Benchmarking Predictive Coding Networks -- Made Simple

In this work, we tackle the problems of efficiency and scalability for predictive coding networks in machine learning. To do so, we first propose a library called PCX, whose focus lies on performance and simplicity, and provides a user-friendly, deep-learning oriented interface. Second, we use PCX to implement a large set of benchmarks for the community to use for their experiments. As most works propose their own tasks and architectures, do not compare one against each other, and focus on small-scale tasks, a simple and fast open-source library adopted by the whole community would address all of these concerns. Third, we perform extensive benchmarks using multiple algorithms, setting new state-of-the-art results in multiple tasks and datasets, as well as highlighting limitations inherent to PC that should be addressed. Thanks to the efficiency of PCX, we are able to analyze larger architectures than commonly used, providing baselines to galvanize community efforts towards one of the main open problems in the field: scalability. The code for PCX is available at \textit{https://github.com/liukidar/pcax}.

Sequential Memory with Temporal Predictive Coding

Memorizing the temporal order of event sequences is critical for the survival of biological agents. However, the computational mechanism underlying sequential memory in the brain remains unclear. Inspired by neuroscience theories and recent successes in applying predictive coding (PC) to static memory tasks, in this work we propose a novel PC-based model for sequential memory, called temporal predictive coding (tPC). We show that our tPC models can memorize and retrieve sequential inputs accurately with a biologically plausible neural implementation. Importantly, our analytical study reveals that tPC can be viewed as a classical Asymmetric Hopfield Network (AHN) with an implicit statistical whitening process, which leads to more stable performance in sequential memory tasks of structured inputs. Moreover, we find that tPC with a multi-layer structure can encode context-dependent information, thus distinguishing between repeating elements appearing in a sequence, a computation attributed to the hippocampus. Our work establishes a possible computational mechanism underlying sequential memory in the brain that can also be theoretically interpreted using existing memory model frameworks.

Biologically Plausible Training Mechanisms for Self-Supervised Learning in Deep Networks

We develop biologically plausible training mechanisms for self-supervised learning (SSL) in deep networks. SSL, with a contrastive loss, is more natural as it does not require labelled data and its robustness to perturbations yields more adaptable embeddings. Moreover the perturbation of data required to create positive pairs for SSL is easily produced in a natural environment by observing objects in motion and with variable lighting over time. We propose a contrastive hinge based loss whose error involves simple local computations as opposed to the standard contrastive losses employed in the literature, which do not lend themselves easily to implementation in a network architecture due to complex computations involving ratios and inner products. Furthermore we show that learning can be performed with one of two more plausible alternatives to backpropagation. The first is difference target propagation (DTP), which trains network parameters using target-based local losses and employs a Hebbian learning rule, thus overcoming the biologically implausible symmetric weight problem in backpropagation. The second is simply layer-wise learning, where each layer is directly connected to a layer computing the loss error. The layers are either updated sequentially in a greedy fashion (GLL) or in random order (RLL), and each training stage involves a single hidden layer network. The one step backpropagation needed for each such network can either be altered with fixed random feedback weights as proposed in Lillicrap et al. (2016), or using updated random feedback as in Amit (2019). Both methods represent alternatives to the symmetric weight issue of backpropagation. By training convolutional neural networks (CNNs) with SSL and DTP, GLL or RLL, we find that our proposed framework achieves comparable performance to its implausible counterparts in both linear evaluation and transfer learning tasks.