Mike's Notes
Alex Shkotin kindly shared two links to websites with me last night. One is the Verses Research Roadmap, which looks close to CAS. Here is an interesting discussion on the Ontolog Forum and a fascinating article from Verses.
It's the same approach I used to successfully build Pipi 9. The main difference is that Pipi is software running on a server containing hundreds of interacting agents causing emergent and adaptive properties. Pipi also sets out to provide a Complex Adaptive System (CAS) as a SAAS platform to host SAAS CAS Applications.
I did this through curiosity-led experimentation inspired by the computer modelling of biological cells. Verses' approach is led by the research-led theory of the brain. So, I found the research reading below a possible insight into why my experiments worked. I need to do some reading to understand the theory better.
Here is a number of extracts from multiple websites covering the discussion and background.
Resources
- https://groups.google.com/g/ontolog-forum/c/SWoioGgyx3g/m/Ut2DOEcXAQAJ
- https://www.verses.ai/research-development-roadmap
- https://arxiv.org/pdf/2212.01354.pdf
References
- Reference
Repository
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Last Updated
14/05/2025
From the Verses AI website
"Biological agents are efficient, curious, self-organizing systems that anticipate the effects of their actions on the world while smoothly coping with noise and uncertainty. The human brain, while an essential source of inspiration for AI, is only one manifestation of such capacities, which characterize intelligence in nature at many scales.
The hypothesis guiding research and development at VERSES AI is that artificial general intelligence (AGI) can be attained by discovering the deeper principles underlying biological intelligence and deploying them as design principles to construct cyber-physical ecosystems of intelligent agents in which humans are integral participants — what we call “shared intelligence”.
We originally laid out this vision for the present and future of AI in our white paper at the end of 2022. ..."
Ontolog Forum
However, it's unlikely that any company would hire somebody as chief scientist without a considerable amount of prior work. And I doubt that any company would make an announcement in a full-page ad in the New York Times unless they already had some kind of prototype. ..." - From the Ontolog Forum
A recent book (2022) from MIT Press with a foreword by Friston covers the field: "Active Inference: The Free Energy Principle in Mind, Brain, and Behavior." Chapters of that book can be downloaded for free. Appendix C has an annotated example of the Mathlab code.
From Wikipedia
Karl John Friston FRS FMedSci FRSB (born 12 July 1959) is a British neuroscientist and theoretician at University College London. He is an authority on brain imaging and theoretical neuroscience, especially the use of physics-inspired statistical methods to model neuroimaging data and other random dynamical systems.
Friston is a key architect of the free energy principle and active inference. In imaging neuroscience, he is best known for statistical parametric mapping and dynamic causal modelling.
In October 2022, he joined VERSES Inc, a California-based cognitive computing company focusing on artificial intelligence designed using the principles of active inference, as Chief Scientist.
Friston is one of the most highly cited living scientists and in 2016 was ranked No. 1 by Semantic Scholar in the list of top 10 most influential neuroscientists.
In the discussion, Dan Brickley of W3C, Dublin Core, Schema.org and Google Research shared this GIT hub
Repository maintained by Beren Millidge. who is a Postdoctoral Researcher in Machine Learning and Computational Neuroscience at the University of Oxford. Unravelling intelligence in both brains and machines.
Predictive Coding Paper Repository
This repository provides a list of papers that are interesting or influential about Predictive Coding. If you believe I have missed any papers, please contact me at beren@millidge.name or make a pull request with the information about the paper. I will be happy to include it.
Predictive Coding
Predictive Coding is a neurophysiologically-grounded theory of perception and learning in the brain. The core idea is that the brain always maintains a prediction of the expected state of the world, and that this prediction is then compared against the true sensory data. Where this prediction is wrong, prediction errors are generated and propagated throughout the brain. The brain's 'task' then is simply to minimize prediction errors.
The key distinction of this theory is that it proposes that prediction-errors, rather than predictions, or direct representation of sense-data is in some sense the core computational primitive in the brain.
Predictive coding originated in studies of ganglion cells in the retina, in light of theories in signal processing, about how it is much more efficient to send only 'different' or 'unpredicted signals' than repeating the whole signal every time -- see delta-encoding.
