The Brain’s Learning Algorithm Isn’t Backpropagation

Predictive coding derives a biologically realistic learning rule from energy minimization that avoids backpropagation's core contradictions with brain physiology.

Credit Assignment Problem

• The brain must determine which synapses to change and by how much after an outcome (0:00-10:01).
• Backpropagation requires a distinct backward pass with precise global coordination and frozen activity, violating the brain's parallel, continuous operation.

Foundations of Predictive Coding

• The network minimizes total prediction error across layers using an energy function (10:02-20:04).
• Separate error neurons explicitly represent mismatches between predictions and actual activity.

Activity and Weight Updates

• Neural activity settles to a compromise between top-down predictions and bottom-up input (10:02-20:04).
• Synaptic weights follow a local Hebbian rule proportional to pre- and post-synaptic activity.

Complete System Behavior

• Clamping inputs or labels drives the network to equilibrium states that encode mappings or generate outputs (20:05-26:35).
• Local autonomy enables parallel computation and avoids catastrophic forgetting.

00:00 Introduction

Introduction

• Speaker: Artem ( neuroscience PhD student at Harvard ) introduces the central question: how does the brain learn so effectively, and why backpropagation (the standard in machine learning) is biologically implausible. The video proposes predictive coding as a biologically plausible alternative, derived from first principles, and aims to show how it works and what it implies for AI.
• Backpropagation is described as powerful but biologically incompatible with neural hardware due to two main constraints: lack of local autonomy and the need for discontinuous processing. The brain processes information and learns concurrently rather than in strictly separated forward/ backward phases.
• The promise of predictive coding: a framework where the brain predicts sensory input, and learning reduces prediction error through local, parallel updates. This could align neural dynamics with metabolic efficiency and local learning rules.

00:01:15 Credit Assignment Problem

Credit Assignment Problem

• The core challenge in any learning system with many adjustable parameters (weights) is how to assign credit to the right parameters for a given outcome. In ML, automatic differentiation and backpropagation provide a mathematically exact way to compute gradients for all parameters.
• The video notes that for the brain, the exact biological implementation of backpropagation is questionable because it requires precise, global error signals and phase-based computation, which conflicts with neural hardware.

02:49 Problems with Backprop

Problems with Backprop

• The brain cannot freeze forward activity to perform a backward pass; neural processing is continuous and parallel across layers, with no distinct forward and backward phases.
• Global coordination is hard to justify biologically: error signals would need to propagate with precise timing across the entire network, which seems unlikely given neural variability, neuromodulation, and local synaptic dynamics.
• The gist: backprop relies on nonlocal information and temporally precise sequences that biology does not obviously implement. This motivates looking for local, autonomous learning rules that still support effective credit assignment.

06:05 Foundations of Predictive Coding

Foundations of Predictive Coding

• Predictive coding frames learning as minimizing a global energy function defined by prediction errors across a hierarchy: higher levels predict the activity of lower levels, and lower levels generate prediction errors if predictions diverge from actual activity.
• Hierarchy: low level encodes raw sensory input; higher levels encode abstract features that help predict lower levels. Information flows bidirectionally: top-down predictions and bottom-up prediction errors.
• This architecture supports a continuous, distributed process rather than phase-separated learning, aligning with brain physiology.

08:07 Energy Formalism

Energy Formalism

• The brain is treated as an energy-based model: each network state has an energy representing total prediction error across layers. The system evolves to minimize this energy.
• Analogy: a network of springs and platforms where each node has an activity (height) and a platform above it that carries the predicted activity; the spring tension corresponds to squared prediction error.
• Prediction error for a neuron is the difference between its actual activity and its predicted activity. The total energy sums the squared errors across all layers.
• The objective is to minimize the total energy by optimally configuring both neural activities and synaptic weights.

11:08 Activity Update Rule

Activity Update Rule

• To minimize energy with respect to a neuron’s activity, take the derivative of the energy with respect to that activity. The update rule emerges as a balance between two forces:

- The negative of the neuron’s own prediction error (pulls activity toward its own prediction). - A term that incorporates how changes in this neuron’s activity affect downstream prediction errors via connections to lower layers (a kind of top-down influence).

