Bidirectional predictive coding

Predictive coding (PC) is an influential computational model of visual learning and inference in the brain. Classical PC was proposed as a top-down generative model, where the brain actively predicts upcoming visual inputs, and inference minimises the prediction errors. Recent studies have also shown that PC can be formulated as a discriminative model, where sensory inputs predict neural activities in a feedforward manner. However, experimental evidence suggests that the brain employs both generative and discriminative inference, while unidirectional PC models show degraded performance in tasks requiring bidirectional processing. In this work, we propose bidirectional PC (bPC), a PC model that incorporates both generative and discriminative inference while maintaining a biologically plausible circuit implementation. We show that bPC matches or outperforms unidirectional models in their specialised generative or discriminative tasks, by developing an energy landscape that simultaneously suits both tasks. We also demonstrate bPC’s superior performance in two biologically relevant tasks including multimodal learning and inference with missing information, suggesting that bPC resembles biological visual inference more closely.

💡 Research Summary

Predictive coding (PC) has long been championed as a biologically plausible framework for visual inference, but existing implementations fall into two mutually exclusive camps: generative PC (genPC), which uses top‑down predictions to reconstruct sensory inputs, and discriminative PC (discPC), which uses bottom‑up predictions to map inputs to higher‑level representations such as labels. While genPC excels at unsupervised tasks like image generation and associative memory, it performs poorly on supervised classification. Conversely, discPC matches back‑propagation on classification but cannot learn useful unsupervised representations. Hybrid approaches that combine the two (e.g., hybridPC) typically initialise the network with a bottom‑up pass but still rely on a single direction of error minimisation, leading to sub‑optimal performance in at least one domain.

The authors introduce bidirectional predictive coding (bPC), a single model that simultaneously carries out both top‑down and bottom‑up inference within a unified energy function. The energy is defined as

E(x,W,V)=∑{l=1}^{L‑1}α_gen‖x_l‑W{l+1}f(x_{l+1})‖² + ∑{l=2}^{L}α_disc‖x_l‑V{l‑1}f(x_{l‑1})‖²,

where W are top‑down weights, V are bottom‑up weights, and α_gen, α_disc balance the two error streams. In each trial the network first performs a fast feed‑forward sweep using V to initialise hidden activities (amortised inference). Then, neural dynamics iteratively update each layer’s value neurons x_l by gradient descent on E, driven by two separate error neurons that encode the top‑down (ε_gen) and bottom‑up (ε_disc) prediction errors. The update rule (Eq. 4) is fully local: each value neuron receives only its own activity, the two error signals, and the synaptic weights from adjacent layers. Weight updates (Eq. 6) are Hebbian products of presynaptic activity and the corresponding error, preserving the biological plausibility of genPC and discPC while adding a second error channel.

bPC can be trained in supervised, unsupervised, or mixed regimes. In supervised mode, the input layer x₁ is clamped to the image and the top layer x_L to the label; in unsupervised mode, x_L is left free, allowing the network to learn a compressed latent representation. The mixed mode clamps only a subset of top‑layer units, enabling simultaneous label inference and representation learning.

Empirical evaluation uses identical two‑hidden‑layer (256 units each) architectures across four models: discPC, genPC, hybridPC, and bPC (plus back‑propagation baselines). On MNIST and Fashion‑MNIST, bPC attains classification accuracies indistinguishable from discPC while achieving substantially lower reconstruction error than genPC when generating class‑conditional images. Visual inspection shows that bPC’s generated samples are closer to the class mean (lower RMSE) than any competitor, confirming that the unified energy landscape captures the data distribution more faithfully than separate unidirectional energies.

Beyond standard benchmarks, the authors test bPC on two biologically motivated tasks. First, a bimodal architecture links visual and auditory streams; training with both modalities demonstrates that bidirectional learning reduces reconstruction error in each modality compared with separate uni‑directional models. Second, they occlude portions of test images and clamp the label; bPC successfully infers the missing pixels, outperforming hybridPC and discPC, illustrating robust inference under incomplete sensory evidence.

The paper’s contributions are threefold: (1) a principled energy‑based formulation that unifies generative and discriminative predictive coding; (2) a fully local neural implementation with Hebbian plasticity that matches or exceeds the performance of existing models on both supervised and unsupervised tasks; (3) demonstration that the bidirectional error minimisation yields a smoother, more data‑aligned energy landscape, which explains the superior performance on multimodal learning and occlusion‑filled inference.

In discussion, the authors note that while α_gen and α_disc were fixed in experiments, they could be learned as precision parameters, potentially allowing the network to adaptively weight top‑down versus bottom‑up information. Future work is suggested on deeper hierarchies, alternative nonlinearities, and direct comparison with neural recordings to validate bPC as a mechanistic model of cortical visual inference. Overall, bPC offers a compelling bridge between the generative Bayesian view of the brain and the fast discriminative processing required for behavior, all within a biologically plausible computational substrate.