🧠 neuroscience

Learning complex temporal dependencies via local synaptic plasticity

This paper demonstrates that temporal predictive coding (tPC), a biologically plausible framework utilizing local synaptic plasticity, can effectively learn complex temporal dependencies and rival traditional backpropagation-based methods by leveraging reservoir dynamics, hierarchical structures, and eligibility traces.

Original authors: Ng-Kee-Kwong, J., Tang, M., Akam, T., Bogacz, R.

Published 2026-11-03

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Ng-Kee-Kwong, J., Tang, M., Akam, T., Bogacz, R.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

To navigate the world, our brains must constantly track how events unfold over time. Whether we are predicting the next word in a sentence, timing a tennis swing, or simply remembering where we left our keys, the ability to extract patterns from a sequence of moments is fundamental to human thought. For decades, scientists trying to understand this process have relied on powerful computer models called recurrent neural networks. These digital systems are excellent at learning sequences, but they are often built on a foundation that does not match how real brains work. The standard method for teaching these networks involves a mathematical trick that requires the system to look backward through time, storing every past state and sending error signals in reverse. While this works well for computers, it is considered biologically impossible for neurons, which can only react to signals arriving at their immediate location and cannot access information from the distant past. This gap between effective artificial intelligence and plausible biology has left a major question unanswered: how does the brain actually learn complex temporal dependencies using only local, biological rules?

A team of researchers at the University of Oxford has taken a significant step toward answering this question by exploring a framework called temporal predictive coding. This approach suggests that the brain does not need to look backward to learn; instead, it constantly generates predictions about what will happen next and updates its internal model based on the difference between those predictions and reality. The researchers, Julian Ng-Kee-Kwong, Mufeng Tang, Thomas Akam, and Rafal Bogacz, investigated whether this local learning method could handle the complex, time-based tasks usually reserved for more powerful, biologically unrealistic algorithms. They found that by refining this predictive coding framework, they could create networks that learn to remember context, solve intricate puzzles involving time delays, and remain robust against distractions, all while using only the simple, local rules that real neurons are known to follow.

The core of their investigation involved testing a specific version of this predictive coding system against a standard, truncated version of the backward-learning algorithm. In the standard backward method, the computer calculates how much a mistake at the end of a sequence was caused by events that happened just one step ago. The researchers showed that their predictive coding system produces mathematically similar updates to this one-step backward method, but with a crucial difference in how it processes information. In the predictive coding model, the system does not just pass information forward; it actively refines its internal state at every moment by comparing its prediction with the actual sensory input it receives. This creates a subtle but powerful flow of information from the present observation back into the network's memory, allowing it to correct its course in real time. When they tested this on a simple task of tracking a moving particle's position, the predictive coding model learned the task easily, whereas a standard network using the one-step backward method failed, unable to integrate the velocity information over time without that extra, immediate feedback.

Building on this foundation, the team explored whether these networks could handle more complex sequences where the current moment depends on events from several steps in the past, a type of problem known as non-Markovian. In these scenarios, knowing the immediate past is not enough; the system must hold a longer context in mind. The researchers demonstrated that their predictive coding networks could exploit their internal dynamics to act like a reservoir, a high-dimensional state space where past inputs linger and influence the present. Unlike standard reservoir computers that keep their internal connections fixed, this system could shape its own internal pathways through local learning. By adjusting the connections between neurons based on local errors, the network reorganized its internal state so that different patterns became easier to distinguish. This allowed the system to learn alternating sequences of zeros and ones that required remembering a block of several steps, a task that fixed reservoirs struggled with as the patterns became more complex.

To tackle even more difficult temporal challenges, the researchers introduced a hierarchical structure, stacking multiple layers of these predictive networks on top of each other. In this arrangement, each layer receives information from the layer below, but with a slight time delay, allowing different levels of the network to operate on different timescales. This architecture proved remarkably effective at solving tasks that required combining information from widely separated moments, such as a parity check where the system had to count the total number of specific signals over a long sequence to determine if the count was odd or even. While a single-layer network failed when the sequence became too long or the time gaps too wide, the multi-layered system succeeded. Furthermore, this hierarchical design provided a shield against interference. When the researchers introduced strong, distracting signals into the input stream, the single-layer network lost the memory of the original cue, but the hierarchical network retained it, selectively integrating the relevant information while filtering out the noise.

