curb your enthusiasm - predictiveprocessing2018.weebly.com · curb your enthusiasm. Krzysztof Dolega 2 curb your enthusiasm free-energy. Goals: 1. How should we think of FEP? A principle,

Krzysztof Dolega1

curb your enthusiasm

Krzysztof Dolega2

curb your enthusiasm free-energy

Goals:

1. How should we think of FEP? A principle, but what kind of principle?

2. What is the scope of FEP?

3.How is FEP explanatory? What kind of explanations does it offer?

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Goals:

1. How should we think of FEP? A principle, but what kind of principle?

2. What is the scope of FEP?

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Plan:

1. What kind of principle is FEP?

2. FEP and the problem of scope

3. Example of models in science

4. Conclusion

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1. A principle, but what kind of a principle?

Friston talks about “[…] the difference between a normative principle that things may or may not conform to, and a process theory or hypothesis about how that principle is realized. Under this distinction, the free energy principle stands in stark distinction to things like predictive coding and the Bayesian brain hypothesis. This is because the free energy principle is what it is — a principle. Like Hamilton’s Principle of Stationary Action, it cannot be falsified. It cannot be disproven. In fact, there’s not much you can do with it, unless you ask whether measurable systems conform to the principle.” (Friston, 2018: 21)

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1. A principle, but what kind of a principle?

Friston talks about “[…] the difference between a normative principle that things may or may not conform to, and a process theory or hypothesis about how that principle is realized. Under this distinction, the free energy principle stands in stark distinction to things like predictive coding and the Bayesian brain hypothesis. This is because the free energy principle is what it is — a principle. Like Hamilton’s Principle of Stationary Action, it cannot be falsified. It cannot be disproven. In fact, there’s not much you can do with it, unless you ask whether measurable systems conform to the principle.” (Friston, 2018: 21)

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1. A principle, but what kind of a principle?

• “[…] the Bayesian brain hypothesis and predictive coding are incomplete theories

of how we infer states of affairs.”

• “This missing bit is the enactive compass of the free energy principle. In other words,

the free energy principle is not just about making the best (Bayesian) sense of sensory impressions of what’s “out there”. It tries to understand how we sample the world

and author our own sensations. […] It is this enactive, embodied, extended, emb-edded, and encultured aspect that is lacking from the Bayesian brain and predictive coding theories; precisely because they do not consider entropy reduction.”

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1. A principle, but what kind of a principle?

• FEP is non-falsifiable

• Physical systems can either obey it or not…

• Its scope is wider than just perception or cognition, it aims to explain embodiment, culture, etc.

• And it can do all that because it offers an account of how living systems reduce entropy*

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1. A principle, but what kind of a principle?

• Free-energy provides an an upper bound on the information-theoretic surprise (negative log-likelihood) of sensory samples

• Entropy is the long-term average of surprise (under certain assumptions)

• This means that minimizing free-energy indirectly minimizes the surprise (and therefore the entropy) of sensory states

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1. A principle, but what kind of a principle?

• A living organism is supposed to maintain homeostasis by minimizing the entropy of sensory-states

• The organism needs to minimize the extent to which the states it experiences differ from its optimal states specified by its phenotype, it needs to avoid surprising states (in IT sense)

•This can be done by either updating the model of how the world is or by resampling the sensory states (active-inference)

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2. Problem of scope (Sims 2016)

“[C]an be expressed in the form of three commitments which are jointly incompatible, but which will cohere if one of them is rejected.” (ibid: 4)

I. Explanatory power: FEP is a self-sufficient account of cognition

II. Explanatory scope: FEP is meant to account for adaptive behavior in all biological self-organizing systems

III. Non-ubiquity: Cognition is not coextensive with biological self-organization

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2. Problem of scope (Sims 2016)

I. Explanatory power: FEP is a self-sufficient account of cognition

• FEP and views in its vicinity, like predictive processing, can explain all aspects of cognition

• “It is just the mathematico-functional structure given by the free energy principle […] that constitutes the explanation” (ibid: 5)

Rejection: we loose a shot at a unifying account of cognitive functions14

2. Problem of scope (Sims 2016)

II. Explanatory scope: FEP is meant to account for adaptive behavior in all biological self-organizing systems

• FEP is supposed to provide an account of how biological systems maintain homeostasis through adaptive behavior

