Every learning system must answer a deceptively simple question: when performance improves or degrades, which of its parameters deserve the credit or the blame? Artificial neural networks answer it with backpropagation. The algorithm uses the chain rule to compute the exact gradient of a loss function with respect to every weight. It is extraordinarily effective. In its canonical form, it is also biologically implausible by almost every criterion neuroscientists can articulate.

Yet cortex learns representations that closely resemble those produced by gradient-trained deep networks. Convolutional networks optimised for object recognition predict ventral stream responses remarkably well. This suggests that whatever the brain does, it arrives somewhere near where gradient descent arrives. The convergence poses a sharp theoretical question. Does synaptic plasticity implement an approximation to backpropagation, or does the brain use a fundamentally different optimisation principle that happens to reach similar solutions?

The answer matters beyond neuroscience. A learning rule is a theory of what a circuit is for. It states which quantity the system is trying to minimise and what information each synapse can access. Asking how local modification rules might approximate global optimisation exposes the computational architecture hidden in dendritic compartments, feedback projections, and diffuse neuromodulatory signals. What emerges is not a single algorithm. It is a layered solution to credit assignment, assembled by evolution from strictly local parts.

Marvin Minsky named the credit assignment problem in 1961, and it remains the central obstacle for any theory of learning in hierarchical systems. A behavioural error arrives as a low-dimensional outcome, often a single scalar. The synapses responsible may sit several processing stages away from both sensory input and motor output, and every downstream nonlinearity filters their contribution. Working out how a particular weight should change to reduce that error requires knowledge the synapse does not obviously possess.

Classical Hebbian plasticity, in which co-active neurons strengthen their connection, is admirably local but computationally blind. Variants such as Oja's rule extract principal components of input statistics. Spike-timing-dependent plasticity captures causal temporal structure. Yet correlation is not contribution. A Hebbian synapse cannot tell whether its own strengthening improves task performance. Purely correlational rules can discover structure in data, but on their own they cannot optimise an arbitrary objective across multiple layers.

Backpropagation solves this by computing an error term for each layer, working backward from the output. Each hidden unit's error equals the downstream errors, weighted by the transpose of the forward connections and scaled by the local derivative of the unit's activation function. The final weight update is the product of presynaptic activity and postsynaptic error. That form is perfectly local, essentially a Hebbian rule with one extra factor. The difficulty is not the update itself but delivering the error that drives it.

That delivery mechanism violates several biological constraints. The most cited is the weight transport problem. Feedback pathways would need synaptic strengths exactly matching the transposed forward weights, yet cortical feedback projections are anatomically distinct, and no known mechanism mirrors them. Backpropagation also requires separate forward and backward phases with activity held fixed. It needs signed, continuous errors, but neurons communicate through non-negative spike trains. And each unit must somehow know the derivative of its own activation function.

The problem compounds across time. Rewards often arrive seconds after the neural activity that produced them. Backpropagation through time would require storing a complete history of network states. A more productive framing asks a weaker question: what minimal information must reach a synapse for its expected update to correlate positively with the true gradient? Descent does not require exact gradients, only updates that lie within ninety degrees of them. That relaxation opens a large space of biologically feasible solutions.

Takeaway

The credit assignment problem is less about computing errors than about delivering them. Any rule whose updates point, on average, within ninety degrees of the true gradient will still descend the loss.

In 2016, Timothy Lillicrap and colleagues reported a result that unsettled the weight transport objection. They replaced the transposed forward weights with a fixed random feedback matrix, and the network still learned effectively. The mechanism, called feedback alignment, works because the forward weights gradually align with the random feedback pathway. The network never receives the true gradient. Instead, it reshapes itself until the error signals it does receive become useful, with updates settling well within ninety degrees of backpropagation's.

Feedback alignment has limits. It performs well on shallow and fully connected architectures but degrades on deep convolutional networks trained on large-scale image benchmarks. Several variants address this. Direct feedback alignment sends output errors straight to every hidden layer. Sign-symmetric feedback shares only the signs of the forward weights. Schemes such as weight mirroring use local plasticity to push feedback weights toward symmetry, showing that the transpose can be learned rather than assumed.

Predictive coding offers a different route. Rao and Ballard first formulated it as a model of hierarchical visual inference. Each cortical level predicts activity in the level below, and dedicated units encode the remaining prediction errors. In 2017, Whittington and Bogacz showed that, under specific conditions, the error units of a predictive coding network at equilibrium approximate backpropagated gradients. Throughout, the weight updates remain strictly local: products of presynaptic activity and postsynaptic error.

