transition model

\mathbb{B}

and an identity likelihood

\mathbb{A}

(fully observed states); the action

u_{t}\in\{\mathrm{Stay},\mathrm{Up},\mathrm{Down}\}

enters the ‘ball-x’ transition. c: Parameters of interest, their array shapes, and the schemes that learn and use them. All abbreviations are collected in Table 1 .

Source	Group	Replicates	Sessions	Episodes
In vitro	MCC	7 chips	110	7,317
In vitro	HCC	12 chips	138	9,528
In silico	CFL- $T$ (each $T$ )	100 seeds	100	7,000
In silico	AIF-1	99 seeds	99	6,930
In silico	DP- $T$ (each $T$ )	99 seeds	99	6,930

Table 3: Units of analysis. Episode counts are matched by design between in-vitro and in-silico groups, but the biological sessions are nested within a small number of cultures.

Group	$\Delta$ rally length		$\Delta$ % long rallies		$\Delta$ % aces
MCC	+0.147 [0.090, 0.204]	$<$ 0.001	+3.421 [2.102, 4.740]	$<$ 0.001	-1.580 [-3.948, 0.788]	0.274
HCC	+0.243 [0.190, 0.296]	$<$ 0.001	+4.323 [3.426, 5.220]	$<$ 0.001	-2.482 [-4.382, -0.583]	0.026
CFL-1	+0.147 [-0.013, 0.307]	0.139	+0.577 [-1.287, 2.440]	0.619	-2.124 [-5.276, 1.029]	0.274
CFL-2	+0.176 [0.063, 0.289]	0.007	+1.211 [-0.456, 2.877]	0.255	-0.648 [-3.859, 2.563]	0.714
CFL-3	+0.450 [0.252, 0.648]	$<$ 0.001	+2.788 [0.872, 4.704]	0.012	-2.326 [-5.400, 0.747]	0.253
CFL-4	+1.158 [0.486, 1.830]	0.002	+5.674 [3.297, 8.051]	$<$ 0.001	-5.314 [-8.342, -2.286]	0.002

Table S1: Change from the first (0–5 min) to the second (6–20 min) window, from a mixed-effects model with a random intercept on replicate. Each cell gives the estimate with its 95% confidence interval and the corrected

p

-value.

Group	Window 1	Window 2	Absolute gain	Relative improvement (%)
CFL-4	1.325	2.482	+1.157	+106.2
CFL-3	0.988	1.439	+0.450	+75.6
DP-5	0.885	1.189	+0.304	+70.9
DP-10	0.825	1.179	+0.354	+66.9
CFL-1	0.873	1.019	+0.147	+47.2
CFL-2	0.835	1.011	+0.176	+40.7

Table S2: Average rally length reached in each window, the absolute gain between them, and the relative improvement. Relative improvement normalises by each session’s own first-window mean, so it rewards a low starting point.

Group	Rally length	% long rallies	% aces
MCC	0.85 [0.81, 0.91]	9.23 [8.69, 10.49]	54.26 [52.35, 55.55]
HCC	0.88 [0.82, 0.95]	8.06 [7.17, 8.95]	53.94 [52.54, 55.07]
CFL-1	1.02 [0.90, 1.18]	11.19 [10.13, 12.28]	56.75 [54.82, 58.65]
CFL-2	1.01 [0.92, 1.11]	11.10 [9.95, 12.29]	57.09 [54.66, 59.51]
CFL-3	1.44 [1.26, 1.64]	14.10 [12.64, 15.65]	54.19 [51.80, 56.56]
CFL-4	2.47 [1.80, 3.59]	19.05 [17.08, 21.36]	47.03 [44.75, 49.25]

Table S3: Absolute performance in the second window (6–20 min), with 95% intervals from a replicate-level bootstrap.

