Tight Stability, Convergence, and Robustness Bounds for Predictive Coding Networks

Energy-based learning algorithms, such as predictive coding (PC), have garnered significant attention in the machine learning community due to their theoretical properties, such as local operations and biologically plausible mechanisms for error correction. In this work, we rigorously analyze the stability, robustness, and convergence of PC through the lens of dynamical systems theory. We show that, first, PC is Lyapunov stable under mild assumptions on its loss and residual energy functions, which implies intrinsic robustness to small random perturbations due to its well-defined energy-minimizing dynamics. Second, we formally establish that the PC updates approximate quasi-Newton methods by incorporating higher-order curvature information, which makes them more stable and able to converge with fewer iterations compared to models trained via backpropagation (BP). Furthermore, using this dynamical framework, we provide new theoretical bounds on the similarity between PC and other algorithms, i.e., BP and target propagation (TP), by precisely characterizing the role of higher-order derivatives. These bounds, derived through detailed analysis of the Hessian structures, show that PC is significantly closer to quasi-Newton updates than TP, providing a deeper understanding of the stability and efficiency of PC compared to conventional learning methods.

R-AIF: Solving Sparse-Reward Robotic Tasks from Pixels with Active Inference and World Models

Although research has produced promising results demonstrating the utility of active inference (AIF) in Markov decision processes (MDPs), there is relatively less work that builds AIF models in the context of environments and problems that take the form of partially observable Markov decision processes (POMDPs). In POMDP scenarios, the agent must infer the unobserved environmental state from raw sensory observations, e.g., pixels in an image. Additionally, less work exists in examining the most difficult form of POMDP-centered control: continuous action space POMDPs under sparse reward signals. In this work, we address issues facing the AIF modeling paradigm by introducing novel prior preference learning techniques and self-revision schedules to help the agent excel in sparse-reward, continuous action, goal-based robotic control POMDP environments. Empirically, we show that our agents offer improved performance over state-of-the-art models in terms of cumulative rewards, relative stability, and success rate. The code in support of this work can be found at https://github.com/NACLab/robust-active-inference.

Contrastive Learning in Memristor-based Neuromorphic Systems

Spiking neural networks, the third generation of artificial neural networks, have become an important family of neuron-based models that sidestep many of the key limitations facing modern-day backpropagation-trained deep networks, including their high energy inefficiency and long-criticized biological implausibility. In this work, we design and investigate a proof-of-concept instantiation of contrastive-signal-dependent plasticity (CSDP), a neuromorphic form of forward-forward-based, backpropagation-free learning. Our experimental simulations demonstrate that a hardware implementation of CSDP is capable of learning simple logic functions without the need to resort to complex gradient calculations.

Deep Domain Adaptation: A Sim2Real Neural Approach for Improving Eye-Tracking Systems

Eye image segmentation is a critical step in eye tracking that has great influence over the final gaze estimate. Segmentation models trained using supervised machine learning can excel at this task, their effectiveness is determined by the degree of overlap between the narrow distributions of image properties defined by the target dataset and highly specific training datasets, of which there are few. Attempts to broaden the distribution of existing eye image datasets through the inclusion of synthetic eye images have found that a model trained on synthetic images will often fail to generalize back to real-world eye images. In remedy, we use dimensionality-reduction techniques to measure the overlap between the target eye images and synthetic training data, and to prune the training dataset in a manner that maximizes distribution overlap. We demonstrate that our methods result in robust, improved performance when tackling the discrepancy between simulation and real-world data samples.

Neuro-mimetic Task-free Unsupervised Online Learning with Continual Self-Organizing Maps

An intelligent system capable of continual learning is one that can process and extract knowledge from potentially infinitely long streams of pattern vectors. The major challenge that makes crafting such a system difficult is known as catastrophic forgetting - an agent, such as one based on artificial neural networks (ANNs), struggles to retain previously acquired knowledge when learning from new samples. Furthermore, ensuring that knowledge is preserved for previous tasks becomes more challenging when input is not supplemented with task boundary information. Although forgetting in the context of ANNs has been studied extensively, there still exists far less work investigating it in terms of unsupervised architectures such as the venerable self-organizing map (SOM), a neural model often used in clustering and dimensionality reduction. While the internal mechanisms of SOMs could, in principle, yield sparse representations that improve memory retention, we observe that, when a fixed-size SOM processes continuous data streams, it experiences concept drift. In light of this, we propose a generalization of the SOM, the continual SOM (CSOM), which is capable of online unsupervised learning under a low memory budget. Our results, on benchmarks including MNIST, Kuzushiji-MNIST, and Fashion-MNIST, show almost a two times increase in accuracy, and CIFAR-10 demonstrates a state-of-the-art result when tested on (online) unsupervised class incremental learning setting.