Predictive coding has several potential neurobiologically plausible process theories proposed for it -- see 'Process Theories' section, although the empirical evidence for precise prediction error minimization in the brain is mixed.
Predictive coding has also been extended in several ways. It can be understood as a variational inference algorithm under a Gaussian generative model and variational distribution. It can be setup as an autoencoder (predict your input, or next-state), or else in a supervised learning fashion.
Predictive coding can also be extended to a hierarchical model of multiple predictive coding layers -- as in the brain -- as well as using 'generalised coordinates' which explicitly model the higher order derivatives a state in order to be able to explicitly model dynamical systems.
More recent work has also focused on the relationship between predictive coding and the backpropagation of error algorithm in machine learning where under certain assumptions, predictive coding can approximate this fundamental algorithm in a biologically plausible fashion. Although the exact details and conditions still need to be worked out.
There has also been much exciting work trying to merge predictive coding with machine learning to produce highly performant predictive-coding-inspired architectures.
- Surveys and Tutorials
- Classics
- Neurobiological Process Theories
- Neuroscience applications
- Relationship to Backpropagation
- PC-inspired machine learning
- Extensions and Developments
- Relationship to FEP
Surveys and Tutorials
- A tutorial on the free-energy framework for modelling perception and learning , (2017) by Bogacz, Rafal [bib]
This is a great review which introduces the basics of predictive coding and its interpretation as variational inference. It also contains sample MATLAB code that implements a simple predictive coding network. I would start here.
- Predictive Coding: a Theoretical and Experimental Review , (2021) by Millidge, Beren, Seth, Anil and Buckley, Christopher L [bib]
This review walks through the mathematical framework and potential neural implementations in predictive coding, and also covers much recent work on the relationship between predictive coding and machine learning.
- The free energy principle for action and perception: A mathematical review , (2017) by Buckley, Christopher L, Kim, Chang Sub, McGregor, Simon and Seth, Anil K [bib]
This is a fantastic review which presents a complete walkthrough of the mathematical basis of the Free Energy Principle and Variational Inference, and derives predictive coding and (continuous time and state) active inference. It also presents the 'full-construct' predictive coding including with hierarchical layers and generalised coordinates in an accessible fashion. I would reccomend reading this after Bogacz' tutorial (although be prepared -- it is a long and serious read)
- A review of predictive coding algorithms , (2017) by Spratling, Michael W [bib]
A short and concise review of predictive coding algorithms up to 2017.
- Predictive coding , (2011) by Huang, Yanping and Rao, Rajesh PN [bib]
A nice review of simple predictive coding architectures with a focus on their potential implementation in the brain.
Classics
- Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects , (1999) by Rao, Rajesh PN and Ballard, Dana H [bib]
A key influential early paper proposing predictive coding as a general theory of cortical function.
- Predictive coding: a fresh view of inhibition in the retina , (1982) by Srinivasan, Mandyam Veerambudi, Laughlin, Simon Barry and Dubs, Andreas [bib]
One of the earliest works proposing predictive coding in the retina.
- A theory of cortical responses , (2005) by Friston, Karl [bib]
An early but complete description of predictive coding as an application of the FEP and variational inference under Gaussian and Laplace assumptions. Also surprisingly readable. This is core reading on predictive coding and the FEP
- Learning and inference in the brain , (2003) by Friston, Karl [bib]
The first paper establishing the links between predictive coding and variational inference.
- Attention, uncertainty, and free-energy , (2010) by Feldman, Harriet and Friston, Karl [bib]
Makes a conjectured link between precision in predictive coding and attention in the brain.
- Hierarchical models in the brain , (2008) by Friston, Karl [bib]
Presents the 'full-construct' predictive coding model with both hierarchies and generalised coordinates.
- DEM: a variational treatment of dynamic systems , (2008) by Friston, Karl J, Trujillo-Barreto, N and Daunizeau, Jean [bib]
Extends predictive coding to generalised coordinates, and derives the necessary inference algorithms for working with them -- i.e. DEM, dynamic expectation maximisation.
