Thursday, 3 February 2022

The Free Energy Principle For Dummies

This is an excerpt from the book: The Knowing Universe.

A philosophical and scientific theory with the potential to explain existence appears to be coalescing around the variational free-energy principle (FEP). Almost two decades ago, Karl Friston introduced the FEP as a unified neuroscientific theory. These initial papers are now some of the most cited in the field and have inspired thousands of other papers developing his principle and applying it to everything. Great excitement is building from a growing body of evidence hinting that the same general strategy brains use to keep their hosts in existence may be common to all forms of existence.

While this approach has gained tremendous popularity among researchers, it has also baffled many experts. As Wikipedia tells us (Wikipedia):

The free energy principle has been criticized for being very difficult to understand, even for experts.

Although this simple-sounding principle is transforming cognitive neuroscience and is considered by many  (myself included) as the most promising approach to a theory of everything, the bafflement it induces in smart people is legendary.

In contrast to its supposed difficulty, I marvel that it makes such clear sense. How could I so easily comprehend this principle, which seems to escape much brighter people? Perhaps the answer is that my unusual intellectual journey has arrived independently at many of the conclusions underlying this principle, and without these distinctive insights, it may well have remain incomprehensible to me. The upside is that perhaps this background may offer some assistance to those struggling to understand the FEP.  

We can easily state the principle: everything attempts to minimize the surprise it experiences. It sounds pretty innocuous for a theory of everything; in fact, it has an almost Zenlike simplicity. But like a Zen koan, its meaning is elusive. Many papers fail to fully explain the principle before diving into complex mathematics and computer simulations, and some readers are left wondering about the claimed links between surprise and existence.

The ability of all things to experience surprise contains one critical assumption that is rarely explicitly mentioned. The assumption is this: the existence of every ‘thing’ depends on a model having knowledge for its self-creation and maintenance. This model provides an expected roadmap for existence, and surprise occurs when its expectations are unmet. For many of us, the idea of everything having built-in models that can be surprised is a little hard to accept. But consider that all life has genetic models and complex animals have neural models, and humans have cultural models. Each of these models can be surprised by the evidence. Friston sometimes uses the example of a fish whose genetic and neural models expect it to be in the water and are surprised if it is not. Surprised genetic and neural models are often precursors of death, and surprised cultural models are often precursors of cultural extinction. That is why all things attempt to avoid surprising their models; things that don't trend towards non-existence.

What about physical existence? As we discuss in chapter 8, it turns out that the quantum wave function may form a similar model for quantum existence, but the argument is somewhat more complicated (Friston, 2019), so here we start with more familiar examples.

This connection between models and existence is profound and deserves some explanation. Why should existence require a model? The short answer is that the challenges to existence are formidable, and existence does not occur without following a detailed, knowledgeable model. But we see existence all around us. In what sense is it challenging to achieve? A law of nature, the second law of thermodynamics, summarizes the challenges to existence: disorder increases in all things. If a thing's disorder increases enough, it ceases to be that thing; it becomes non-existent. As we see a little later, the second law and the free energy principle say much the same thing, but while the second law focuses on existence's challenges, the free energy principle focuses on their circumvention through reducing their models' surprise.

But how do things act to minimize surprising evidence? There are two answers: things can accurately follow their models and produce evidence confirming their model predictions, or secondly, they can improve their models to make better predictions. In short entities can either cause reality to conform to their model or cause their model to better conform to reality. The first strategy is easy to comprehend as our genetic, neural, and cultural models predict existence enhancing outcomes and, as a bonus, provide algorithms for achieving those outcomes. Thus this route to minimal surprise only involves following the models as accurately as possible - anything's best strategy for existence is to reduce errors in executing their finely-honed models. The second answer is the evolutionary processes that create and hones more knowledgeable models. This process called inference uses a thing's relative ability to achieve existence as evidence and uses this evidence of existence to update their models' accuracy; think natural selection where evidence generated by the struggle for existence updates the genetic model — the more knowledgeable the model, the fewer surprises it experiences in the world.

This principle's beauty is in its mathematical depth; Friston and colleagues have developed mathematics to approximate surprise experienced in complex, real-world phenomena.  Here we only scratch the mathematical surface to reveal a bit of its potential.