Agent	Culture	$\Delta$ RI (%)	95% CI	Hedges’ $g$	$p_{\mathrm{adj}}$	Outcome
CFL-1	MCC	+4.0	[-31.6, 35.6]	+0.08	0.875	inconclusive
CFL-1	HCC	-10.1	[-42.1, 21.2]	-0.11	0.725	inconclusive
CFL-2	MCC	-2.5	[-35.5, 24.9]	+0.02	0.952	inconclusive
CFL-2	HCC	-16.6	[-46.2, 10.4]	-0.21	0.481	inconclusive
CFL-3	MCC	+32.4	[-4.0, 65.2]	+0.36	0.298	inconclusive
CFL-3	HCC	+18.3	[-15.1, 50.7]	+0.19	0.482	inconclusive

Table S4: Relative improvement of each in-silico agent against the two cultures, reported for continuity with the original DishBrain analysis. Outcomes are three-way: “different” where the contrast is significant after correction, “equivalent” where the interval falls entirely within a margin of

\pm 18

percentage points (approximately the MCC–HCC gap), and “inconclusive” otherwise.

Class	Group	Rally length (6–20 min)	Change across trial	$p_{\mathrm{adj}}$
In vitro	MCC	0.85 [0.81, 0.91]	+0.15 [0.08, 0.29]	$<$ 0.001
In vitro	HCC	0.88 [0.82, 0.95]	+0.24 [0.12, 0.36]	$<$ 0.001
Active inference	AIF-1	0.80 [0.77, 0.84]	-0.02 [-0.09, 0.06]	0.682
Active inference	CFL-1	1.02 [0.90, 1.18]	+0.15 [0.00, 0.32]	0.093
Active inference	CFL-2	1.01 [0.92, 1.11]	+0.18 [0.07, 0.29]	0.005
Active inference	CFL-3	1.44 [1.26, 1.64]	+0.45 [0.26, 0.65]	$<$ 0.001

Table S5: Non-active-inference baselines beside the published agents and the cultures. Absolute rally length is the second-window mean; the change across the trial is the paired within-session difference. Intervals are replicate-level bootstraps.

A	B	$\Delta$ rally	95% CI	Hedges’ $g$	$p_{\mathrm{adj}}$	Outcome
DynaQ	CFL-1	+0.15	[-0.03, 0.29]	+0.26	0.108	comparable
DynaQ	CFL-2	+0.16	[0.04, 0.27]	+0.36	0.018	A higher
DynaQ	CFL-3	-0.27	[-0.48, -0.08]	-0.37	0.009	B higher
DynaQ	CFL-4	-1.30	[-2.43, -0.62]	-0.37	$<$ 0.001	B higher
DynaQ	DP-5	-0.02	[-0.18, 0.12]	-0.04	0.861	comparable
DynaQ	AIF-1	+0.37	[0.29, 0.44]	+1.33	$<$ 0.001	A higher

Table S6: Baseline contrasts on second-window rally length. Benjamini-Hochberg correction is applied within this family of twelve comparisons, which is separate from the agent-versus-culture family of the main analysis.

Agent	Parameter	$\mathrm{TE}_{\max}$	NTE 0–5	NTE 6–20	$\Delta$	Fall (% of max)
CFL-1	$\mathbb{CL}$	2671.83	0.9987	0.9956	-0.0031	1.2
CFL-2	$\mathbb{CL}$	2671.83	0.9976	0.9922	-0.0054	2.0
CFL-3	$\mathbb{CL}$	2671.83	0.9960	0.9884	-0.0076	2.9
CFL-4	$\mathbb{CL}$	2671.83	0.9936	0.9814	-0.0122	4.3
AIF-1	$\mathbb{B}$ (ball-x)	414.68	0.4148	0.3616	-0.0532	83.8
DP-2	$\mathbb{B}$ (ball-x)	414.68	0.2758	0.2177	-0.0580	71.3

Table S7: Normalised total entropy against the analytic maximum, by time window. NTE is one when the parameter is uniform and approaches zero as it becomes fully determined, so values are comparable across agents and parameters.