- Generalised filtering , (2010) by Friston, Karl, Stephan, Klaas, Li, Baojuan and Daunizeau, Jean [bib]
- Variational filtering , (2008) by Friston, Karl J [bib]
Foundational treatment of variational inference for dynamical systems, as represented in generalised coordinates. Also relates variational filtering to other non-variational schemes like particle filtering and Kalman filtering.
- Surfing uncertainty: Prediction, action, and the embodied mind , (2015) by Clark, Andy [bib]
Andy's book is great for a high level overview, strong intuition pumps for understanding the theory, and a fantastic review of potential evidence and neuropyschiatric applications.
Neurobiological Process Theories
- Dynamic predictive coding by the retina , (2005) by Hosoya, Toshihiko, Baccus, Stephen A and Meister, Markus [bib]
- Canonical microcircuits for predictive coding , (2012) by Bastos, Andre M, Usrey, W Martin, Adams, Rick A, Mangun, George R, Fries, Pascal and Friston, Karl J [bib]
A key process theory paper. Proposing perhaps the default implementation of predictive coding in cortical layers.
- Predictive coding as a model of biased competition in visual attention , (2008) by Spratling, Michael W [bib]
Demonstrates that predictive coding is equivalent to popular biased competition models of neural function.
- Dopamine role in learning and action inference , (2020) by Bogacz, Rafal [bib]
- Reconciling predictive coding and biased competition models of cortical function , (2008) by Spratling, Michael W [bib]
- Neural elements for predictive coding , (2016) by Shipp, Stewart [bib]Another great overview of a potentially neurobiologiclaly plausible process theory for predictive coding.
- Reflections on agranular architecture: predictive coding in the motor cortex , (2013) by Shipp, Stewart, Adams, Rick A and Friston, Karl J [bib]
A process theory of predictive coding including action predictions which implement active inference (continuous version).
- Cerebral hierarchies: predictive processing, precision and the pulvinar , (2015) by Kanai, Ryota, Komura, Yutaka, Shipp, Stewart and Friston, Karl [bib]
- Great expectations: is there evidence for predictive coding in auditory cortex? , (2018) by Heilbron, Micha and Chait, Maria [bib]
- Predictive coding in sensory cortex , (2015) by Kok, Peter and de Lange, Floris P [bib]
- Evaluating the neurophysiological evidence for predictive processing as a model of perception , (2020) by Walsh, Kevin S, McGovern, David P, Clark, Andy and O'Connell, Redmond G [bib]
A great review delving deep into the evidence for predictive coding being implemented in the brain. Evidence is currently somewhat lacking, although the flexibility of the predictive coding framework allows it to encompass a lot of the findings here.
- Fitting predictive coding to the neurophysiological data , (2019) by Spratling, MW [bib]
- Predictive processing: a canonical cortical computation , (2018) by Keller, Georg B and Mrsic-Flogel, Thomas D [bib]
Neuroscience applications
- Predictive coding is a consequence of energy efficiency in recurrent neural networks , (2021) by Ali, Abdullahi, Ahmad, Nasir, de Groot, Elgar, van Gerven, Marcel AJ and Kietzmann, Tim C [bib]
- The predictive coding account of psychosis , (2018) by Sterzer, Philipp, Adams, Rick A, Fletcher, Paul, Frith, Chris, Lawrie, Stephen M, Muckli, Lars, Petrovic, Predrag, Uhlhaas, Peter, Voss, Martin and Corlett, Philip R [bib]
- An interoceptive predictive coding model of conscious presence , (2012) by Seth, Anil K, Suzuki, Keisuke and Critchley, Hugo D [bib]
- Extending predictive processing to the body: emotion as interoceptive inference , (2013) by Seth, Anil K and Critchley, Hugo D [bib]
- An aberrant precision account of autism , (2014) by Lawson, Rebecca P, Rees, Geraint and Friston, Karl J [bib]
- A predictive coding perspective on autism spectrum disorders , (2013) by Van Boxtel, Jeroen JA and Lu, Hongjing [bib]
- Predictive coding: an account of the mirror neuron system , (2007) by Kilner, James M, Friston, Karl J and Frith, Chris D [bib]