We should probably start with the mathematical definition of surprise; it is -ln(p), where p is a probability that some hypothesis is true. How does evidence create this surprise? When sufficient evidence reveals the truth of a particular hypothesis, then -ln(p) is the surprise experienced; if the initial probability assigned to the hypothesis is small but the evidence indicates that the hypothesis is true, there is much surprise.

What does -ln(p) have to do with an entity's model? Models used by real-world things to achieve their existence are probabilistic models. Genetic, neural and cultural models involve a family of competing hypotheses, each of which is assigned a probability that they are the one true hypotheses. For example, at each of an organism's genetic locations or locus, various individuals from the population may have different genetic sequences or alleles. The probability assigned to each specific sequence is its relative frequency within the population, and this probability is the fitness of the sequence.  If over many generations a population evolves from having multiple alleles at a locus to having only one, the probability for that sequence is 1, and we might say that the evidence has proven it to be the fittest among the initial family of alleles; it is the one proven to produce the least surprise among the options.

We can consider the hypothesis assigned probability p as one in a mutually exclusive and exhaustive family of hypotheses offering solutions to a real-world existential challenge. Being mutually exclusive and exhaustive has a couple of consequences. The first is that one and only one of the hypotheses must be true. The second is that the sum of the probabilities over the family of hypotheses must equal 1. If the probabilities add to less than 1, then the hypotheses are not exhaustive; some other possibility exists. If the probabilities add to more than 1, they are not mutually exclusive; the hypotheses have some logical overlap.

Real-world instances simplify these mathematical complexities. For example, the family of alleles at a genetic locus within a population of organisms is naturally mutually exclusive and exhaustive. It is mutually exclusive because each allele is unique, and it is exhaustive because the family consists of all the alleles within the population. Thus the sum of the relative frequencies of alleles in the population must equal 1 as that is implicit in the meaning of relative frequency.

Because the probabilities assigned to the family of hypotheses sum to 1, they form a probability distribution, and a good deal of mathematical machinery is available for analyzing probability distributions. For example, every probability distribution has the property of entropy or the amount of expected surprise: Sum(-p ln(p)). Thus minimizing free energy is equivalent to minimizing model entropy. But the second law of thermodynamics states that the entropy of isolated systems must always increase.

It is in this seeming contradiction that it all comes together. Systems having unconstrained entropy are subject to unconstrained surprise and dissipate into non-existence. An alternative statement of the free energy principle is that existence depends on minimal surprise.  Systems only achieve existence if they know how to avoid isolation and exploit outside energy sources to decrease their entropy. And they must accomplish this while following the second law in producing entropy increases in the combined system plus environment. For example, a photosynthetic cell's existence depends on its genetic knowledge for using the sun's energy to counter the second law's tendency towards disintegration; the combined cell-plus-sun system's entropy increases as dictated by the second law and more than pays for the cell's entropy reduction.

Existing systems follow their models' knowledge to navigate the environment and fend off nature's relentless forces towards dissipation. In short, existence is fiendishly tricky; it requires a great deal of knowledge to achieve and must follow that knowledge without errors or surprises. The free-energy principle is important because it is a road map, perhaps nature's only roadmap, for achieving existence, and that is why it provides a principled account of all things.

 

References

Friston Karl A free energy principle for a particular physics [Journal]. - [s.l.] : arXiv:1906.10184 [q-bio.NC], 2019.

Raviv Shaun The Genius Neuroscientist Who Might Hold the Key to True AI [Online] // Wired. - Wired Magazine, November 13, 2018. - https://www.wired.com/story/karl-friston-free-energy-principle-artificial-intelligence/.

Wikipedia Free energy principle [Online] // Wikipedia. - 3 11, 2019. - https://en.wikipedia.org/wiki/Free_energy_principle.

 

Friday, 28 January 2022

Following the FEP to self-actualization

 

 John O. Campbell

Looking back over a long life, my efforts at self development or self-actualization appear meandering and ineffectual. Where did I go wrong and what might I have done to navigate a more direct course? At long last I may have found an answer – one that might be of some utility for those setting course towards this destination.

But first, a quick review of the goal. What is self-actualization, or as some call it, self-authenticity?

