Evolutionary algorithms as an alternative to backpropagation for supervised training of Biophysical Neural Networks and Neural ODEs

Training networks consisting of biophysically accurate neuron models could allow for new insights into how brain circuits can organize and solve tasks. We begin by analyzing the extent to which the central algorithm for neural network learning -- stochastic gradient descent through backpropagation (BP) -- can be used to train such networks. We find that properties of biophysically based neural network models needed for accurate modelling such as stiffness, high nonlinearity and long evaluation timeframes relative to spike times makes BP unstable and divergent in a variety of cases. To address these instabilities and inspired by recent work, we investigate the use of "gradient-estimating" evolutionary algorithms (EAs) for training biophysically based neural networks. We find that EAs have several advantages making them desirable over direct BP, including being forward-pass only, robust to noisy and rigid losses, allowing for discrete loss formulations, and potentially facilitating a more global exploration of parameters. We apply our method to train a recurrent network of Morris-Lecar neuron models on a stimulus integration and working memory task, and show how it can succeed in cases where direct BP is inapplicable. To expand on the viability of EAs in general, we apply them to a general neural ODE problem and a stiff neural ODE benchmark and find again that EAs can out-perform direct BP here, especially for the over-parameterized regime. Our findings suggest that biophysical neurons could provide useful benchmarks for testing the limits of BP-adjacent methods, and demonstrate the viability of EAs for training networks with complex components.

Learning Time-Invariant Representations for Individual Neurons from Population Dynamics

Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal activity is a combination of its time-invariant identity and the inputs the neuron receives from the rest of the circuit. Here, we propose a self-supervised learning based method to assign time-invariant representations to individual neurons based on permutation-, and population size-invariant summary of population recordings. We fit dynamical models to neuronal activity to learn a representation by considering the activity of both the individual and the neighboring population. Our self-supervised approach and use of implicit representations enable robust inference against imperfections such as partial overlap of neurons across sessions, trial-to-trial variability, and limited availability of molecular (transcriptomic) labels for downstream supervised tasks. We demonstrate our method on a public multimodal dataset of mouse cortical neuronal activity and transcriptomic labels. We report > 35% improvement in predicting the transcriptomic subclass identity and > 20% improvement in predicting class identity with respect to the state-of-the-art.

Physics-Driven Diffusion Models for Impact Sound Synthesis from Videos

Modeling sounds emitted from physical object interactions is critical for immersive perceptual experiences in real and virtual worlds. Traditional methods of impact sound synthesis use physics simulation to obtain a set of physics parameters that could represent and synthesize the sound. However, they require fine details of both the object geometries and impact locations, which are rarely available in the real world and can not be applied to synthesize impact sounds from common videos. On the other hand, existing video-driven deep learning-based approaches could only capture the weak correspondence between visual content and impact sounds since they lack of physics knowledge. In this work, we propose a physics-driven diffusion model that can synthesize high-fidelity impact sound for a silent video clip. In addition to the video content, we propose to use additional physics priors to guide the impact sound synthesis procedure. The physics priors include both physics parameters that are directly estimated from noisy real-world impact sound examples without sophisticated setup and learned residual parameters that interpret the sound environment via neural networks. We further implement a novel diffusion model with specific training and inference strategies to combine physics priors and visual information for impact sound synthesis. Experimental results show that our model outperforms several existing systems in generating realistic impact sounds. More importantly, the physics-based representations are fully interpretable and transparent, thus enabling us to perform sound editing flexibly.

TKIL: Tangent Kernel Approach for Class Balanced Incremental Learning

When learning new tasks in a sequential manner, deep neural networks tend to forget tasks that they previously learned, a phenomenon called catastrophic forgetting. Class incremental learning methods aim to address this problem by keeping a memory of a few exemplars from previously learned tasks, and distilling knowledge from them. However, existing methods struggle to balance the performance across classes since they typically overfit the model to the latest task. In our work, we propose to address these challenges with the introduction of a novel methodology of Tangent Kernel for Incremental Learning (TKIL) that achieves class-balanced performance. The approach preserves the representations across classes and balances the accuracy for each class, and as such achieves better overall accuracy and variance. TKIL approach is based on Neural Tangent Kernel (NTK), which describes the convergence behavior of neural networks as a kernel function in the limit of infinite width. In TKIL, the gradients between feature layers are treated as the distance between the representations of these layers and can be defined as Gradients Tangent Kernel loss (GTK loss) such that it is minimized along with averaging weights. This allows TKIL to automatically identify the task and to quickly adapt to it during inference. Experiments on CIFAR-100 and ImageNet datasets with various incremental learning settings show that these strategies allow TKIL to outperform existing state-of-the-art methods.

STNDT: Modeling Neural Population Activity with a Spatiotemporal Transformer

Modeling neural population dynamics underlying noisy single-trial spiking activities is essential for relating neural observation and behavior. A recent non-recurrent method - Neural Data Transformers (NDT) - has shown great success in capturing neural dynamics with low inference latency without an explicit dynamical model. However, NDT focuses on modeling the temporal evolution of the population activity while neglecting the rich covariation between individual neurons. In this paper we introduce SpatioTemporal Neural Data Transformer (STNDT), an NDT-based architecture that explicitly models responses of individual neurons in the population across time and space to uncover their underlying firing rates. In addition, we propose a contrastive learning loss that works in accordance with mask modeling objective to further improve the predictive performance. We show that our model achieves state-of-the-art performance on ensemble level in estimating neural activities across four neural datasets, demonstrating its capability to capture autonomous and non-autonomous dynamics spanning different cortical regions while being completely agnostic to the specific behaviors at hand. Furthermore, STNDT spatial attention mechanism reveals consistently important subsets of neurons that play a vital role in driving the response of the entire population, providing interpretability and key insights into how the population of neurons performs computation.

