Leveraging Intermediate Neural Collapse with Simplex ETFs for Efficient Deep Neural Networks

Neural collapse is a phenomenon observed during the terminal phase of neural network training, characterized by the convergence of network activations, class means, and linear classifier weights to a simplex equiangular tight frame (ETF), a configuration of vectors that maximizes mutual distance within a subspace. This phenomenon has been linked to improved interpretability, robustness, and generalization in neural networks. However, its potential to guide neural network training and regularization remains underexplored. Previous research has demonstrated that constraining the final layer of a neural network to a simplex ETF can reduce the number of trainable parameters without sacrificing model accuracy. Furthermore, deep fully connected networks exhibit neural collapse not only in the final layer but across all layers beyond a specific effective depth. Using these insights, we propose two novel training approaches: Adaptive-ETF, a generalized framework that enforces simplex ETF constraints on all layers beyond the effective depth, and ETF-Transformer, which applies simplex ETF constraints to the feedforward layers within transformer blocks. We show that these approaches achieve training and testing performance comparable to those of their baseline counterparts while significantly reducing the number of learnable parameters.

Semi-Supervised Neural Processes for Articulated Object Interactions

The scarcity of labeled action data poses a considerable challenge for developing machine learning algorithms for robotic object manipulation. It is expensive and often infeasible for a robot to interact with many objects. Conversely, visual data of objects, without interaction, is abundantly available and can be leveraged for pretraining and feature extraction. However, current methods that rely on image data for pretraining do not easily adapt to task-specific predictions, since the learned features are not guaranteed to be relevant. This paper introduces the Semi-Supervised Neural Process (SSNP): an adaptive reward-prediction model designed for scenarios in which only a small subset of objects have labeled interaction data. In addition to predicting reward labels, the latent-space of the SSNP is jointly trained with an autoencoding objective using passive data from a much larger set of objects. Jointly training with both types of data allows the model to focus more effectively on generalizable features and minimizes the need for extensive retraining, thereby reducing computational demands. The efficacy of SSNP is demonstrated through a door-opening task, leading to better performance than other semi-supervised methods, and only using a fraction of the data compared to other adaptive models.

Structured Latent Variable Models for Articulated Object Interaction

In this paper, we investigate a scenario in which a robot learns a low-dimensional representation of a door given a video of the door opening or closing. This representation can be used to infer door-related parameters and predict the outcomes of interacting with the door. Current machine learning based approaches in the doors domain are based primarily on labelled datasets. However, the large quantity of available door data suggests the feasibility of a semisupervised approach based on pretraining. To exploit the hierarchical structure of the dataset where each door has multiple associated images, we pretrain with a structured latent variable model known as a neural statistician. The neural satsitician enforces separation between shared context-level variables (common across all images associated with the same door) and instance-level variables (unique to each individual image). We first demonstrate that the neural statistician is able to learn an embedding that enables reconstruction and sampling of realistic door images. Then, we evaluate the correspondence of the learned embeddings to human-interpretable parameters in a series of supervised inference tasks. It was found that a pretrained neural statistician encoder outperformed analogous context-free baselines when predicting door handedness, size, angle location, and configuration from door images. Finally, in a visual bandit door-opening task with a variety of door configuration, we found that neural statistician embeddings achieve lower regret than context-free baselines.