Related papers: Sorting as Gradient Flow on the Permutohedron
While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…
This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
We study sorting by queues that can rearrange their content by applying permutations from a predefined set. These new sorting devices are called shuffle queues and we investigate those of them corresponding to sets of permutations defining…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
In an online decision problem, one makes decisions often with a pool of decision sequence called experts but without knowledge of the future. After each step, one pays a cost based on the decision and observed rate. One reasonal goal would…
Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining non-isomorphic principal order ideals is described and applied for small lengths. The permutations…
Database query processing requires algorithms for duplicate removal, grouping, and aggregation. Three algorithms exist: in-stream aggregation is most efficient by far but requires sorted input; sort-based aggregation relies on external…
Sequential learning in deep models often suffers from challenges such as catastrophic forgetting and loss of plasticity, largely due to the permutation dependence of gradient-based algorithms, where the order of training data impacts the…
Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small…
We introduce a partial order on the set of all reduced words of a given permutation $\omega$, called \emph{directed-braid poset} of $\omega$. This poset enables us to produce two algorithms: One is a sorting algorithm applied on any reduced…
Sorting and searching are large parts of database query processing, e.g., in the forms of index creation, index maintenance, and index lookup; and comparing pairs of keys is a substantial part of the effort in sorting and searching. We have…
Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Join ordering is the NP-hard problem of selecting the most efficient order in which to evaluate joins (conjunctive, binary operators) in a database query. Because query execution performance critically depends on this choice, join ordering…