• “[…] this second horn means that any functional architecture that appears in any biological system must be explicable in terms of free-energy minimization.” (ibid: 5)

Rejection: we loose active-inference and the solution to the dark room problem15

2. Problem of scope (Sims 2016)

III. Non-ubiquity: Cognition is not co-extensive with biological self-organization

• “[…] researchers in cognitive science generally do not expect that phenomena like attention and rational deliberation exist in very simple creatures like plants and bacteria.” (ibid: 5)

Rejection: homeostatic pancognitivism

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2. Problem of scope (Sims 2016)

• Sims rejects the non-ubiquity thesis and settles for an autopoietic and enactive account of cognition

• Consequence: plant cognition

• Is there another way to limit the scope of FEP and save its explanatory power without trivializing it?

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3. Models in science

Models are everywhere in science (Black, 1962): • scale models • analog models • mathematical models • theoretical models

• static vs. dynamical (Hartmann, 1996)

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3. Models in science

What are models?

Usually they are characterized in terms of their function (Giere, 1999; Gelfert, 2017): • Instantiating axioms of a theory (a mean to interpret a formal system) • Representing the phenomena (via similarity or analogy)

- Informational (observer independent) - Pragmatic (observer dependent)

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3. Models in science

The Ising Model • A ferromagnetic model in statistical mechanics • Each element of the lattice represents a magnetic

dipole moment of atomic spins which can occupy one of two states (+1 or -1)

• Their alignment determines the overall magnetization of the system, but it can be changed -either by external magnetic field or when the system undergoes a phase transition below a critical temperature

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3. Models in science

The Ising Model • Whether the system will undergo a phase

transition depends on its energy function, which is determined by the interactions between components:

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3. Models in science

The Hopfield network: • a recurrent neural network with non-linear

binary units • a network operates on a manner analogous

to spin glasses (which are disordered magnets) • The system works by being ‘cooled’ or

‘relaxed’ in to a (local) energy minimum

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3. Models in science

The Hopfield network: • The energy of the network is described by the equation:

• The algorithm for ‘relaxing’ the net:

“Pick any unit at random, flip it; i.e. change its 0 or 1 value. If the overall effect is to lower the energy level of the net, accept the change; otherwise refuse it. Do this again and again to arbitrarily chosen units until no single flip of a given unit will reduce the energy level of the entire net.” (Churchland & Sejnowski, 1992: 87)

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3. Models in science

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Cian O’Donnell @cian_neuro

3. Models in science

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Cian O’Donnell @cian_neuro

3. Models in science

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4. FEP as a modeling principle

1. The ‘as-if ’ talk is already present in the literature:

• “[…] there’s not much you can do with it, unless you ask whether measurable systems conform

to the principle.” (Friston, 2018: 21)

•“[…] the internal states […] will appear to engage in active Bayesian inference. In other words,

they will appear to model—and act on—their world to preserve their functional and structural integrity,

[…]” (Friston, 2013: 1)

2. FEP trades in idealizations and simplifications (e.g. the Laplacian assumption, ergodicity)

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4. FEP as a modeling principle

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Cian O’Donnell @cian_neuro

4. FEP as a modeling principle

A solution which avoids the problem of scope:

• If FEP is considered a modeling principle then its applicability depends on explanatory interests and tradeoffs

• For example, we don’t have to worry about the dark room problem, if we are modeling the functioning of the primary visual cortex or binocular rivalry

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4. FEP as a modeling principle

This solution also preserves FEPs unificatory ambitions:

• FEP can integrate many different models on many different levels of description (approximate Bayesian inference, PP, Gibbs sampling)

• It offers a formal framework within which different models can be compared and integrated

• While preserving the intuition that there is more to explanations in cognitive science and biology than what is given by the ‘mathematico-functional structure’

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4. FEP as a modeling principle

The prize to pay:

• Loose some of the explanatory power

• Not all models formulated within FEP will be explanatory (how-possibly vs. how-actually)

• What are the criteria for legitimate applications of FEP?

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The alternative is:

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[email protected]

@krysdolega

thank you