BZPEERReading, trust and collaboration for research
Menu

Discover

GraphFollow connections around a paper, topic or saved view.

Workspaces

HomePick up where your research flow left off.InboxHandle requests, replies and notifications from one place.CollectionsCurate reading lists, evidence sets and shareable dossiers.ResearchSee your private provenance graph, trail and imports.CollaborationMove from discovery into focused discussion rooms.PublishDraft, preview and publish full-text research articles.

Network

ExpertsFind specialists worth following or asking for help.CommunitiesJoin research circles organized around shared work.PartnersSee external organizations active around the same topics.

Opportunities

ListingsBrowse roles, calls and collaborations with clearer fit signals.

Account

Log inReturn to your reading and collaboration workspace.Create accountStart saving work, following people and joining teams.
Log inCreate account

Researcher profile

Rafal Bogacz

Rafal Bogacz contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceNeural and Evolutionary Computingeess.SPNeurons and Cognition

Trust snapshot

Quick read

Trust 21 - EmergingVerification L1Unclaimed author
6works
0followers
5topics
4close collaborators

Actions

Decide how to stay connected

Follow researcher0

Identity and collaboration

How to connect with this researcher

Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.

Log in to claim

Direct collaboration

Open a focused conversation when the fit is right

Claim this author entity first to unlock direct invitations.

Research graph

See the researcher in context

Open full explorer

Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.

Building this graph slice

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

6 published item(s)

preprint2026arXiv

Normative Networks for Source Separation via Local Plasticity and Dendritic Computation

Blind source separation (BSS) is a natural framework for studying how latent causes may be recovered from sensory mixtures, but deriving online and biologically plausible algorithms for structured (i.e., constrained to known domains) and potentially correlated sources remains challenging. Recent work has derived neural networks for BSS from maximization of an entropy measure, yet its online implementations involve complex and nonlocal recurrent dynamics. Motivated by this perspective, we propose Predictive Entropy Maximization, which achieves competitive performance in BSS, using only local weight updates. The method employs a close approximation of an entropy measure, yielding an objective function with easily interpretable components. Minimizing this objective leads to a predictive neural architecture in which feedforward synapses follow an error-driven rule (that can be realized through dendritic mechanisms), lateral inhibitory connections are learned with local Hebbian plasticity, and source-domain constraints are enforced through simple output nonlinearities. We derive explicit spectral bounds on the surrogate error, characterizing when the approximation is accurate. Empirically, Predictive Entropy Maximization remains robust under increasing source correlation and observation noise, outperforms biologically plausible algorithms that rely on stronger independence or decorrelation assumptions, and remains competitive with exact determinant- and correlative-information-based baselines. These results show how local plasticity and adaptive lateral inhibition can emerge from maximizing a regularized second-order entropy over structured source domains. Our implementation code is available at https://github.com/BariscanBozkurt/Predictive-Entropy-Maximization.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Understanding Sample Efficiency in Predictive Coding

Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Theoretical Framework for Inference and Learning in Predictive Coding Networks

Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are trained in two phases. First, neural activities are updated to optimize the network's response to external stimuli. Second, synaptic weights are updated to consolidate this change in activity -- an algorithm called \emph{prospective configuration}. While previous work has shown how in various limits, PCNs can be found to approximate backpropagation (BP), recent work has demonstrated that PCNs operating in this standard regime, which does not approximate BP, nevertheless obtain competitive training and generalization performance to BP-trained networks while outperforming them on tasks such as online, few-shot, and continual learning, where brains are known to excel. Despite this promising empirical performance, little is understood theoretically about the properties and dynamics of PCNs in this regime. In this paper, we provide a comprehensive theoretical analysis of the properties of PCNs trained with prospective configuration. We first derive analytical results concerning the inference equilibrium for PCNs and a previously unknown close connection relationship to target propagation (TP). Secondly, we provide a theoretical analysis of learning in PCNs as a variant of generalized expectation-maximization and use that to prove the convergence of PCNs to critical points of the BP loss function, thus showing that deep PCNs can, in theory, achieve the same generalization performance as BP, while maintaining their unique advantages.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learning

How the brain performs credit assignment is a fundamental unsolved problem in neuroscience. Many `biologically plausible' algorithms have been proposed, which compute gradients that approximate those computed by backpropagation (BP), and which operate in ways that more closely satisfy the constraints imposed by neural circuitry. Many such algorithms utilize the framework of energy-based models (EBMs), in which all free variables in the model are optimized to minimize a global energy function. However, in the literature, these algorithms exist in isolation and no unified theory exists linking them together. Here, we provide a comprehensive theory of the conditions under which EBMs can approximate BP, which lets us unify many of the BP approximation results in the literature (namely, predictive coding, equilibrium propagation, and contrastive Hebbian learning) and demonstrate that their approximation to BP arises from a simple and general mathematical property of EBMs at free-phase equilibrium. This property can then be exploited in different ways with different energy functions, and these specific choices yield a family of BP-approximating algorithms, which both includes the known results in the literature and can be used to derive new ones.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield networks (MCHNs), which possesses close links with self-attention in machine learning. In this paper, we propose a general framework for understanding the operation of such memory networks as a sequence of three operations: similarity, separation, and projection. We derive all these memory models as instances of our general framework with differing similarity and separation functions. We extend the mathematical framework of Krotov et al (2020) to express general associative memory models using neural network dynamics with only second-order interactions between neurons, and derive a general energy function that is a Lyapunov function of the dynamics. Finally, using our framework, we empirically investigate the capacity of using different similarity functions for these associative memory models, beyond the dot product similarity measure, and demonstrate empirically that Euclidean or Manhattan distance similarity metrics perform substantially better in practice on many tasks, enabling a more robust retrieval and higher memory capacity than existing models.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networks

Predictive coding networks (PCNs) are an influential model for information processing in the brain. They have appealing theoretical interpretations and offer a single mechanism that accounts for diverse perceptual phenomena of the brain. On the other hand, backpropagation (BP) is commonly regarded to be the most successful learning method in modern machine learning. Thus, it is exciting that recent work formulates inference learning (IL) that trains PCNs to approximate BP. However, there are several remaining critical issues: (i) IL is an approximation to BP with unrealistic/non-trivial requirements, (ii) IL approximates BP in single-step weight updates; whether it leads to the same point as BP after the weight updates are conducted for more steps is unknown, and (iii) IL is computationally significantly more costly than BP. To solve these issues, a variant of IL that is strictly equivalent to BP in fully connected networks has been proposed. In this work, we build on this result by showing that it also holds for more complex architectures, namely, convolutional neural networks and (many-to-one) recurrent neural networks. To our knowledge, we are the first to show that a biologically plausible algorithm is able to exactly replicate the accuracy of BP on such complex architectures, bridging the existing gap between IL and BP, and setting an unprecedented performance for PCNs, which can now be considered as efficient alternatives to BP.

0 citations0 reviewsNo code linkedOpen access