Related papers: Determining Smallest Path Size of Multiplication T…
Ikenmeyer et al. (JACM'19) proved an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions. This raises the question: which classes of functions permit efficient…
Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple…
In this paper, we study a general optimization model, which covers a large class of existing models for many applications in imaging sciences. To solve the resulting possibly nonconvex, nonsmooth and non-Lipschitz optimization problem, we…
We prove that transformers can exactly interpolate datasets of finite input sequences in $\mathbb{R}^d$, $d\geq 2$, with corresponding output sequences of smaller or equal length. Specifically, given $N$ sequences of arbitrary but finite…
CMOS-transistors circuits have been used as a conventional approach for designing an analog multiplier in modern era of industrial electronics. However, previous studies have shown, that based on the working region of transistors, such as…
Borradaile et al. (2017) investigated orientations of an undirected graph in which the sequence of in-degrees of the nodes is lexicographically minimal, which we call decreasingly minimal (=dec-min). They proved that an orientation is…
On the string of finite length, a (genomic) transposition is defined as the operation of exchanging two consecutive substrings. The minimum number of transpositions needed to transform one into the other is the transposition distance, that…
In this paper a low power multiplier is proposed. The proposed multiplier utilizes Broken-Array Multiplier approximation method on the conventional modified Booth multiplier. This method reduces the total power consumption of multiplier up…
Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the…
This paper proposes an low power approximate multiplier architecture for deep neural network (DNN) applications. A 4:2 compressor, introducing only a single combination error, is designed and integrated into an 8x8 unsigned multiplier. This…
We study neural networks whose only non-linear components are multipliers, to test a new training rule in a context where the precise representation of data is paramount. These networks are challenged to discover the rules of matrix…
Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of…
In fields such as medicine and drug discovery, the ultimate goal of a classification is not to guess a class, but to choose the optimal course of action among a set of possible ones, usually not in one-one correspondence with the set of…
Low Diameter Decompositions (LDDs) are invaluable tools in the design of combinatorial graph algorithms. While historically they have been applied mainly to undirected graphs, in the recent breakthrough for the negative-length Single Source…
In this paper, we present a multiplier based on a sequence of approximated accumulations. According to a given splitting point of the carry chains, the technique herein introduced allows varying the quality of the accumulations and,…
Approximate computing is a nascent energy-efficient computing paradigm suitable for error-tolerant applications. However, the value of approximation error depends on the applied inputs where individual output error may reach intolerable…
Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this…
We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$,…
We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data…
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. Consequently, various methods have been proposed for designing MDS matrices, including search…