• The resulting dynamic shows the neuron adjusting its activity to compromise between aligning with top-down predictions and better predicting the layer below.
• A key insight: activity updates are local, driven by prediction errors at the neuron and its immediate connections, not by global signals.

15:12 Neural Connectivity

Neural Connectivity

• Predictive coding requires two distinct neural populations within each layer:

- Representational neurons (X_sub_i^L) that encode predictions passed to the layer below. - Error neurons that encode the deviation between the representational neuron’s value and its prediction.

• This separation yields local connectivity patterns:

- Representational neurons are inhibited by their error neurons and excited by error neurons conveying feedback from the layer below. - Error neurons receive excitatory input from their own layer’s representational neurons and inhibitory input from выше-layer neurons that carry predictions.

• The two populations together implement the comparison between predictions and actual activities in a biologically plausible way.

17:42 Weight Update Rule

Weight Update Rule

• Weights update according to gradient descent on the energy, and for a weight between neuron I in layer L and neuron K in layer L−1, the update is proportional to the product of the presynaptic activity (I) and postsynaptic prediction error (K’s error).
• This rule resembles Hebbian plasticity: “cells that fire together wire together,” but here it’s tied to the predictive coding objective (minimizing errors across the hierarchy).
• A practical issue: weight transport problem – to compute weight updates, the same connection must serve both feedforward predictions and feedback error signals. In the brain, feedforward and feedback synapses are separate physically, so exact symmetry isn’t guaranteed. The update rules are similar but not identical, and exact symmetry may not be essential for functioning.
• Nonlinearities (activation functions) complicate exact symmetry, but approximate symmetry and local learning can still yield useful learning dynamics.

20:05 Putting all together

Putting all together

• If all parameters were free to move, the system would converge to a trivial zero-energy state; to avoid this, certain layers are clamped (e.g., bottom layer with sensory input, and sometimes the top layer with a target label during supervised tasks).
• Training proceeds as iterative relaxation: for a given input, neural activities and weights update locally until an energy minimum is reached. Repeating across examples refines the internal predictive model.
• Generative use: unclamp the output layer and let the network run to equilibrium to generate data consistent with its learned model.
• Supervised use: clamp the top layer to the target label, let inference determine the optimal input-to-output mapping encoded in weights, then read off the label from the top-layer activity after settling.
• Benefits of locality: learning updates are local to a neuron and its immediate neighbors, enabling parallelism and biological plausibility, and potentially better handling of information retention (less catastrophic forgetting) than global error-driven updates.

25:15 Brilliant

Brilliant

• Sponsor discussion: Brilliant.org offers interactive visualizations and problem-solving that build intuition for neural networks and related topics. A relevant course is Introduction to Neural Networks.
• The sponsor link is included to invite viewers to try Brilliant for 30 days and receive a discount.

26:27 Outro

Outro

• Recap: predictive coding provides a framework for learning that is neurally plausible, energy-minimizing, local, and parallel, potentially offering a bridge to next-generation AI architectures.
• The video invites further reading and exploration of the literature on predictive coding and brain-inspired learning.

Notable Quotes (verbatim)

The back propagation algorithm contradicts essential biological principles of brain function, making its exact implementation in neural tissue virtually impossible. The brain operates in a massively parallel locally autonomous system where computation and learning occurs simultaneously throughout the network in a distributed manner without centralized control. Neurons receive, process, and adapt to information in parallel without pausing computation to accommodate learning. The key advantage of predictive coding lies in its locality. Weight transport problem affects both back propagation and predictive coding. Neurons must be inhibited by their corresponding error neuron and excited by error neurons sending feedback signals from the layer below. The network's fundamental objective is to minimize the total prediction error by finding the optimal configuration of neural activities and connection weights. This algorithm operates with complete local autonomy.

