Convolutional Neural Generative Coding: Scaling Predictive Coding to Natural Images

In this work, we develop convolutional neural generative coding (Conv-NGC), a generalization of predictive coding to the case of convolution/deconvolution-based computation. Specifically, we concretely implement a flexible neurobiologically-motivated algorithm that progressively refines latent state maps in order to dynamically form a more accurate internal representation/reconstruction model of natural images. The performance of the resulting sensory processing system is evaluated on several benchmark datasets such as Color-MNIST, CIFAR-10, and Street House View Numbers (SVHN). We study the effectiveness of our brain-inspired neural system on the tasks of reconstruction and image denoising and find that it is competitive with convolutional auto-encoding systems trained by backpropagation of errors and notably outperforms them with respect to out-of-distribution reconstruction (including on the full 90k CINIC-10 test set)

The Predictive Forward-Forward Algorithm

We propose the predictive forward-forward (PFF) algorithm for conducting credit assignment in neural systems. Specifically, we design a novel, dynamic recurrent neural system that learns a directed generative circuit jointly and simultaneously with a representation circuit. Notably, the system integrates learnable lateral competition, noise injection, and elements of predictive coding, an emerging and viable neurobiological process theory of cortical function, with the forward-forward (FF) adaptation scheme. Furthermore, PFF efficiently learns to propagate learning signals and updates synapses with forward passes only, eliminating key structural and computational constraints imposed by backpropagation-based schemes. Besides computational advantages, the PFF process could prove useful for understanding the learning mechanisms behind biological neurons that use local signals despite missing feedback connections. We run experiments on image data and demonstrate that the PFF procedure works as well as backpropagation, offering a promising brain-inspired algorithm for classifying, reconstructing, and synthesizing data patterns.Comment: More revisions/edits, update to key diagram depicting PFF process, link to algorithm / simulation code (repo) now include

Active Predicting Coding: Brain-Inspired Reinforcement Learning for Sparse Reward Robotic Control Problems

In this article, we propose a backpropagation-free approach to robotic control through the neuro-cognitive computational framework of neural generative coding (NGC), designing an agent built completely from powerful predictive coding/processing circuits that facilitate dynamic, online learning from sparse rewards, embodying the principles of planning-as-inference. Concretely, we craft an adaptive agent system, which we call active predictive coding (ActPC), that balances an internally-generated epistemic signal (meant to encourage intelligent exploration) with an internally-generated instrumental signal (meant to encourage goal-seeking behavior) to ultimately learn how to control various simulated robotic systems as well as a complex robotic arm using a realistic robotics simulator, i.e., the Surreal Robotics Suite, for the block lifting task and can pick-and-place problems. Notably, our experimental results demonstrate that our proposed ActPC agent performs well in the face of sparse (extrinsic) reward signals and is competitive with or outperforms several powerful backprop-based RL approaches.Comment: Contains appendix with pseudocode and additional detail

Lifelong Neural Predictive Coding: Learning Cumulatively Online without Forgetting

In lifelong learning systems, especially those based on artificial neural networks, one of the biggest obstacles is the severe inability to retain old knowledge as new information is encountered. This phenomenon is known as catastrophic forgetting. In this article, we propose a new kind of connectionist architecture, the Sequential Neural Coding Network, that is robust to forgetting when learning from streams of data points and, unlike networks of today, does not learn via the immensely popular back-propagation of errors. Grounded in the neurocognitive theory of predictive processing, our model adapts its synapses in a biologically-plausible fashion, while another, complementary neural system rapidly learns to direct and control this cortex-like structure by mimicking the task-executive control functionality of the basal ganglia. In our experiments, we demonstrate that our self-organizing system experiences significantly less forgetting as compared to standard neural models and outperforms a wide swath of previously proposed methods even though it is trained across task datasets in a stream-like fashion. The promising performance of our complementary system on benchmarks, e.g., SplitMNIST, Split Fashion MNIST, and Split NotMNIST, offers evidence that by incorporating mechanisms prominent in real neuronal systems, such as competition, sparse activation patterns, and iterative input processing, a new possibility for tackling the grand challenge of lifelong machine learning opens up.Comment: Key updates including results on standard benchmarks, e.g., split mnist/fmnist/not-mnist. Task selection/basal ganglia model has been integrate

Provably Stable Interpretable Encodings of Context Free Grammars in RNNs with a Differentiable Stack

Given a collection of strings belonging to a context free grammar (CFG) and another collection of strings not belonging to the CFG, how might one infer the grammar? This is the problem of grammatical inference. Since CFGs are the languages recognized by pushdown automata (PDA), it suffices to determine the state transition rules and stack action rules of the corresponding PDA. An approach would be to train a recurrent neural network (RNN) to classify the sample data and attempt to extract these PDA rules. But neural networks are not a priori aware of the structure of a PDA and would likely require many samples to infer this structure. Furthermore, extracting the PDA rules from the RNN is nontrivial. We build a RNN specifically structured like a PDA, where weights correspond directly to the PDA rules. This requires a stack architecture that is somehow differentiable (to enable gradient-based learning) and stable (an unstable stack will show deteriorating performance with longer strings). We propose a stack architecture that is differentiable and that provably exhibits orbital stability. Using this stack, we construct a neural network that provably approximates a PDA for strings of arbitrary length. Moreover, our model and method of proof can easily be generalized to other state machines, such as a Turing Machine.Comment: 20 pages, 2 figure

On the Tensor Representation and Algebraic Homomorphism of the Neural State Turing Machine

Recurrent neural networks (RNNs) and transformers have been shown to be Turing-complete, but this result assumes infinite precision in their hidden representations, positional encodings for transformers, and unbounded computation time in general. In practical applications, however, it is crucial to have real-time models that can recognize Turing complete grammars in a single pass. To address this issue and to better understand the true computational power of artificial neural networks (ANNs), we introduce a new class of recurrent models called the neural state Turing machine (NSTM). The NSTM has bounded weights and finite-precision connections and can simulate any Turing Machine in real-time. In contrast to prior work that assumes unbounded time and precision in weights, to demonstrate equivalence with TMs, we prove that a $13$-neuron bounded tensor RNN, coupled with third-order synapses, can model any TM class in real-time. Furthermore, under the Markov assumption, we provide a new theoretical bound for a non-recurrent network augmented with memory, showing that a tensor feedforward network with $25$th-order finite precision weights is equivalent to a universal TM.Comment: 14 pages, 7 table