Edward A. Rietman

Adam Kohan, Edward A. Rietman, Hava T. Siegelmann

We propose a new learning framework, signal propagation (sigprop), for propagating a learning signal and updating neural network parameters via a forward pass, as an alternative to backpropagation. In sigprop, there is only the forward path for inference and learning. So, there are no structural or computational constraints necessary for learning to take place, beyond the inference model itself, such as feedback connectivity, weight transport, or a backward pass, which exist under backpropagation based approaches. That is, sigprop enables global supervised learning with only a forward path. This is ideal for parallel training of layers or modules. In biology, this explains how neurons without feedback connections can still receive a global learning signal. In hardware, this provides an approach for global supervised learning without backward connectivity. Sigprop by construction has compatibility with models of learning in the brain and in hardware than backpropagation, including alternative approaches relaxing learning constraints. We also demonstrate that sigprop is more efficient in time and memory than they are. To further explain the behavior of sigprop, we provide evidence that sigprop provides useful learning signals in context to backpropagation. To further support relevance to biological and hardware learning, we use sigprop to train continuous time neural networks with Hebbian updates, and train spiking neural networks with only the voltage or with biologically and hardware compatible surrogate functions.

Peter DelMastro, Rushiv Arora, Edward Rietman et al.

Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during training. To address this gap, we use timed automata (TA) to introduce a family of supervised learning tasks modeling behavior dependent on hidden temporal variables whose complexity is directly controllable. Building upon past studies from the perspective of dynamical systems, we train RNNs to emulate temporal flipflops, a new collection of TA that emphasizes the need for time-awareness over long-term memory. We find that these RNNs learn in phases: they quickly perfect any time-independent behavior, but they initially struggle to discover the hidden time-dependent features. In the case of periodic "time-of-day" aware automata, we show that the RNNs learn to switch between periodic orbits that encode time modulo the period of the transition rules. We subsequently apply fixed point stability analysis to monitor changes in the RNN dynamics during training, and we observe that the learning phases are separated by a bifurcation from which the periodic behavior emerges. In this way, we demonstrate how dynamical systems theory can provide insights into not only the learned representations of these models, but also the dynamics of the learning process itself. We argue that this style of analysis may provide insights into the training pathologies of recurrent architectures in contexts outside of time-awareness.

Thomas Buckley, Leslie Schumm, Manor Askenazi et al.

In this paper we extend our earlier work of (Rietman et al. 2022) presenting an application of physical Reservoir Computing (RC) to the classification of handwritten and spoken digits. We utilize an unpoled cube of Lead Zirconate Titanate (PZT) as a computational substrate to process these datasets. Our results demonstrate that the PZT reservoir achieves 89.0% accuracy on MNIST handwritten digits, representing a 2.4 percentage point improvement over logistic regression baselines applied to the same preprocessed data. However, for the AudioMNIST spoken digits dataset, the reservoir system (88.2% accuracy) performs equivalently to baseline methods (88.1% accuracy), suggesting that reservoir computing provides the greatest benefits for classification tasks of intermediate difficulty where linear methods underperform but the problem remains learnable. PZT is a well-known material already used in semiconductor applications, presenting a low-power computational substrate that can be integrated with digital algorithms. Our findings indicate that physical reservoirs excel when the task difficulty exceeds the capability of simple linear classifiers but remains within the computational capacity of the reservoir dynamics.

Jack Kenney, John Valcore, Scott Riggs et al.

In computer chip manufacturing, the study of etch patterns on silicon wafers, or metrology, occurs on the nano-scale and is therefore subject to large variation from small, yet significant, perturbations in the manufacturing environment. An enormous amount of information can be gathered from a single etch process, a sequence of actions taken to produce an etched wafer from a blank piece of silicon. Each final wafer, however, is costly to take measurements from, which limits the number of examples available to train a predictive model. Part of the significance of this work is the success we saw from the models despite the limited number of examples. In order to accommodate the high dimensional process signatures, we isolated important sensor variables and applied domain-specific summarization on the data using multiple feature engineering techniques. We used a neural network architecture consisting of the summarized inputs, a single hidden layer of 4032 units, and an output layer of one unit. Two different models were learned, corresponding to the metrology measurements in the dataset, Recess and Remaining Mask. The outputs are related abstractly and do not form a two dimensional space, thus two separate models were learned. Our results approach the error tolerance of the microscopic imaging system. The model can make predictions for a class of etch recipes that include the correct number of etch steps and plasma reactors with the appropriate sensors, which are chambers containing an ionized gas that determine the manufacture environment. Notably, this method is not restricted to some maximum process length due to the summarization techniques used. This allows the method to be adapted to new processes that satisfy the aforementioned requirements. In order to automate semiconductor manufacturing, models like these will be needed throughout the process to evaluate production quality.

Adam A. Kohan, Edward A. Rietman, Hava T. Siegelmann

We introduce Error Forward-Propagation, a biologically plausible mechanism to propagate error feedback forward through the network. Architectural constraints on connectivity are virtually eliminated for error feedback in the brain; systematic backward connectivity is not used or needed to deliver error feedback. Feedback as a means of assigning credit to neurons earlier in the forward pathway for their contribution to the final output is thought to be used in learning in the brain. How the brain solves the credit assignment problem is unclear. In machine learning, error backpropagation is a highly successful mechanism for credit assignment in deep multilayered networks. Backpropagation requires symmetric reciprocal connectivity for every neuron. From a biological perspective, there is no evidence of such an architectural constraint, which makes backpropagation implausible for learning in the brain. This architectural constraint is reduced with the use of random feedback weights. Models using random feedback weights require backward connectivity patterns for every neuron, but avoid symmetric weights and reciprocal connections. In this paper, we practically remove this architectural constraint, requiring only a backward loop connection for effective error feedback. We propose reusing the forward connections to deliver the error feedback by feeding the outputs into the input receiving layer. This mechanism, Error Forward-Propagation, is a plausible basis for how error feedback occurs deep in the brain independent of and yet in support of the functionality underlying intricate network architectures. We show experimentally that recurrent neural networks with two and three hidden layers can be trained using Error Forward-Propagation on the MNIST and Fashion MNIST datasets, achieving $1.90\%$ and $11\%$ generalization errors respectively.