Finally, the team addressed the challenge of learning across very long delays, where the reward or error signal arrives long after the initial event. In biology, this is often handled by a mechanism called an eligibility trace, which acts like a temporary tag on a synapse, marking it as eligible for change until a global signal arrives to confirm the learning. The researchers incorporated this concept into their predictive coding framework, creating a system that could maintain a decaying memory of past activity. This allowed the network to link an event that happened several seconds ago with a learning signal that arrived much later. In tests involving a delayed response task, where the model had to remember a cue presented at the start of a trial and reproduce it after a variable delay, the system with these eligibility traces succeeded where the standard version failed. It could bridge gaps of up to ten time steps, successfully reproducing the original cue even after the delay, demonstrating that local plasticity rules can indeed support learning over extended periods.

The findings suggest that the brain may not need the complex, non-local machinery of backward error propagation to learn from time. Instead, relatively simple networks governed by local rules, when organized with predictive dynamics, hierarchical layers, and eligibility traces, can support sophisticated temporal learning. While these models are still simulations and not yet a complete account of the human brain, they offer a compelling alternative to the standard algorithms used in artificial intelligence. They show that biological plausibility does not require sacrificing the ability to learn complex patterns. By combining predictive coding with these additional mechanisms, the researchers have revealed a path toward understanding how biological systems might solve the difficult problem of temporal credit assignment, learning from the past without needing to look backward.

Technical Summary: Learning Complex Temporal Dependencies via Local Synaptic Plasticity

Problem Statement

The ability to extract and exploit temporal structure is fundamental to human cognition, underlying tasks such as decision-making, motor control, and speech processing. In computational neuroscience, Recurrent Neural Networks (RNNs) trained with Backpropagation Through Time (BPTT) are the standard tool for modeling these processes. However, BPTT is widely considered biologically implausible because it requires the precise storage of past neural states and the backward propagation of error signals across time, mechanisms not known to exist in the brain. Consequently, the computational principles enabling efficient learning of temporal dependencies under biologically plausible constraints (specifically, local synaptic plasticity) remain unresolved. While Predictive Coding (PC) offers a biologically plausible framework for perception, traditional formulations have largely focused on static settings, lacking explicit modeling of temporal structure.

Methodology

The authors investigate Temporal Predictive Coding (tPC), a framework that extends predictive coding to the temporal domain while adhering to local Hebbian update rules. The study employs a combination of theoretical analysis and empirical simulation to extend tPC and compare it against established learning algorithms.

Core Framework: Temporal Predictive Coding (tPC)

The tPC framework models the world as a sequence of hidden latent states ( $z^g_t$ ) generating observations ( $y_t$ ) based on inputs ( $x_t$ ).

Objective: The model performs Bayesian inference to minimize variational free energy ( $F_t$ ), which is approximated as a sum of squared prediction errors: a "temporal" error (difference between inferred and predicted hidden state) and a "sensory" error (difference between true and predicted observation).
Dynamics: Inference involves gradient descent on the hidden state to minimize free energy, while learning involves gradient descent on the weights.
Locality: Crucially, the resulting weight update rules depend only on quantities available locally at the synapse (pre-synaptic activity, post-synaptic error, and current input), satisfying biological plausibility constraints.