Agent	Seeds	Pearson $r$	$p_{\mathrm{adj}}$	Spearman $\rho$	$p_{\mathrm{adj}}$
CFL-1	100	-0.205	0.238	-0.122	0.941
CFL-2	100	-0.168	0.284	-0.008	0.941
CFL-3	100	-0.054	0.671	+0.024	0.941
CFL-4	100	-0.119	0.534	+0.040	0.941
AIF-1	99	+0.062	0.671	+0.028	0.941
DP-2	99	+0.070	0.671	+0.015	0.941

Table S8: Across-seed association between the change in parameter entropy over a trial and the change in average rally length. A negative coefficient would indicate that seeds whose parameters became more informed improved more.

Setting	CFL- $T$	DP- $T$	AIF-1	Status
Episodes per trial	70	70	70	shared
Action precision	1024	1024	1024	shared
Transition learning rate	$10^{16}$	$10^{16}$	$10^{16}$	shared
Numerical floor	$10^{-16}$	$10^{-16}$	$10^{-16}$	shared
Prior preferences $\mathbb{C}$	uniform	uniform	random categorical	differs
Initial state prior $\mathbb{D}$	uniform	uniform	random categorical	differs

Table S9: Hyperparameters of the three decision-making schemes, read directly from the simulation code. All settings that the schemes share are identical; the quantities that differ are the ones that define the schemes, together with the prior specification of AIF-1.

Depth $h$	Normalised entropy	SD
1	0.324	0.054
2	0.513	0.066
3	0.605	0.071
4	0.666	0.075
5	0.707	0.078
10	0.810	0.088

Table S10: Predictive information of the learned transition model as a function of rollout depth. Entries are the entropy of the

h

-step-ahead prediction, normalised by the entropy of the uniform distribution over the same support. The value of one means the rollout carries no information about the future state. Here, normalised entropy is computed from the transition parameters of the DP-5 agent on 3 seeds, averaged over the three actions and over all starting states. The environment itself is deterministic; what decays with depth is the information carried by the agent’s estimate of it.

Agent	Condition	Seeds	0–5 min	6–20 min	Median	$\Delta$	$p$
CFL-4	control	100	1.08	2.39	1.83	+1.31	$<$ 0.001
CFL-4	obs. $\varepsilon=0.05$	100	2.40	6.29	2.81	+3.89	$<$ 0.001
CFL-4	obs. $\varepsilon=0.15$	100	1.94	4.75	3.27	+2.81	$<$ 0.001
CFL-4	act. $\eta=0.10$	100	1.01	1.46	1.24	+0.44	$<$ 0.001
DP-5	control	6	0.91	1.30	1.21	+0.38	0.273
DP-5	obs. $\varepsilon=0.05$	6	0.85	1.12	1.10	+0.27	0.117

Table S11: Performance under observation noise and unreliable action execution. The first row of each block is the control condition, in which both manipulations are switched off and the published run is recovered.

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Hierarchical Active Inference using Successor Representations

Prashant Rangarajan, Rajesh P. N. Rao

Paul G. Allen Center for Computer Science and Engineering, University of Washington, Seattle, USA

Hierarchical Reinforcement Learning Classical Planning Successor Representations Abstraction Navigation

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Active inference, a neurally-inspired model for inferring actions based on the free energy principle (FEP), has been proposed as a unifying framework for understanding perception, action, and learning in the brain. Active inference has previously been used to model ecologically important tasks such as navigation and planning, but scaling it to solve complex large-scale problems in real-world environments has remained a challenge. Inspired by the existence of multi-scale hierarchical representations in the brain, we propose a model for planning of actions based on hierarchical active inference. Our approach combines a hierarchical model of the environment with successor representations for efficient planning. We present results demonstrating (1) how lower-level successor representations can be used to learn higher-level abstract states, (2) how planning based on active inference at the lower-level can be used to bootstrap and learn higher-level abstract actions, and (3) how these learned higher-level abstract states and actions can facilitate efficient planning. We illustrate the performance of the approach on several planning and reinforcement learning (RL) problems including a variant of the well-known four rooms task, a key-based navigation task, a partially observable planning problem, the Mountain Car problem, and PointMaze, a family of navigation tasks with continuous state and action spaces. Our results represent, to our knowledge, the first application of learned hierarchical state and action abstractions to active inference in FEP-based theories of brain function.

Abstract

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