Related papers: Shape Preserving Tree Transducers
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…
Learning to encode differences in the geometry and (topological) structure of the shapes of ordinary objects is key to generating semantically plausible variations of a given shape, transferring edits from one shape to another, and many…
We study the intrinsic transformation of feature maps across convolutional network layers with explicit top-down control. To this end, we develop top-down feature transformer (TFT), under controllable parameters, that are able to account…
We show that equivalence of deterministic linear tree transducers can be decided in polynomial time when their outputs are interpreted over the free group. Due to the cancellation properties offered by the free group, the required…
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…
There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our…
We study the orientation preserving involutions of the orientable 3-dimensional handlebody $H_g$, for any genus $g$. A complete classification of such involutions is given in terms of their fixed points.
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…
Overparameterized transformer networks have obtained state of the art results in various natural language processing tasks, such as machine translation, language modeling, and question answering. These models contain hundreds of millions of…
Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive…
Semiconductivity and superconductivity are remarkable quantum phenomena that have immense impact on science and technology, and materials that can be tuned, usually by pressure or doping, to host both types of quantum states are of great…
In various models of one-way pushdown automata, the explicit use of two designated endmarkers on a read-once input tape has proven to be extremely useful for making a conscious, final decision on the acceptance/rejection of each input word…
A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed…
For studying the local topology of maps, one uses deformations which split the singularities into simpler ones while preserving the general fibres. We give conditions under which such conservation holds.
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are…
We study finite state transduction of automatic and morphic sequences. Dekking proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in…
Parameterized verification of coverability in broadcast networks with finite state processes has been studied for different types of models and topologies. In this paper, we attempt to develop a theory of broadcast networks in which the…
Estimating path loss for a transmitter-receiver location is key to many use-cases including network planning and handover. Machine learning has become a popular tool to predict wireless channel properties based on map data. In this work, we…
Conventional decision trees have a number of favorable properties, including interpretability, a small computational footprint and the ability to learn from little training data. However, they lack a key quality that has helped fuel the…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…