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Visual illusions teach us that what we see is not always what it is represented in the physical world. Its special nature make them a fascinating tool to test and validate any new vision model proposed. In general, current vision models are…
Increasing the information capacity of communication channels is a pressing need, driven by growing data demands and the consequent impending data crunch with existing modulation schemes. In this regard, mode division multiplexing (MDM),…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…
We consider a class of visual analogical reasoning problems that involve discovering the sequence of transformations by which pairs of input/output images are related, so as to analogously transform future inputs. This program synthesis…
Neural networks are commonly regarded as black boxes performing incomprehensible functions. For classification problems networks provide maps from high dimensional feature space to K-dimensional image space. Images of training vector are…
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios.…
Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack…
Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output…
Path loss prediction is a beneficial tool for efficient use of the radio frequency spectrum. Building on prior research on high-resolution map-based path loss models, this paper studies convolutional neural network input representations in…
Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires…
Classical light field rendering for novel view synthesis can accurately reproduce view-dependent effects such as reflection, refraction, and translucency, but requires a dense view sampling of the scene. Methods based on geometric…
Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can…
The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a…
Spatial light modulators enable arbitrary control of the intensity of optical light fields and facilitate a variety of applications in biology, astronomy and atomic, molecular and optical physics. For coherent light fields, holography,…
Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal…
With the substantial performance of neural networks in sensitive fields increases the need for interpretable deep learning models. Major challenge is to uncover the multiscale and distributed representation hidden inside the basket mappings…
Large language models are remarkably capable, yet how computation propagates through their layers remains poorly understood. A growing line of work treats depth as discrete time and the residual stream as a dynamical system, where each…
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in…