Dendritic models exploit the anatomy of pyramidal neurons directly. Basal dendrites receive feedforward input, while apical tufts in layer one receive top-down projections. Sacramento and colleagues proposed that apical compartments represent error as a mismatch between top-down feedback and predictions from lateral inhibitory interneurons. Payeur and colleagues extended this with burst-dependent plasticity. Single spikes carry feedforward information, while the probability of bursting carries feedback error. Separation in space within a single cell replaces the separate time phases backpropagation demands.

These proposals share a deeper structure. Equilibrium propagation, contrastive Hebbian learning, predictive coding, and dendritic error models all represent errors as differences between two activity states. One state is shaped by feedforward drive, the other is nudged toward top-down targets. Lillicrap and colleagues formalised this convergence as the NGRAD hypothesis. Its value lies in testable predictions. Plasticity should depend on apical activity, on bursting, and on the contrast between free and nudged dynamics.

Takeaway

Many candidate algorithms converge on one idea: an error need not be a separate signal at all. It can be encoded as the difference between what a neuron does with and without top-down influence.

Local error signals answer the question of direction, but learning also needs a signal about outcome. Here the dopaminergic system provides one of the clearest matches between neural data and algorithmic theory. In 1997, Schultz, Dayan, and Montague showed that phasic firing of midbrain dopamine neurons matches the temporal difference error of reinforcement learning. That error is the gap between what the system predicted and what it actually received, counting both the immediate reward and the discounted value of what comes next.

Three-factor learning rules formalise how this works at the synapse. Coincident presynaptic and postsynaptic activity does not change a synapse immediately. Instead, it creates an eligibility trace, a decaying molecular tag that lasts from hundreds of milliseconds to seconds. A later neuromodulatory signal converts that trace into lasting potentiation or depression. Experiments on striatal spines show that dopamine is effective only within a narrow window after pairing. This provides a cellular bridge across the temporal gap that credit assignment must span.

Yet a single broadcast signal faces a fundamental scaling problem. If every synapse receives the same reward signal, learning reduces to correlating random perturbations with outcomes, as in weight perturbation or the REINFORCE algorithm. The noise in such gradient estimates grows with the number of adjustable parameters, making pure reward-modulated learning prohibitively slow in large networks. Recent findings complicate the scalar picture. Distributional reinforcement learning suggests dopamine neurons span a range of optimism, collectively encoding a distribution of possible rewards.

Other neuromodulators appear to regulate learning rather than specify its content. Yu and Dayan proposed that acetylcholine signals expected uncertainty and norepinephrine signals unexpected uncertainty. Together they would set how strongly new evidence revises existing beliefs. Acetylcholine also shifts cortical processing toward bottom-up input and gates plasticity in sensory cortex. Kenji Doya extended this framing, suggesting that neuromodulators collectively tune the metaparameters of learning, including learning rate, exploration, and temporal discounting.

The emerging picture is a hybrid architecture. Feedback through dendrites and cortical hierarchies carries rich, neuron-specific information about the direction of change. Neuromodulators, by contrast, determine whether, when, and how strongly that change should occur. Roelfsema's attention-gated reinforcement learning illustrates the synergy. Top-down attentional feedback tags the neurons that contributed to a chosen action and restricts plasticity to them. This sharply reduces the noise that cripples pure reward learning and recovers performance close to backpropagation.

Takeaway

Neuromodulators may not carry the gradient at all. They decide when the gradient is worth following, turning a learning rule into a learning policy.

Asking whether the brain implements backpropagation may be the wrong question. Theory increasingly suggests that cortex approximates gradient descent through a distributed set of parts. Dendritic compartments separate feedforward drive from top-down error. Feedback pathways need not be symmetric. Neuromodulatory systems decide when plasticity happens.

This reframing has consequences. Learning rules become hypotheses about what circuits optimise and what information synapses can access. Those hypotheses make testable predictions about bursting, apical activity, and eligibility windows. The resemblance between deep network representations and cortical responses may reflect shared objectives rather than shared algorithms.

Perhaps the deepest lesson is that the brain may not compute gradients so much as arrange itself so that local changes tend to move downhill. If so, understanding learning means understanding how evolution split a global optimisation problem across billions of synapses, each seeing only its own small neighbourhood of activity.