NEURAL NETWORKS AND DEEP LEARNING CST 395 CS 5TH SEMESTER HONORS COURSE- Dr Binu V P, 9847390760

In its most general form, convolution is an operation on two functions of a real valued argument. To motivate the definition of convolution, we start with examples of two functions we might use. Suppose we are tracking the location of a spaceship with a laser sensor. Our laser sensor provides a single output $x(t)$, the position of the spaceship at time $t$. Both $x$ and $t$ are real-valued, i.e., we can get a different reading from the laser sensor at any instant in time.Now suppose that our laser sensor is somewhat noisy. To obtain a less noisy estimate of the spaceship’s position, we would like to average together several measurements. Of course, more recent measurements are more relevant, so we will want this to be a weighted average that gives more weight to recent measurements. We can do this with a weighting function $w(a)$, where $a$ is the age of a measurement.If we apply such a weighted average operation at every moment, we obtain a new function providing a smoothed estimate

 Convolutional networks (LeCun, 1989), also known as convolutional neural networks or CNNs , are a specialized kind of neural network for processing data that has a known, grid-like topology. Examples include time-series data, which can be thought of as a 1D grid taking samples at regular time intervals, and image data, which can be thought of as a 2D grid of pixels. Convolutional networks have been tremendously successful in practical applications. The name “convolutional neural network” indicates that the network employs a mathematical operation called convolution. Convolution is a specialized kind of linear operation. Convolutional networks are simply neural networks that use convolution in place of general matrix multiplication in at least one of their layers.The vast majority of applications of convolutional neural networks focus on image data, although one can also use these networks for all types of temporal, spatial, and spatiotemporal data.An important property of image dat