Related papers: Low-Memory Numerical Certification

We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general…

Today's high performance deep learning architectures involve large models with numerous parameters. Low precision numerics has emerged as a popular technique to reduce both the compute and memory requirements of these large models. However,…

In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…

We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…

The compact Merkle multiproof is a new and significantly more memory-efficient way to generate and verify sparse Merkle multiproofs. A standard sparse Merkle multiproof requires to store an index for every non-leaf hash in the multiproof.…

The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $\alpha$-theory…

Quantum memories represent one of the main ingredients of future quantum communication networks. Their certification is therefore a key challenge. Here we develop efficient certification methods for quantum memories. Considering a…

Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…

In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions for polynomials to be nonnegative as well as to have a sum of binomial squares…

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell…

Multiprocess systems, including grid systems, multiprocessors and multicore computers, incorporate a variety of specialized hardware and software mechanisms, which speed computation, but result in complex memory behavior. As a consequence,…

Catastrophic forgetting can be trivially alleviated by keeping all data from previous tasks in memory. Therefore, minimizing the memory footprint while maximizing the amount of relevant information is crucial to the challenge of continual…

Convexification is a core technique in global polynomial optimization. Currently, there are two main approaches competing in theory and practice: the approach of nonlinear programming and the approach based on positivity certificates from…

Despite the outstanding performance of deep neural networks in different applications, they are still computationally extensive and require a great number of memories. This motivates more research on reducing the resources required for…

Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…

This short paper describes a numerical method for optimising the conservative confidence bound on the reliability of a system based on tests of its individual components. This is an alternative to the algorithmic approaches identified in…

Flash memory-based processing-in-memory (flash-based PIM) offers high storage capacity and computational efficiency but faces significant reliability challenges due to noise in high-density multi-level cell (MLC) flash memories. Existing…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

Both in electronics and biology, physical implementations of neural networks have severe energy and memory constraints. We propose a hardware-software co-design approach for minimizing the use of memory resources in multi-core neuromorphic…