Minimally Supervised Learning using Topological Projections in Self-Organizing Maps

Parameter prediction is essential for many applications, facilitating insightful interpretation and decision-making. However, in many real life domains, such as power systems, medicine, and engineering, it can be very expensive to acquire ground truth labels for certain datasets as they may require extensive and expensive laboratory testing. In this work, we introduce a semi-supervised learning approach based on topological projections in self-organizing maps (SOMs), which significantly reduces the required number of labeled data points to perform parameter prediction, effectively exploiting information contained in large unlabeled datasets. Our proposed method first trains SOMs on unlabeled data and then a minimal number of available labeled data points are ultimately assigned to key best matching units (BMU). The values estimated for newly-encountered data points are computed utilizing the average of the $n$ closest labeled data points in the SOM's U-matrix in tandem with a topological shortest path distance calculation scheme. Our results indicate that the proposed semi-supervised model significantly outperforms traditional regression techniques, including linear and polynomial regression, Gaussian process regression, K-nearest neighbors, as well as various deep neural network models.

A Neuro-Mimetic Realization of the Common Model of Cognition via Hebbian Learning and Free Energy Minimization

Over the last few years, large neural generative models, capable of synthesizing intricate sequences of words or producing complex image patterns, have recently emerged as a popular representation of what has come to be known as "generative artificial intelligence" (generative AI). Beyond opening the door to new opportunities as well as challenges for the domain of statistical machine learning, the rising popularity of generative AI brings with it interesting questions for Cognitive Science, which seeks to discover the nature of the processes that underpin minds and brains as well as to understand how such functionality might be acquired and instantiated in biological (or artificial) substrate. With this goal in mind, we argue that a promising long-term pathway lies in the crafting of cognitive architectures, a long-standing tradition of the field, cast fundamentally in terms of neuro-mimetic generative building blocks. Concretely, we discuss the COGnitive Neural GENerative system, which is an architecture that casts the Common Model of Cognition in terms of Hebbian adaptation operating in service of optimizing a variational free energy functional.

On the Computational Complexity and Formal Hierarchy of Second Order Recurrent Neural Networks

Artificial neural networks (ANNs) with recurrence and self-attention have been shown to be Turing-complete (TC). However, existing work has shown that these ANNs require multiple turns or unbounded computation time, even with unbounded precision in weights, in order to recognize TC grammars. However, under constraints such as fixed or bounded precision neurons and time, ANNs without memory are shown to struggle to recognize even context-free languages. In this work, we extend the theoretical foundation for the $2^{nd}$-order recurrent network ($2^{nd}$ RNN) and prove there exists a class of a $2^{nd}$ RNN that is Turing-complete with bounded time. This model is capable of directly encoding a transition table into its recurrent weights, enabling bounded time computation and is interpretable by design. We also demonstrate that $2$nd order RNNs, without memory, under bounded weights and time constraints, outperform modern-day models such as vanilla RNNs and gated recurrent units in recognizing regular grammars. We provide an upper bound and a stability analysis on the maximum number of neurons required by $2$nd order RNNs to recognize any class of regular grammar. Extensive experiments on the Tomita grammars support our findings, demonstrating the importance of tensor connections in crafting computationally efficient RNNs. Finally, we show $2^{nd}$ order RNNs are also interpretable by extraction and can extract state machines with higher success rates as compared to first-order RNNs. Our results extend the theoretical foundations of RNNs and offer promising avenues for future explainable AI research.

Brain-Inspired Computational Intelligence via Predictive Coding

Artificial intelligence (AI) is rapidly becoming one of the key technologies of this century. The majority of results in AI thus far have been achieved using deep neural networks trained with the error backpropagation learning algorithm. However, the ubiquitous adoption of this approach has highlighted some important limitations such as substantial computational cost, difficulty in quantifying uncertainty, lack of robustness, unreliability, and biological implausibility. It is possible that addressing these limitations may require schemes that are inspired and guided by neuroscience theories. One such theory, called predictive coding (PC), has shown promising performance in machine intelligence tasks, exhibiting exciting properties that make it potentially valuable for the machine learning community: PC can model information processing in different brain areas, can be used in cognitive control and robotics, and has a solid mathematical grounding in variational inference, offering a powerful inversion scheme for a specific class of continuous-state generative models. With the hope of foregrounding research in this direction, we survey the literature that has contributed to this perspective, highlighting the many ways that PC might play a role in the future of machine learning and computational intelligence at large.

Backpropagation-Free 4D Continuous Ant-Based Neural Topology Search

Continuous Ant-based Topology Search (CANTS) is a previously introduced novel nature-inspired neural architecture search (NAS) algorithm that is based on ant colony optimization (ACO). CANTS utilizes a continuous search space to indirectly-encode a neural architecture search space. Synthetic ant agents explore CANTS' continuous search space based on the density and distribution of pheromones, strongly inspired by how ants move in the real world. This continuous search space allows CANTS to automate the design of artificial neural networks (ANNs) of any size, removing a key limitation inherent to many current NAS algorithms that must operate within structures of a size that is predetermined by the user. This work expands CANTS by adding a fourth dimension to its search space representing potential neural synaptic weights. Adding this extra dimension allows CANTS agents to optimize both the architecture as well as the weights of an ANN without applying backpropagation (BP), which leads to a significant reduction in the time consumed in the optimization process. The experiments of this study - using real-world data - demonstrate that the BP-Free~CANTS algorithm exhibits highly competitive performance compared to both CANTS and ANTS while requiring significantly less operation time.