Lyapunov-Guided Embedding for Hyperparameter Selection in Recurrent Neural Networks

Recurrent Neural Networks (RNN) are ubiquitous computing systems for sequences and multivariate time series data. While several robust architectures of RNN are known, it is unclear how to relate RNN initialization, architecture, and other hyperparameters with accuracy for a given task. In this work, we propose to treat RNN as dynamical systems and to correlate hyperparameters with accuracy through Lyapunov spectral analysis, a methodology specifically designed for nonlinear dynamical systems. To address the fact that RNN features go beyond the existing Lyapunov spectral analysis, we propose to infer relevant features from the Lyapunov spectrum with an Autoencoder and an embedding of its latent representation (AeLLE). Our studies of various RNN architectures show that AeLLE successfully correlates RNN Lyapunov spectrum with accuracy. Furthermore, the latent representation learned by AeLLE is generalizable to novel inputs from the same task and is formed early in the process of RNN training. The latter property allows for the prediction of the accuracy to which RNN would converge when training is complete. We conclude that representation of RNN through Lyapunov spectrum along with AeLLE, and assists with hyperparameter selection of RNN, provides a novel method for organization and interpretation of variants of RNN architectures.

Knowledge Distillation Circumvents Nonlinearity for Optical Convolutional Neural Networks

In recent years, Convolutional Neural Networks (CNNs) have enabled ubiquitous image processing applications. As such, CNNs require fast runtime (forward propagation) to process high-resolution visual streams in real time. This is still a challenging task even with state-of-the-art graphics and tensor processing units. The bottleneck in computational efficiency primarily occurs in the convolutional layers. Performing operations in the Fourier domain is a promising way to accelerate forward propagation since it transforms convolutions into elementwise multiplications, which are considerably faster to compute for large kernels. Furthermore, such computation could be implemented using an optical 4f system with orders of magnitude faster operation. However, a major challenge in using this spectral approach, as well as in an optical implementation of CNNs, is the inclusion of a nonlinearity between each convolutional layer, without which CNN performance drops dramatically. Here, we propose a Spectral CNN Linear Counterpart (SCLC) network architecture and develop a Knowledge Distillation (KD) approach to circumvent the need for a nonlinearity and successfully train such networks. While the KD approach is known in machine learning as an effective process for network pruning, we adapt the approach to transfer the knowledge from a nonlinear network (teacher) to a linear counterpart (student). We show that the KD approach can achieve performance that easily surpasses the standard linear version of a CNN and could approach the performance of the nonlinear network. Our simulations show that the possibility of increasing the resolution of the input image allows our proposed 4f optical linear network to perform more efficiently than a nonlinear network with the same accuracy on two fundamental image processing tasks: (i) object classification and (ii) semantic segmentation.

Sparse Semi-Supervised Action Recognition with Active Learning

Current state-of-the-art methods for skeleton-based action recognition are supervised and rely on labels. The reliance is limiting the performance due to the challenges involved in annotation and mislabeled data. Unsupervised methods have been introduced, however, they organize sequences into clusters and still require labels to associate clusters with actions. In this paper, we propose a novel approach for skeleton-based action recognition, called SESAR, that connects these approaches. SESAR leverages the information from both unlabeled data and a handful of sequences actively selected for labeling, combining unsupervised training with sparsely supervised guidance. SESAR is composed of two main components, where the first component learns a latent representation for unlabeled action sequences through an Encoder-Decoder RNN which reconstructs the sequences, and the second component performs active learning to select sequences to be labeled based on cluster and classification uncertainty. When the two components are simultaneously trained on skeleton-based action sequences, they correspond to a robust system for action recognition with only a handful of labeled samples. We evaluate our system on common datasets with multiple sequences and actions, such as NW UCLA, NTU RGB+D 60, and UWA3D. Our results outperform standalone skeleton-based supervised, unsupervised with cluster identification, and active-learning methods for action recognition when applied to sparse labeled samples, as low as 1% of the data.

Multi-Instrumentalist Net: Unsupervised Generation of Music from Body Movements

We propose a novel system that takes as an input body movements of a musician playing a musical instrument and generates music in an unsupervised setting. Learning to generate multi-instrumental music from videos without labeling the instruments is a challenging problem. To achieve the transformation, we built a pipeline named 'Multi-instrumentalistNet' (MI Net). At its base, the pipeline learns a discrete latent representation of various instruments music from log-spectrogram using a Vector Quantized Variational Autoencoder (VQ-VAE) with multi-band residual blocks. The pipeline is then trained along with an autoregressive prior conditioned on the musician's body keypoints movements encoded by a recurrent neural network. Joint training of the prior with the body movements encoder succeeds in the disentanglement of the music into latent features indicating the musical components and the instrumental features. The latent space results in distributions that are clustered into distinct instruments from which new music can be generated. Furthermore, the VQ-VAE architecture supports detailed music generation with additional conditioning. We show that a Midi can further condition the latent space such that the pipeline will generate the exact content of the music being played by the instrument in the video. We evaluate MI Net on two datasets containing videos of 13 instruments and obtain generated music of reasonable audio quality, easily associated with the corresponding instrument, and consistent with the music audio content.