Diagrams and Visuals (described)

• Springs-and-Platforms analogy: Each neuron is a node with an activity level; a top-down platform above each node represents its predicted activity; a spring connects the node to the platform; the energy grows with squared length of the spring (i.e., squared prediction error).
• A two-population per layer layout: representational neurons (that carry predictions downward) and error neurons (that carry prediction errors upward) with specific excitatory/inhibitory connections.
• The energy landscape is a high-dimensional surface where the network “rolls downhill” toward energy minima by adjusting activities and weights.

Resources Mentioned

• Books / Papers:

- Bogacz, R., 2017. A tutorial on the free-energy framework for modelling perception and learning. Journal of Mathematical Psychology 76, 198–211. https://doi.org/10.1016/j.jmp.2015.11.003 - Friston, K., 2018. Does predictive coding have a future? Nat Neurosci 21, 1019–1021. https://doi.org/10.1038/s41593-018-0200-7 - Huang, Y., Rao, R.P.N., 2011. Predictive coding. WIRES Cognitive Science 2, 580–593. https://doi.org/10.1002/wcs.142 - Keller, G.B., Mrsic-Flogel, T.D., 2018. Predictive Processing: A Canonical Cortical Computation. Neuron 100, 424–435. https://doi.org/10.1016/j.neuron.2018.10.003 - Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G., 2020. Backpropagation and the brain. Nat Rev Neurosci 21, 335–346. https://doi.org/10.1038/s41583-020-0277-3 - Marino, J., 2021. Predictive Coding, Variational Autoencoders, and Biological Connections. https://doi.org/10.48550/arXiv.2011.07464 - Millidge, B., Salvatori, T., Song, Y., Bogacz, R., Lukasiewicz, T., 2022a. Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation? - Millidge, B., Seth, A., Buckley, C.L., 2022b. Predictive Coding: a Theoretical and Experimental Review. https://doi.org/10.48550/arXiv.2107.12979 - Millidge, B., Song, Y., Salvatori, T., Lukasiewicz, T., Bogacz, R., 2023. A THEORETICAL FRAMEWORK FOR INFERENCE AND LEARNING IN PREDICTIVE CODING NETWORKS. - Millidge, B., Tschantz, A., Buckley, C.L., 2022c. Predictive Coding Approximates Backprop Along Arbitrary Computation Graphs. Neural Computation 34, 1329–1368. https://doi.org/10.1162/neco_a_01497 - Millidge, B., Tschantz, A., Seth, A., Buckley, C.L., 2020. Relaxing the Constraints on Predictive Coding Models. https://doi.org/10.48550/arXiv.2010.01047 - Rao, R.P.N., Ballard, D.H., 1999. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nat Neurosci 2, 79–87. https://doi.org/10.1038/4580 - Rosenbaum, R., 2022. On the relationship between predictive coding and backpropagation. PLoS ONE 17, e0266102. https://doi.org/10.1371/journal.pone.0266102 - Salvatori, T., Mali, A., Buckley, C.L., Lukasiewicz, T., Rao, R.P.N., Friston, K., Ororbia, A., 2025. A Survey on Brain-Inspired Deep Learning via Predictive Coding. https://doi.org/10.48550/arXiv.2308.07870 - Salvatori, T., Song, Y., Lukasiewicz, T., Bogacz, R., Xu, Z., 2023. Reverse Differentiation via Predictive Coding. https://doi.org/10.48550/arXiv.2103.04689 - Salvatori, T., Song, Y., Yordanov, Y., Millidge, B., Xu, Z., Sha, L., Emde, C., Bogacz, R., Lukasiewicz, T., 2024. A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks. https://doi.org/10.48550/arXiv.2212.00720 - Song, Y., Lukasiewicz, T., Xu, Z., Bogacz, R., n.d. Can the Brain Do Backpropagation? — Exact Implementation of Backpropagation in Predictive Coding Networks. - Song, Y., Millidge, B., Salvatori, T., Lukasiewicz, T., Xu, Z., Bogacz, R., 2024. Inferring neural activity before plasticity as a foundation for learning beyond backpropagation. Nat Neurosci 27, 348–358. https://doi.org/10.1038/s41593-023-01514-1 - Whittington, J.C.R., Bogacz, R., 2019. Theories of Error Back-Propagation in the Brain. Trends in Cognitive Sciences 23, 235–250. https://doi.org/10.1016/j.tics.2018.12.005 - Whittington, J.C.R., Bogacz, R., 2017. An Approximation of the Error Backpropagation Algorithm in a Predictive Coding Network with Local Hebbian Synaptic Plasticity. Neural Computation 29, 1229–1262. https://doi.org/10.1162/NECO_a_00949