Perhaps its roots in western philosophy extend to Friedrich Nietzsche (1844–1900) who is largely remembered for his pronouncement that God is dead and esteem for the will to power and for supermen. These memes may seem incongruent with self-actualization but when properly understood they reinforce it. Nietzsche was an atheist and viewed religious indoctrination of the young as one of the main barriers to their formation of authentic worldviews, a necessary accomplishment for a strong moral character or a ‘superman’ who would be immune to the herd mentality. Having studied Darwin, he concluded that Christianity had lost its hold on humanity and that this offered potential for self-actualization as well as terror at being cast adrift in an unfamiliar universe.

This theme was developed by existentialist philosophers of the mid twentieth century, perhaps reaching its culmination in the writings of the great humanist psychologist Abraham Maslow, best remembered for introducing a hierarchy of human needs and placing self-actualization at its pinnacle.

 


But he gradually became aware of an ultimate stage even beyond self-actualization, just prior to his untimely death in 1970 Maslow had increasingly become convinced that self-actualization is healthy self-realization on the path to self-transcendence. And psychological studies have since demonstrated that self-actualization does show a strong positive correlation with increased feelings of oneness with the world (Kaufman, 2018).

Young adults, especially students have long been prone to rebellious tendencies. A natural urge towards freedom drives young adults to cast off the social constraints imposed by prior generations in forms such as religion and strident demands of a consumer society in favour of developing one’s true self. But the road to freedom is not easy and after a few years of the highs and lows of turning on, tuning in, and dropping out, for example, many revert to more traditional world views.

What has been lacking is a reliable road map that might aid us in our journey towards freedom and self-actualization. Well, science may now have provided an answer, in the form of the variational free energy principle (FEP). In a nutshell the FEP, developed by renowned neuroscientist Karl Friston, states that all existence depends upon reducing the surprise or difference between an entities model for existence and its experience in achieving existence. This can be done in two fundamental ways, either make the model closer to reality or cause reality to follow the model more closely.

We may illustrate these two methods as a cyclical process where entities are created through the autopoietic process of carefully following the model and then the entity’s experience in achieving existence is used as evidence to update the model in a Bayesian manner.

 

For example, the model underlying biological existence might be the inherited genetic and epi-genetic model, autopoietic creation takes place as described by developmental biology, the existing entity is the resulting phenotype and the experience of the phenotype in achieving existence updates the model through natural selection. This describes an evolutionary process where knowledge for more resilient forms of existence is accumulated in the genetic model (Campbell 2022).

So, what could this have to do with self-actualization. Well, a self-actualized person is an existing entity whose evolution is described by this paradigm. Her model is her world view, including plans and expectations for her life - the self she strives to be. Her autopoietic self-creation occurs through faithful adherence to her model - she attempts to follow her life plans and these attempts result in an actual self that may conform to the plan in some areas and deviate from it in others. And this experienced actual self provides a test of her model or life plan that she may use to update and fine-tune it. Best of all this is an evolutionary process; over many cycles she continuously approaches the person she envisions in a process of self-actualization. 

One extremely important recent finding is that over time, evolving under the FEP, the model becomes ever closer to the world it is modelling (Fields et al, 2022). And applied to self-actualization this might imply the eventual realization of Maslow’s goal of self-transcendence – becoming one with the world. 

But wait a minute, how could an abstract scientific model lead to self transcendence? In part the answer might be that the FEP is moving from the realm of scientific abstraction to the realm of natural processes, one capable of typifying all other natural processes. If we were to align our self development with this process, we could begin the long journey of connecting to the world and cognitively merging with it.

References

Campbell, J. O. (2022). The Knowing Universe. KDP. Retrieved from https://www.amazon.com/Knowing-Universe-John-Campbell/dp/B09JJFF771/ref=sr_1_1?crid=MKS7ZHOB6X6Y&keywords=the+knowing+universe&qid=1643396653&sprefix=the+knowing+universe%2Caps%2C122&sr=8-1

Chris Fields, K. F. (2022). A free energy principle for generic quantum systems. ArXiv preprint. Retrieved from https://arxiv.org/pdf/2112.15242.pdf

Kaufman, S. B. (2018, November). What Does It Mean to Be Self-Actualized in the 21st Century? Scientific American. Retrieved from https://blogs.scientificamerican.com/beautiful-minds/what-does-it-mean-to-be-self-actualized-in-the-21st-century/