DeepPCR: Parallelizing Sequential Operations in Neural Networks

Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes are executed layer-by-layer, and the output of diffusion models is produced by applying a sequence of denoising steps. This sequential approach results in a computational cost proportional to the number of steps involved, presenting a potential bottleneck as the number of steps increases. In this work, we introduce DeepPCR, a novel algorithm which parallelizes typically sequential operations in order to speed up inference and training of neural networks. DeepPCR is based on interpreting a sequence of $L$ steps as the solution of a specific system of equations, which we recover using the Parallel Cyclic Reduction algorithm. This reduces the complexity of computing the sequential operations from $\mathcal{O}(L)$ to $\mathcal{O}(\log_2L)$, thus yielding a speedup for large $L$. To verify the theoretical lower complexity of the algorithm, and to identify regimes for speedup, we test the effectiveness of DeepPCR in parallelizing the forward and backward pass in multi-layer perceptrons, and reach speedups of up to $30\times$ for the forward and $200\times$ for the backward pass. We additionally showcase the flexibility of DeepPCR by parallelizing training of ResNets with as many as 1024 layers, and generation in diffusion models, enabling up to $7\times$ faster training and $11\times$ faster generation, respectively, when compared to the sequential approach

Designing Data: Proactive Data Collection and Iteration for Machine Learning

Lack of diversity in data collection has caused significant failures in machine learning (ML) applications. While ML developers perform post-collection interventions, these are time intensive and rarely comprehensive. Thus, new methods to track and manage data collection, iteration, and model training are necessary for evaluating whether datasets reflect real world variability. We present designing data, an iterative, bias mitigating approach to data collection connecting HCI concepts with ML techniques. Our process includes (1) Pre-Collection Planning, to reflexively prompt and document expected data distributions; (2) Collection Monitoring, to systematically encourage sampling diversity; and (3) Data Familiarity, to identify samples that are unfamiliar to a model through Out-of-Distribution (OOD) methods. We instantiate designing data through our own data collection and applied ML case study. We find models trained on "designed" datasets generalize better across intersectional groups than those trained on similarly sized but less targeted datasets, and that data familiarity is effective for debugging datasets

The Role of Entropy and Reconstruction in Multi-View Self-Supervised Learning

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.Comment: 18 pages: 9 of main text, 2 of references, and 7 of supplementary material. Appears in the proceedings of ICML 202

DUET: 2D Structured and Approximately Equivariant Representations

Multiview Self-Supervised Learning (MSSL) is based on learning invariances with respect to a set of input transformations. However, invariance partially or totally removes transformation-related information from the representations, which might harm performance for specific downstream tasks that require such information. We propose 2D strUctured and EquivarianT representations (coined DUET), which are 2d representations organized in a matrix structure, and equivariant with respect to transformations acting on the input data. DUET representations maintain information about an input transformation, while remaining semantically expressive. Compared to SimCLR (Chen et al., 2020) (unstructured and invariant) and ESSL (Dangovski et al., 2022) (unstructured and equivariant), the structured and equivariant nature of DUET representations enables controlled generation with lower reconstruction error, while controllability is not possible with SimCLR or ESSL. DUET also achieves higher accuracy for several discriminative tasks, and improves transfer learning.Comment: Accepted at ICML 202

Manifold clustering for motion segmentation

En aquesta tesi s’estudia el problema de la segmentació del moviment. La tesi presenta una revisió dels principals algoritmes de segmentació del moviment, s’analitzen les característiques principals i es proposa una classificació de les tècniques més recents i importants. La segmentació es pot entendre com un problema d’agrupament d’espais (manifold clustering). Aquest estudi aborda alguns dels reptes més difícils de la segmentació de moviment a través l’agrupament d’espais. S’han proposat nous algoritmes per a l’estimació del rang de la matriu de trajectòries, s’ha presenta una mesura de similitud entre subespais, s’han abordat problemes relacionats amb el comportament dels angles canònics i s’ha desenvolupat una eina genèrica per estimar quants moviments apareixen en una seqüència. L´ultima part de l’estudi es dedica a la correcció de l’estimació inicial d’una segmentació. Aquesta correcció es du a terme ajuntant els problemes de la segmentació del moviment i de l’estructura a partir del moviment.IN THIS STUDY THE PROBLEM OF MOTION SEGMENTATION IS DISCUSSED. MOTION SEGMENTATION STATE OF THE ART IS PRESENTED, THE MAIN FEATURES OF MOTION SEGMENTATION ALGORITHMS ARE ANALYSED, AND A CLASSIFICATION OF THE RECENT AND MOST IMPORTANT TECHNIQUES IS PROPOSED. THE SEGMENTATION PROBLEM COULD BE CAST INTO A MANIFOLD CLUSTERING PROBLEM. IN THIS STUDY SOME OF THE MOST CHALLENGING ISSUES RELATED TO MOTION SEGMENTATION VIA MANIFOLD CLUSTERING ARE TACKLED. NEW ALGORITHMS FOR THE RANK ESTIMATION OF THE TRAJECTORY MATRIX ARE PROPOSED. A MEASURE OF SIMILARITY BETWEEN SUBSPACES IS PRESENTED. THE BEHAVIOUR OF PRINCIPAL ANGLES IS DISCUSSED. A GENERIC TOOL FOR THE ESTIMATION OF THE NUMBER OF MOTIONS IS DEVELOPED. THE LAST PART OF THE STUDY IS DEDICATED TO THE DEVELOPMENT OF AN ALGORITHM FOR THE CORRECTION OF AN INITIAL MOTION SEGMENTATION SOLUTION. SUCH A CORRECTION IS ACHIEVED BY BRINGING TOGETHER THE PROBLEMS OF MOTION SEGMENTATION AND STRUCTURE FROM MOTION

New Trends in Motion Segmentation

Non

Enhanced Model Selection for motion segmentation

In this paper a novel rank estimation technique for trajectories motion segmentation within the Local Subspace Affinity (LSA) framework is presented. This technique, called Enhanced Model Selection (EMS), is based on the relationship between the estimated rank of the trajectory matrix and the affinity matrix built by LSA. The results on synthetic and real data show that without any a priori knowledge, EMS automatically provides an accurate and robust rank estimation, improving the accuracy of the final motion segmentatio