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Approximate computing is an emerging paradigm where design accuracy can be traded off for benefits in design metrics such as design area, power consumption or circuit complexity. In this work, we present a novel paradigm to synthesize…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…

Non-determinism and non-reproducibility present significant challenges in deep learning, leading to inconsistent results across runs and platforms. These issues stem from two origins: random number generation and floating-point computation.…

We consider the problem of continuous quantum error correction from a Bayesian perspective, proposing a pair of digital filters using logarithmic probabilities that are able to achieve near-optimal performance on a three-qubit bit-flip…

We consider a novel and general approach to easily compute the Cram\'er-Rao Lower Bounds (CRLBs) of rigid body localization (RBL) problem using arbitrary types of information. To that end, we adopt an information-centric construction of the…

Pretrained large language models (LLMs) exhibit exceptional general language processing capabilities but come with significant demands on memory and computational resources. As a powerful compression technology, binarization can extremely…

Given a compact semialgebraic set S of R^n and a polynomial map f from R^n to R^m, we consider the problem of approximating the image set F = f(S) in R^m. This includes in particular the projection of S on R^m for n greater than m. Assuming…

With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…

Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

Modern neural-network-based speech processing systems are typically required to be robust against reverberation, and the training of such systems thus needs a large amount of reverberant data. During the training of the systems, on-the-fly…

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schr\"odinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based…

We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…

With the proliferation of embedded systems requiring intelligent behavior, custom number systems to optimize performance per Watt of the entire system become essential components for successful commercial products. We present the Universal…

Incorporating fairness constructs into machine learning algorithms is a topic of much societal importance and recent interest. Clustering, a fundamental task in unsupervised learning that manifests across a number of web data scenarios, has…

Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive…

The study of the expressive power of neural networks has investigated the fundamental limits of neural networks. Most existing results assume real-valued inputs and parameters as well as exact operations during the evaluation of neural…

We give near-optimal algorithms for computing an ellipsoidal rounding of a convex polytope whose vertices are given in a stream. The approximation factor is linear in the dimension (as in John's theorem) and only loses an excess logarithmic…

Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…