Related papers: Confluent Persistence Revisited
In this paper, we systematically analyze the connecting architectures of recurrent neural networks (RNNs). Our main contribution is twofold: first, we present a rigorous graph-theoretic framework describing the connecting architectures of…
In the field of topological data analysis, persistence modules are used to express geometrical features of data sets. The matching distance $d_\mathcal{M}$ measures the difference between $2$-parameter persistence modules by taking the…
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms…
A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is…
More often than not in benchmark supervised ML, tabular data is flat, i.e. consists of a single $m \times d$ (rows, columns) file, but cases abound in the real world where observations are described by a set of tables with structural…
A fundamental question in computational geometry is for a set of input points in the Euclidean space, that is subject to discrete changes (insertion/deletion of points at each time step), whether it is possible to maintain an approximate…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
This paper investigates how the compositional structure of neural networks shapes their optimization landscape and training dynamics. We analyze the gradient flow associated with overparameterized optimization problems, which can be…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully…
While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between attention mechanisms and multinomial regression. Specifically,…
We study the classic problem of correlation clustering in dynamic node streams. In this setting, nodes are either added or randomly deleted over time, and each node pair is connected by a positive or negative edge. The objective is to…
Data is one of the most important factors in machine learning. However, even if we have high-quality data, there is a situation in which access to the data is restricted. For example, access to the medical data from outside is strictly…
Document coherence describes how much sense text makes in terms of its logical organisation and discourse flow. Even though coherence is a relatively difficult notion to quantify precisely, it can be approximated automatically. This type of…
Continual Learning (CL) aims to incrementally acquire new knowledge while mitigating catastrophic forgetting. Within this setting, Online Continual Learning (OCL) focuses on updating models promptly and incrementally from single or small…
We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
We develop dynamic data structures for maintaining a hierarchical k-center clustering when the points come from a discrete space $\{1,\ldots,\Delta\}^d$. Our first data structure is for the low dimensional setting, i.e., d is a constant,…
A key issue in the handling of temporal data is the treatment of persistence; in most approaches it consists in inferring defeasible confusions by extrapolating from the actual knowledge of the history of the world; we propose here a…