Inferring neural activity before plasticity as a foundation for learning beyond backpropagation
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Abstract
Abstract For both humans and machines, the essence of learning is to pinpoint which components in its information processing pipeline are responsible for an error in its output — a challenge that is known as credit assignment . How the brain solves credit assignment is a key question in neuroscience, and also of significant importance for artificial intelligence. It has long been assumed that credit assignment is best solved by backpropagation, which is also the foundation of modern machine learning. However, it has been questioned whether it is possible for the brain to implement backpropagation and learning in the brain may actually be more efficient and effective than backpropagation. Here, we set out a fundamentally different principle on credit assignment, called prospective configuration . In prospective configuration, the network first infers the pattern of neural activity that should result from learning, and then the synaptic weights are modified to consolidate the change in neural activity. We demonstrate that this distinct mechanism, in contrast to backpropagation, (1) underlies learning in a well-established family of models of cortical circuits, (2) enables learning that is more efficient and effective in many contexts faced by biological organisms, and (3) reproduces surprising patterns of neural activity and behaviour observed in diverse human and animal learning experiments. Our findings establish a new foundation for learning beyond backpropagation, for both understanding biological learning and building artificial intelligence.
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The large majority of predictive coding networks developed for machine-learning tasks fix precisions to the identity throughout training, effectively assuming homoscedastic noise and reducing the free energy to a sum of unweighted squared errors.
“The large majority of PCNs developed for machine-learning tasks [Whittington and Bogacz, 2017, Salvatori et al., 2021, 2024, Millidge et al., 2022, Pinchetti et al., 2025, Oliviers et al., 2025, Song et al., 2024] fix precisions to the identity throughout training, effectively assuming homoscedastic noise and reducing the free energy to a sum of unweighted squared errors.”
From Closed-form predictive coding via hierarchical Gaussian filters (2026) · cites this paper as Song et al., 2024
Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredEq. (3) is the standard Hebbian rule used in predictive coding networks with fixed identity precision.
“Eq. ( 3) is the standard rule used in predictive coding networks with fixed identity precision [Whittington andBogacz, 2017, Song et al., 2024].”
From Closed-form predictive coding via hierarchical Gaussian filters (2026) · cites this paper as Song et al., 2024
The Methods > Models passage describes the predictive-coding weight update in Eq. (13) as simple Hebbian plasticity. Our copy does not specify that this rule uses fixed identity precision, so that qualification is not supported. (LLM, conf=0.83)
Experimental — accuracy not yet measuredIn iterative inference learning, posterior means are obtained by gradient descent run for T approximately 32-128 steps until equilibrium.
“In iterative inference learning, posterior means are obtained by gradient descent μℓ = -∂F/∂µ ℓ run for T ≈ 32-128 steps until equilibrium [Song et al., 2024, Whittington and Bogacz, 2017, Salvatori et al., 2024, Innocenti et al., 2024].”
From Closed-form predictive coding via hierarchical Gaussian filters (2026) · cites this paper as Song et al., 2024
The Methods > Models section describes updating neural activity to decrease energy, followed by relaxation until convergence. It reports a default limit of 128 relaxation steps, often ending early at about 60; Methods > Biologically relevant tasks also reports an experiment using 16 steps. Our copy does not establish a general 32–128-step range or describe the resulting activities specifically as posterior means. (LLM, conf=0.86)
Experimental — accuracy not yet measuredBackpropagation's core assumptions, such as a global error signal and strict separation of inference and learning phases, are incompatible with current knowledge of cortical computations and introduce interference.
“Yet its core assumptions, like a global error signal and strict separation of inference and learning phases, are incompatible with both current knowledge of cortical computations [Whittington and Bogacz, 2019] and introduce interference [Song et al., 2024].”
From Closed-form predictive coding via hierarchical Gaussian filters (2026) · cites this paper as Song et al., 2024
Under appropriate conditions, predictive coding recovers the gradients computed by backpropagation through purely local message passing.
