Modern machine learning applications employ deep neural networks training with the error backpropagation algorithm. Although this algorithm is very effective, it lacks biological realism. For example, backpropagation requires symmetric connectivity, and a separate neural processing channel for error signals. Prior works have therefore proposed a number of more realistic alternatives for error backpropagation. However, most of them still suffer from demanding preassumptions that may be not fulfilled in the real brain, for example, they often still require either symmetric connectivity or two separate processing channels, and often require also special mathematical operations like subtractions or function inversions. Here I propose supervised counterstream learning in deep associative networks as a simpler approach that requires only recognition of errors during training, and then backpropagates correcting target activity through the same activity channel as used for forward propagation. For this, two activity waves are initiated at the same time in input and output layers and then traveling in opposite directions to meet in one of the hidden layers. By employing simple local Hebbian-type learning rules, the corresponding activity pattern sequences get linked bidirectionally, thereby decreasing error rates over time. Despite its simplicity and an incomplete hyperparameter optimzation, a high high test accuracy is achieved on the (binarized) MNIST data set that is comparable to more demanding architectures.
The brain learns abstract representations of high-dimensional sensory input, but the plasticity rules that enable such learning are unknown. We study biologically plausible algorithms on the Random Hierarchy Model (RHM), an artificial dataset designed to investigate how deep neural networks learn the intrinsic hierarchical structure of high-dimensional data. We focus on two types of local learning rules that avoid both a long convergence time and the use of a symmetric error network. The first type uses direct feedback signals to approximate error propagation from the output layer. The second type uses layerwise self-supervised contrastive or non-contrastive loss functions that do not explicitly approximate errors at the output layer. We show that all rules of the first type fail to solve the tasks of the RHM and trace this failure back to input-specific nonlinearities (`masking') that are implemented in full backpropagation and are essential for learning complex tasks. However, algorithms of the second type are able to learn the hierarchical hidden structure of the RHM tasks and are as data-efficient as supervised backpropagation training, while being compatible with known rules of synaptic plasticity in cortex.
Biologically plausible learning models aim to explain how neural circuits can implement effective learning under the constraints of real neurons. Although significant progress has been made, a major remaining challenge is that existing models often allow neurons or synapses to represent mixed-sign values, both positive and negative, in violation of a basic aspect of cortical circuitry -- Dale's constraint: biological neurons are either excitatory or inhibitory, but not both, and synapses cannot change sign. In this work, we address this discrepancy by introducing a biologically motivated neural architecture in which both neural activations and learning signals are represented by non-negative activity, and synapses have fixed sign, while still supporting backpropagation-like learning. Our approach uses two complementary interacting non-negative channels to represent positive and negative contributions, inspired by evidence of on-off representations in the brain. These channels are implemented through a simple neural circuit motif, which is repeated throughout the network in both bottom-up and top-down pathways. Combined with a local Hebbian learning rule, the resulting model propagates learning signals and updates weights using only local interactions between neurons. We show theoretically that our learning scheme can exactly recover the backpropagation update despite relying solely on non-negative error signals. Empirically, beyond satisfying stronger biological constraints, the on-off architecture learns efficient representations, yielding substantial gains over comparable vanilla networks on the Tiny ImageNet benchmark. These results demonstrate that effective learning can emerge from biologically plausible mechanisms without requiring mixed-sign signals, providing a step toward more realistic models of neural computation.
Biological neural circuits obey Dale's principle: each neuron's synapses are uniformly excitatory or inhibitory. Artificial networks that respect this constraint must coordinate separate excitatory and inhibitory populations, fundamentally changing how credit is assigned during learning. Several biologically plausible learning rules avoid backpropagation's weight transport requirement, but it has been difficult to achieve strong performance under Dale's principle beyond MNIST. Error Diffusion (ED) was originally proposed in a dual-stream excitatory/inhibitory architecture, where learning is driven by routing global error signals to all layers without transporting transposed forward weights or relying on random feedback matrices. Whether such a rule can scale under Dale's principle across both supervised classification and reinforcement learning remains unknown. Here, we introduce modulo error routing to extend Error Diffusion beyond binary classification, and show that a dual-stream excitatory/inhibitory architecture trained with this method achieves 96.7% on MNIST and establishes a 61.7% baseline on CIFAR-10, demonstrating that representation learning is possible even when strictly enforcing Dale's principle. For the classification setting, we introduce three domain-specific innovations: layer-specific sigmoid widths, batch-centered class error signals, and asymmetric initialization, and ablation analysis reveals that their relative importance reverses between MNIST and CIFAR-10, exposing task-dependent credit-assignment bottlenecks invisible to single-benchmark evaluation. In reinforcement learning, we integrate ED with Proximal Policy Optimization (PPO) and evaluate it on continuous-control tasks in Google Brax and on Craftax, an open-ended exploration task. We show that ED-PPO achieves competitive performance relative to Direct Feedback Alignment, a backpropagation-free baseline.