- Predictive coding as a model of response properties in cortical area V1 , (2010) by Spratling, Michael W [bib]
- Predictive coding explains binocular rivalry: An epistemological review , (2008) by Hohwy, Jakob, Roepstorff, Andreas and Friston, Karl [bib]
Relationship to Backpropagation
- An approximation of the error backpropagation algorithm in a predictive coding network with local hebbian synaptic plasticity , (2017) by Whittington, James CR and Bogacz, Rafal [bib]
- Predictive Coding Approximates Backprop along Arbitrary Computation Graphs , (2020) by Millidge, Beren, Tschantz, Alexander and Buckley, Christopher L [bib]
- Can the Brain Do Backpropagation?---Exact Implementation of Backpropagation in Predictive Coding Networks , (2020) by Song, Yuhang, Lukasiewicz, Thomas, Xu, Zhenghua and Bogacz, Rafal [bib]
- Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networks , (2021) by Salvatori, Tommaso, Song, Yuhang, Lukasiewicz, Thomas, Bogacz, Rafal and Xu, Zhenghua [bib]
PC-inspired machine learning
- Representation learning with contrastive predictive coding , (2018) by Oord, Aaron van den, Li, Yazhe and Vinyals, Oriol [bib]
- Continual learning of recurrent neural networks by locally aligning distributed representations , (2020) by Ororbia, Alexander, Mali, Ankur, Giles, C Lee and Kifer, Daniel [bib]
- The neural coding framework for learning generative models , (2020) by Ororbia, Alexander and Kifer, Daniel [bib]
- Backprop-Free Reinforcement Learning with Active Neural Generative Coding , (2021) by Ororbia, Alexander and Mali, Ankur [bib]
- Spiking Neural Predictive Coding for Continual Learning from Data Streams , (2019) by Ororbia, Alexander [bib]
- Deep predictive coding networks for video prediction and unsupervised learning , (2016) by Lotter, William, Kreiman, Gabriel and Cox, David [bib]
- Video representation learning by dense predictive coding , (2019) by Han, Tengda, Xie, Weidi and Zisserman, Andrew [bib]
- Deep predictive coding network for object recognition , (2018) by Wen, Haiguang, Han, Kuan, Shi, Junxing, Zhang, Yizhen, Culurciello, Eugenio and Liu, Zhongming [bib]
- Deep predictive coding networks , (2013) by Chalasani, Rakesh and Principe, Jose C [bib]
- Deep predictive coding network with local recurrent processing for object recognition , (2018) by Han, Kuan, Wen, Haiguang, Zhang, Yizhen, Fu, Di, Culurciello, Eugenio and Liu, Zhongming [bib]
- Meaningful representations emerge from sparse deep predictive coding , (2019) by Boutin, Victor, Franciosini, Angelo, Ruffier, Franck and Perrinet, Laurent [bib]
- Hierarchical Predictive Coding Models in a Deep-Learning Framework , (2020) by Hosseini, Matin and Maida, Anthony [bib]
- PredNet and Predictive Coding: A Critical Review , (2020) by Rane, Roshan Prakash, Sz{"u}gyi, Edit, Saxena, Vageesh, Ofner, Andr{'e} and Stober, Sebastian [bib]
Extensions and Developments
- Relaxing the constraints on predictive coding models , (2020) by Millidge, Beren, Tschantz, Alexander, Seth, Anil and Buckley, Christopher L [bib]
This paper investigates how serveral biologically implausible aspects of the standard predictive coding algorithm -- namely requiring symmetric forward and backward weights, nonlinear derivatives, and 1-1 error unit connections can be relaxed without unduly harming performance of the network.
- Making Predictive Coding Networks Generative , (2019) by Orchard, Jeff and Sun, Wei [bib]
- Tightening the Biological Constraints on Gradient-Based Predictive Coding , (2021) by Alonso, Nick and Neftci, Emre [bib]
This paper further looks at how various implausibility of the predictive coding algorithm can be relaxed, and focuses especially on the question of how negative prediction errors could be represented, as well as invents a divisive prediction error scheme -- where prediction errors are the activities divided by the predictions.
- A Predictive-Coding Network That Is Both Discriminative and Generative , (2020) by Sun, Wei and Orchard, Jeff [bib]
- Dopamine role in learning and action inference , (2020) by Bogacz, Rafal [bib]
