One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvectors of the covariance of the trajectory and prove that in the long trajectory and high dimensional limit most of the variance is in the first few PCA components, and that the projection of the trajectory onto any subspace spanned by PCA components is a Lissajous curve. We generalize these results to a random walk with momentum and to an Ornstein-Uhlenbeck processes (i.e., a random walk in a quadratic potential) and show that in high dimensions the walk is not mean reverting, but will instead be trapped at a fixed distance from the minimum. We finally analyze PCA projected training trajectories for: a linear model trained on CIFAR-10; a fully connected model trained on MNIST; and ResNet-50-v2 trained on Imagenet. In all cases, both the distribution of PCA eigenvalues and the projected trajectories resemble those of a random walk with drift.

Neural Information Processing Systems http://nips.cc/

Deep neural networks (NNs) are extremely high dimensional objects.

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvectors of the covariance of the trajectory and prove that in the long trajectory and high dimensional limit most of the variance is in the first few PCA components, and that the projection of the trajectory onto any subspace spanned by PCA components is a Lissajous curve. We generalize these results to a random walk with momentum and to an Ornstein-Uhlenbeck processes (i.e., a random walk in a quadratic potential) and show that in high dimensions the walk is not mean reverting, but will instead be trapped at a fixed distance from the minimum. We finally analyze PCA projected training trajectories for: a linear model trained on CIFAR-10; a fully connected model trained on MNIST; and ResNet-50-v2 trained on Imagenet. In all cases, both the distribution of PCA eigenvalues and the projected trajectories resemble those of a random walk with drift.

Stellar mass is a fundamental quantity that determines the properties and evolution of stars. However, estimating stellar masses in star-forming regions is challenging because young stars are obscured by dense gas and the regions are highly inhomogeneous, making spherical dynamical estimates unreliable. Supervised machine learning could link such complex structures to stellar mass, but it requires large, high-quality labeled datasets from high-resolution magneto-hydrodynamical (MHD) simulations, which are computationally expensive. We address this by pretraining a vision transformer on one million synthetic fractal images using the self-supervised framework DINOv2, and then applying the frozen model to limited high-resolution MHD simulations. Our results demonstrate that synthetic pretraining improves frozen-feature regression stellar mass predictions, with the pretrained model performing slightly better than a supervised model trained on the same limited simulations. Principal component analysis of the extracted features further reveals semantically meaningful structures, suggesting that the model enables unsupervised segmentation of star-forming regions without the need for labeled data or fine-tuning.

Partitioning is a known problem in computer science and is critical in chip design workflows, as advancements in this area can significantly influence design quality and efficiency. Deep Learning (DL) techniques, particularly those involving Graph Neural Networks (GNNs), have demonstrated strong performance in various node, edge, and graph prediction tasks using both inductive and transductive learning methods. A notable area of recent interest within GNNs are pooling layers and their application to graph partitioning. While these methods have yielded promising results across social, computational, and other random graphs, their effectiveness has not yet been explored in the context of VLSI hypergraph netlists. In this study, we introduce a new set of synthetic partitioning benchmarks that emulate real-world netlist characteristics and possess a known upper bound for solution cut quality. We distinguish these benchmarks with the prior work and evaluate existing state-of-the-art partitioning algorithms alongside GNN-based approaches, highlighting their respective advantages and disadvantages.

3D building models with facade details are playing an important role in many applications now. Classifying point clouds at facade-level is key to create such digital replicas of the real world. However, few studies have focused on such detailed classification with deep neural networks. We propose a method fusing geometric features with deep learning networks for point cloud classification at facade-level. Our experiments conclude that such early-fused features improve deep learning methods' performance. This method can be applied for compensating deep learning networks' ability in capturing local geometric information and promoting the advancement of semantic segmentation.

This paper examines the relationship between the behavior of a neural network and the distribution formed from the projections of the data records into the space spanned by the low-order principal components of the training data. For example, in a benchmark calculation involving rotated and unrotated MNIST digits, classes (digits) that are mapped far from the origin in a low-dimensional principal component space and that overlap minimally with other digits converge rapidly and exhibit high degrees of accuracy in neural network calculations that employ the associated components of each data record as inputs. Further, if the space spanned by these low-order principal components is divided into bins and the input data records that are mapped into a given bin averaged, the resulting pattern can be distinguished by its geometric features which interpolate between those of adjacent bins in an analogous manner to variational autoencoders. Based on this observation, a simply realized data balancing procedure can be realized by evaluating the entropy associated with each histogram bin and subsequently repeating the original image data associated with the bin by a number of times that is determined from this entropy.

We introduce a framework for analyzing various types of information in an NLP Transformer. In this approach, we distinguish four layers of information: positional, syntactic, semantic, and contextual. We also argue that the common practice of adding positional information to semantic embedding is sub-optimal and propose instead a Linear-and-Add approach. Our analysis reveals an autogenetic separation of positional information through the deep layers. We show that the distilled positional components of the embedding vectors follow the path of a helix, both on the encoder side and on the decoder side. We additionally show that on the encoder side, the conceptual dimensions generate Part-of-Speech (PoS) clusters. On the decoder side, we show that a di-gram approach helps to reveal the PoS clusters of the next token. Our approach paves a way to elucidate the processing of information through the deep layers of an NLP Transformer.

Turbulence is characterised by chaotic dynamics and a high-dimensional state space, which make this phenomenon challenging to predict. However, turbulent flows are often characterised by coherent spatiotemporal structures, such as vortices or large-scale modes, which can help obtain a latent description of turbulent flows. However, current approaches are often limited by either the need to use some form of thresholding on quantities defining the isosurfaces to which the flow structures are associated or the linearity of traditional modal flow decomposition approaches, such as those based on proper orthogonal decomposition. This problem is exacerbated in flows that exhibit extreme events, which are rare and sudden changes in a turbulent state. The goal of this paper is to obtain an efficient and accurate reduced-order latent representation of a turbulent flow that exhibits extreme events. Specifically, we employ a three-dimensional multiscale convolutional autoencoder (CAE) to obtain such latent representation. We apply it to a three-dimensional turbulent flow. We show that the Multiscale CAE is efficient, requiring less than 10% degrees of freedom than proper orthogonal decomposition for compressing the data and is able to accurately reconstruct flow states related to extreme events. The proposed deep learning architecture opens opportunities for nonlinear reduced-order modeling of turbulent flows from data.