“Under appropriate conditions, PC recovers the gradients computed by BP through purely local message passing [Whittington and Bogacz, 2017, Millidge et al., 2022, Song et al., 2024], making it a leading candidate for the next generation of energy-efficient, brain-inspired algorithms.”
From Closed-form predictive coding via hierarchical Gaussian filters (2026) · cites this paper as Song et al., 2024
FashionMNIST is a standard benchmark with sufficient complexity to differentiate predictive coding methods.
“Following Song et al. [2024], we evaluated on FashionMNIST [Xiao et al., 2017], a standard benchmark with sufficient complexity to differentiate methods, but one that does not establish the scaling potential of the approach to larger natural-image datasets.”
From Closed-form predictive coding via hierarchical Gaussian filters (2026) · cites this paper as Song et al. [2024]
Predictive coding networks have recently been rediscovered as candidates for solving machine learning tasks and as a potential alternative to backpropagation.
“Furthermore, predictive coding networks have recently been rediscovered as potent candidates for solving machine learning tasks (e.g., the classification or generation of static images, Sun & Orchard, 2020; Song et al., 2020) and even a potential alternative to the backpropagation algorithm (Song et al., 2024; Millidge et al., 2022b; Whittington & Bogacz, 2017).”
From The generalized Hierarchical Gaussian Filter (2026) · cites this paper as Song et al., 2024
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Reverse Differentiation via Predictive Coding
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A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding NetworksPreprint
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Minimizing Control for Credit Assignment with Strong FeedbackPreprint
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A survey on neuro-mimetic deep learning via predictive coding
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Self-citationThe generalized Hierarchical Gaussian Filter
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Closed-form predictive coding via hierarchical Gaussian filters
Baskakovs, A., Estebe, S., Enevoldsen, K., Nielbo, K., Mathys, C., & Legrand, N. (2026) · arXiv · doi:10.48550/arxiv.2605.20293
- Authors
- Song, Y., Millidge, B., Salvatori, T., Lukasiewicz, T., Xu, Z., & Bogacz, R.
- Affiliations
- University of Oxford (GB)
- TU Wien (AT)
- Hebei University of Technology (CN)
- Corresponding author
- Song, Yuhang
- Lukasiewicz, Thomas
- Xu, Zhenghua
- Venue
- Nature Neuroscience
- Published
- 2024-01-03
- Volume
- 27
- Issue
- 2
- Pages
- 348-358
- ISSN
- 1097-6256 (ISSN-L)
- 1546-1726
- PMC
- PMC7615830
- OpenAlex
- W4390572244
- Cited by
- 85
- References
- 115
- Citations by year
- 2026: 22 · 2025: 36 · 2024: 22 · 2023: 4 · 2022: 1
- FWCI
- 19.30
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Nature Neuroscience (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- reposiTUm (TU Wien) (submittedVersion, cc-by)
- Funders
- Alan Turing Institute (EP/N510129/1., N510129)
- National Natural Science Foundation of China (61906063, 62276089)
- AXA Research Fund
- Natural Science Foundation of Hebei Province (F2021202064, E2019050017)
- China Scholarship Council (EP/N510129/1)
- Natural Science Foundation of Tianjin City (19JCQNJC00400)
- Hebei University
- Hebei University of Technology
- Directorate for Biological Sciences
- Medical Research Council (MC_UU_00003/1, MC_UU_00003, EP/N510129/1)
- Engineering and Physical Sciences Research Council (N510129, EP/N510129/, EP/N510129/1, EPSRC grant EP/N510129/1)
- Biotechnology and Biological Sciences Research Council (BB/S006338/1)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Keywords
- credit assignment, synaptic plasticity, cortical circuits, backpropagation, learning efficiency
- MeSH terms
- Machine Learning, Animals, Humans, Neuronal Plasticity, Prospective Studies, Neural Networks, Computer, Rats
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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