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Sensory map entropy as a measure of sensorimotor coordination

Sensory map entropy is the Shannon entropy of a compressed record of what an agent's receptors register. Lungarella, Sporns and Pegors, as reported by Zakirov and colleagues, used it to detect active perception, defined as enrichment of the statistical structure of sensory input by coordinated sensory and motor activity.7 Free-energy work treats low entropy of sensory states as a condition of staying alive.4

Earliest held
2009, Friston KJ, Daunizeau J…
Most discussed in
Active perception during angiogenesis…, 2021
In the library
37 passages in 12 works
Rewritten
2026-10-29
18501875190019251950197520002025Friston KJ, Daunizeau J, Kiebel SJ, 20091Friston K, Ao P, 20122Friston K, Schwartenbeck P, Fitzgerald…, 20133Sengupta B, Stemmler MB, Friston KJ, 20134Moore DG, Valentini G, Walker SI, Levin…, 20185Palacios ER, Razi A, Parr T, Kirchhoff…, 20206Zakirov B, Charalambous G, Thuret R…, 20217Zakirov B, Charalambous G, Thuret R…, 20218Zakirov B, Charalambous G, Thuret R…, 20219
01

Sensory mappings in theory

In free-energy work, the sensory map is part of a model of an agent and its world. Friston, Daunizeau and Kiebel (2009) state that under a sensory mapping the equilibrium entropy is bounded by the entropy of sensory signals minus a sensory transfer term.1 Friston and Ao (2012) write the model with a mapping from hidden states to sensory states. In their formulation, sensations are a noisy map of hidden states that evolve as a function of themselves and action.2 In both papers the sensory mapping is a formal term in the equations that describe the environment and the sensations it produces.

02

Entropy and staying alive

A second line ties the entropy of sensory states to survival. Friston and colleagues (2013) argue that agents restrict themselves to a few attracting states, and that this is equivalent to minimizing the Shannon entropy of the outcomes they experience.3 Sengupta, Stemmler and Friston (2013) say that the sensory states of biological systems have characteristically low Shannon entropy, which they link to homeostasis.4 Palacios and colleagues (2020) make the same point for self-organisation. They say the entropy of sensory states is necessarily bounded, because organisms must keep sensory states within physiological bounds.6

03

Entropy as a computed quantity

Moore, Valentini, Walker and Levin (2018) describe Inform, a software library for information-theoretic analysis of collective behaviour. In it, Shannon measures are built around a distribution object. Once the distribution exists, its entropy is computed with a single function call, in Python or in R.5 Inform concerns software, not sensory maps. It shows how the quantity can be computed from recorded observations.

04

Active perception in tip cells

Zakirov and colleagues (2021) apply the idea to angiogenesis. They adopt the formalism of Lungarella, Sporns and Pegors, who probed a sensory map for structure and found reduced Shannon entropy when model systems could coordinate sensing and acting.8 Zakirov and colleagues chose entropy because it is easy to interpret and rises for broader distributions. They use it as a proxy for the spatial spread of activated receptors, while noting it does not strictly model coherence. As entropy falls, the two-cell system moves toward one tip cell and one stalk cell.

SourcesEach quotation was checked word for word against the passage it opens.
  1. Under a sensory mapping, the equilibrium entropy is bounded by the entropy of sensory signals minus a sensory transfer termFriston KJ, Daunizeau J, Kiebel SJ, 2009 · Reinforcement learning or active inference? · open at passage 6
  2. sensations are a noisy map of hidden states that evolve as a function of themselves and actionFriston K, Ao P, 2012 · Free energy, value, and attractors · open at passage 16
  3. This behavior is equivalent to minimizing the Shannon entropy of the distribution over the outcomes they experience.Friston K, Schwartenbeck P, Fitzgerald T, Moutoussis M…, 2013 · The anatomy of choice: active inference and agency · open at passage 13
  4. the (sensory) states of biological systems have characteristically low Shannon entropySengupta B, Stemmler MB, Friston KJ, 2013 · Information and efficiency in the nervous system--a synthesis · open at passage 7
  5. computing its entropy is as simple as performing a single function call to shannon.entropy (in Python) or shannon_entropy (in R).Moore DG, Valentini G, Walker SI, Levin M, 2018 · Inform: Efficient Information-Theoretic Analysis of Collective Behaviors · open at passage 49
  6. This means the Shannon entropy (i.e., dispersion) of sensory states is necessarily bounded.Palacios ER, Razi A, Parr T, Kirchhoff M, Friston K, 2020 · On Markov blankets and hierarchical self-organisation · open at passage 14
  7. define active perception as the enrichment of the statistical structure of an individual's sensory input resulting from coordinated sensory and motor activityZakirov B, Charalambous G, Thuret R, Aspalter IM…, 2021 · Active perception during angiogenesis: filopodia speed up Notch selection of… · open at passage 47
  8. They found that the measures they used have distinctive signatures, such as reduced Shannon entropy when their model systems are allowed to coordinate sensory and motor activityZakirov B, Charalambous G, Thuret R, Aspalter IM…, 2021 · Active perception during angiogenesis: filopodia speed up Notch selection of… · open at passage 47
  9. As the entropy of activations decreases, the two-cell system gets pushed towards the state of one cell being a tip cell and receiving all of the sensory input and the other being a stalk cell and receiving none of it.Zakirov B, Charalambous G, Thuret R, Aspalter IM…, 2021 · Active perception during angiogenesis: filopodia speed up Notch selection of… · open at passage 54
Linked ideas
Zakirov and colleagues' study of filopodia and Notch selection is where the sensory map entropy measure is applied to cells.
Covers the same idea of active perception arising from coordinated sensing and acting.
Source of the claim that agents keep the entropy of sensory states low by minimizing surprise.
Links Shannon entropy as average surprise to an organism's resistance to disorder.
Sengupta and colleagues tie bounded, low-entropy sensory states to homeostatic regulation.
Palacios and colleagues place the bound on sensory-state entropy within Markov blanket accounts of self-organisation.
Passage frames endothelial filopodia probing a VEGF gradient as 'active perception' with signatures to detect; B offers entropy as a sensing-acting coordination measure. Passage never mentions entropy, so the link is conceptual.
Where it is discussedPassages matching sensory map, Shannon entropy, statistical structure of sensory input, coordinated sensory and motor activity
2021Active perception during angiogenesis: filopodia speed up Notch selection of… · Zakirov B, Charalambous G, Thuret R…15
2013Information and efficiency in the nervous system--a synthesis · Sengupta B, Stemmler MB, Friston KJ4
2018Inform: Efficient Information-Theoretic Analysis of Collective Behaviors · Moore DG, Valentini G, Walker SI, Levin…3
2012Free energy, value, and attractors · Friston K, Ao P3
2009Reinforcement learning or active inference? · Friston KJ, Daunizeau J, Kiebel SJ3
2015Active Inference, homeostatic regulation and adaptive behavioural control · Pezzulo G, Rigoli F, Friston K2
2013The anatomy of choice: active inference and agency · Friston K, Schwartenbeck P, Fitzgerald…2
2020On Markov blankets and hierarchical self-organisation · Palacios ER, Razi A, Parr T, Kirchhoff…1
2018The Markov blankets of life: autonomy, active inference and the free energy… · Kirchhoff M, Parr T, Palacios E…1
2017Cellular information dynamics through transmembrane flow of ions · Gatenby RA, Frieden BR1