• Sponsor: Brilliant.org, with ongoing promos and courses (e.g., Introduction to Neural Networks).
• Links:

- https://brilliant.org/ArtemKirsanov - https://brilliant.org/ardamcursenov (as referenced within the video script)

• Platform/context: Brilliant is a sponsor; the reference supports additional learning resources on neural networks.

Notable Concepts DefinedWithin This Video

• Credit Assignment Problem: How a learning system determines which parameters to adjust to improve a given output.
• Backpropagation: A calculus-based method to compute gradients for all parameters in a neural network by chaining derivatives through the entire compute graph.
• Predictive Coding: A brain-inspired framework where each layer predicts the layer below; learning proceeds by minimizing prediction errors through local rules.
• Energy-Based Model: A dynamic system where an energy function evaluates the system state; the goal is to minimize energy via local updates.
• Prediction Error: The difference between what a neuron or layer predicts and what actually occurs.
• Representational Neurons: Neurons that encode predictions passed down the hierarchy.
• Error Neurons: Neurons that encode prediction errors; they signal the discrepancy between actual activity and predicted activity.
• Weight Transport Problem: A challenge in biologically plausible learning where the same synapse would need to convey both feedforward predictions and feedback error signals with symmetric weights.
• Hebbian Plasticity: A learning rule often summarized as “cells that fire together wire together.”
• Clamping: Fixing the activity of certain layers (e.g., input or target output) during learning to drive the network toward a desired mapping.
• Local Autonomy: The idea that learning rules operate at the level of local circuitry without global control signals.
• Generative vs. Discriminative Use: Predictive coding supports generating samples from learned models and also performing supervised tasks via clamped outputs.

Author’s Key Takeaways

• Predictive coding provides a physically plausible alternative to backpropagation that aligns with brain physiology by using local prediction errors and two-population per layer dynamics.
• Learning emerges from the continual balancing act between predicting the layer below and being predicted by the layer above, driving equilibrium states that minimize overall prediction error.
• The brain’s learning rules can be parallel and continuous, avoiding the need for phase-separated forward/backward passes.
• While weight symmetry (the weight transport problem) remains a practical challenge, approximate symmetry and local update rules can still yield effective learning dynamics.
• Predictive coding may offer advantages over backpropagation in terms of robustness to catastrophic forgetting and parallel scalability, making it a compelling direction for AI research.

Executive Summary

The video argues that backpropagation, while effective in machine learning, runs into serious biological plausibility problems when mapped onto brain hardware due to the need for phase separation between computation and learning and the requirement for globally coordinated error signals. Predictive coding emerges as a compelling alternative, deriving from first principles and grounded in biological constraints. In this framework, the brain continually generates predictions across a hierarchical network and updates both neural activities and synaptic weights to minimize the total prediction error, treated as an energy to be minimized. This approach relies on local learning rules, distinct populations of representational and error neurons, and a continuous, parallel mode of operation that aligns with neurophysiology. The video develops the math and intuition from an energy-based perspective, shows how update rules for activities and weights arise, and discusses practical considerations like weight transport and nonlinearities. It then situates predictive coding as not only a plausible explanation of brain learning but also a potential path to more brain-like and robust AI systems. The sponsor section highlights Brilliant.org as a tool to deepen understanding of neural networks and related ideas.