Theoretical Extensions and Comparisons

The paper systematically extends tPC and analyzes its relationship with other algorithms:

Equivalence to Truncated BPTT (tBPTT1): The authors theoretically demonstrate that tPC weight updates are structurally equivalent to tBPTT1 (BPTT truncated to one time step). However, tPC differs in its activity dynamics: the inference process allows current observations to implicitly influence the hidden state, creating an information flow from observation to state that standard RNNs lack.
Reservoir Dynamics: The study investigates tPC's ability to learn non-Markovian sequences (where future states depend on distant past inputs) by leveraging reservoir computing principles. Unlike standard reservoir computing where internal weights are fixed, tPC utilizes local plasticity to "sculpt" neural trajectories in state space, optimizing the reservoir for downstream readout.
Hierarchical Architecture (tPC-H): To address complex cross-temporal dependencies and robustness against distractors, the authors propose a hierarchical tPC model. In this architecture, layers receive inputs from the current and previous hidden states of the layer below, introducing explicit temporal offsets and allowing for integration across multiple timescales.
Eligibility Traces (tPC-E): To bridge long temporal gaps where credit assignment is difficult, tPC is augmented with biologically inspired eligibility traces. This variant (tPC-E) incorporates leaky recurrent dynamics and maintains exponentially decaying traces of past activity, allowing delayed error signals to influence synaptic plasticity, analogous to the e-prop and RFLO algorithms.

Key Results

1. Structural Equivalence and Implicit Information Flow

On a position estimation task (path integration), the authors show that while tPC and tBPTT1 share identical weight update forms, tPC outperforms standard RNNs trained with tBPTT1. This is because tPC's inference dynamics allow the current observation to directly refine the hidden state estimate, effectively solving the path integration problem without needing to accumulate velocity errors over long horizons as strictly as a standard RNN.

2. Learning Non-Markovian Sequences

In an alternating two-state sequence prediction task, tPC with plastic recurrent weights significantly outperformed standard reservoir computing (where internal weights are fixed). The results indicate that tPC does not merely rely on fixed reservoir dynamics; instead, local plasticity actively shapes the neural trajectories in state space to make the temporal context linearly separable for the readout layer.

3. Hierarchical Robustness and Complexity

Complex Dependencies: On delayed parity tasks (requiring the integration of bits separated by time), single-layer tPC failed on 4-bit tasks, whereas hierarchical tPC (tPC-H) with 3 layers successfully learned the task, matching the performance of BPTT with longer truncation horizons.
Distractor Robustness: In a task involving strong distractors, tPC-H demonstrated superior robustness compared to single-layer tPC. The hierarchical structure allowed the network to preserve task-relevant information by selectively integrating partially distinct temporal representations, whereas single-layer models lost the original cue under strong perturbations.

4. Long-Range Credit Assignment

In a delayed response working memory task with variable delays, standard tPC failed to reproduce cues after short delays. However, tPC-E (augmented with eligibility traces) successfully solved the task even with extended delays, performing comparably to e-prop and RFLO. This confirms that eligibility traces enable tPC to support temporally extended credit assignment while maintaining local update rules.

Significance and Claims

The paper claims that relatively simple recurrent networks governed by local Hebbian plasticity can support temporal learning in settings more complex than previously appreciated. Specifically:

Biological Plausibility: The work demonstrates that complex temporal dependencies can be learned without the biologically implausible mechanisms of full BPTT (global error backpropagation and state storage).
Unification of Frameworks: The study clarifies the relationships between tPC, BPTT (specifically tBPTT1), reservoir computing, and eligibility propagation (e-prop). It positions tPC as a unifying framework that can incorporate reservoir dynamics, hierarchical processing, and eligibility traces.
Mechanistic Insight: The findings suggest that biological neural networks may utilize a combination of local plasticity, hierarchical temporal integration, and eligibility traces to achieve robust temporal credit assignment.
Limitations: The authors modestly note that while these mechanisms support learning, further progress is needed to match the performance of BPTT in large-scale settings. They also acknowledge that their discrete-time implementation is a functional approximation and that continuous-time formulations or more complex memory architectures (like LSTMs) may be necessary for very long timescales.

In conclusion, the paper argues that biologically plausible mechanisms are sufficient to explain how neural systems might learn and represent temporal structure, challenging the notion that complex temporal learning strictly requires non-local, global optimization algorithms.