24 accepted papers
We suggest the first system that runs real-time semantic segmentation via deep learning on the weak microcomputer Raspberry Pi Zero v2 (whose price was 15) attached to a toy drone. In particular, since the Raspberry Pi weighs less than 16 grams, and its size is half of a credit card, we could easily…
Radial basis function neural networks (*RBFNN*) are well-known for their capability to approximate any continuous function on a closed bounded set with arbitrary precision given enough hidden neurons. In this paper, we introduce the first algorithm to construct coresets for *RBFNNs*, i.e., small wei…
The input to the {line-sets $k$-median} problem is an integer $k \geq 1$, and a set $\mathcal{L} = \{L_1,\dots,L_n\}$ that contains $n$ sets of lines in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points in $\mathbb{R}^d$) that minimizes the sum $\sum_{L \in \mathcal{L}}\min_{\e…
In the monitoring problem, the input is an unbounded stream $P={p_1,p_2\cdots}$ of integers in $[N]:=\{1,\cdots,N\}$, that are obtained from a sensor (such as GPS or heart beats of a human). The goal (e.g., for anomaly detection) is to approximate the $n$ points received so far in $P$ by a single fr…
Coreset (or core-set) is a small weighted
$(j,k)$-projective clustering is the natural generalization of the family of $k$-clustering and $j$-subspace clustering problems. Given a set of points $P$ in $\mathbb{R}^d$, the goal is to find $k$ flats of dimension $j$, i.e., affine subspaces, that best fit $P$ under a given distance measure. In…
The Perspective-n-Point problem aims to estimate the relative pose between a calibrated monocular camera and a known 3D model, by aligning pairs of 2D captured image points to their corresponding 3D points in the model. We suggest an algorithm that runs on weak IoT devices in real-time but still pro…
Many path planning algorithms are based on sampling the state space. While this approach is very simple, it can become costly when the obstacles are unknown, since samples hitting these obstacles are wasted. The goal of this paper is to efficiently identify obstacles in a map and remove them from th…
We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our algorithm hinges on the idea of compressing each convolutional (or…
A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to a given matrix $D$ of $N$ entries (labels) is the sum of squ…
A common approach for compressing Natural Language Processing (NLP) networks is to encode the embedding layer as a matrix $A\in\mathbb{R}^{n\times d}$, compute its rank-$j$ approximation $A_j$ via SVD (Singular Value Decomposition), and then factor $A_j$ into a pair of matrices that correspond to sm…
The goal of the alignment problem is to align a (given) point cloud P = \ p_1,\cdots,p_n\ to another (observed) point cloud Q = \ q_1,\cdots,q_n\ . That is, to compute a rotation matrix R \in \mathbb R ^ 3 x3 and a translation vector t \in \mathbb R ^ 3 that minimize the sum of paired distances b…
Coreset is usually a small weighted subset of $n$ input points in $\mathbb{R}^d$, that provably approximates their loss function for a given set of queries (models, classifiers, etc.). Coresets become increasingly common in machine learning since existing heuristics or inefficient algorithms may be…
Previous work showed empirically that large neural networks can be significantly reduced in size while preserving their accuracy. Model compression became a central research topic, as it is crucial for deployment of neural networks on devices with limited computational and memory resources. The majo…
We present a provable, sampling-based approach for generating compact Convolutional Neural Networks (CNNs) by identifying and removing redundant filters from an over-parameterized network. Our algorithm uses a small batch of input data points to assign a saliency score to each filter and constructs…
The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of fixed sized sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum $\sum_{P\in \mathcal{P}} \min_{p\in P, c\in C}\le…
We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an importance sampling scheme that judiciously defines a sampli…
Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and matrix factorizations. We suggest an algorithm that gets…
We consider the problem of matching a pair of point sets, each consists of k clusters, where each cluster in the first set is arbitrarily translated with additional noise, resulting in a cluster of the second point set. The goal is to compute k translations and a matching that minimizes the sum of s
The input to the \emph{$k$-mean for lines} problem is a set $L$ of $n$ lines in $\mathbb{R}^d$, and the goal is to compute a set of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum of squared distances over every line in $L$ and its nearest center. This is a straightforward generalizati…
We suggest a novel algorithm that tracks given shapes in real time from a low-quality video stream. The algorithm is based on a careful selection of a small subset of pixels that suffices to obtain an approximation of the observed shape. The shape can then be extracted quickly from the small subset.
We provide a deterministic data summarization algorithm that approximates the mean $\bar{p}=\frac{1}{n}\sum_{p\in P} p$ of a set $P$ of $n$ vectors in $\mathbb{R}^d$, by a weighted mean $\tilde{p}$ of a
In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the Principle Component Analysis (PCA) of any $n\times d$ matrix, using one pass over the stre…
In continuously operating robotic systems, efficient representation of the previously seen camera feed is crucial. Using a highly efficient compression coreset method, we formulate a new method for hierarchical retrieval of frames from large video streams collected online by a moving robot. We demon…