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We present Reversible Vision Transformers, a memory efficient architecture design for visual recognition. By decoupling the GPU memory requirement from the depth of the model, Reversible Vision Transformers enable scaling up architectures…
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS)…
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse…
Mutual exclusion (ME) is a commonly used technique to handle conflicts in concurrent systems. With recent advancements in non-volatile memory technology, there is an increased focus on the problem of recoverable mutual exclusion (RME), a…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…
Safe memory reclamation (SMR) algorithms are crucial for preventing use-after-free errors in optimistic data structures. SMR algorithms typically delay reclamation for safety and reclaim objects in batches for efficiency. It is difficult to…
Differentiable architecture search (DARTS) is successfully applied in many vision tasks. However, directly using DARTS for Transformers is memory-intensive, which renders the search process infeasible. To this end, we propose a multi-split…
This paper presents an algorithm for the integer multiplicative inverse (mod $2^w$) which completes in the fewest cycles known for modern microprocessors, when using the native bit width $w$ for the modulus $2^w$. The algorithm is a…
We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…
This paper presents several new tractability results for planning based on macros. We describe an algorithm that optimally solves planning problems in a class that we call inverted tree reducible, and is provably tractable for several…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
We test iterative algorithms, MR, QMR$\gamma_5$ and BiCG$\gamma_5$, to compare their efficiency in matrix inversion with multi-quarks (shifted matrices) within one iteration process. Our results on the 8^3 x 12 and 16^3 x 24 show that MR…
Machine learning has been getting a large attention in the recent years, as a tool to process big data generated by ubiquitous sensors in our daily life. High speed, low energy computing machines are in demand to enable real-time artificial…
We present an algorithm for the recovery of a matrix $\mathbb{M}$ % (non-singular $\in $ $\mathbb{C}^{N\times N}$) by only being aware of two of its powers, $\mathbb{M}_{k_{1}}:=\mathbb{M}^{k_{1}}$ and $\mathbb{M}%…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…