Related papers: Mixing Condition Numbers and Oracles for Accurate …
The recent hardware trend towards reduced precision computing has reignited the interest in numerical techniques that can be used to enhance the accuracy of floating point operations beyond what is natively supported for basic arithmetic…
This work introduces StageSAT, a new approach to solving floating-point satisfiability that bridges SMT solving with numerical optimization. StageSAT reframes a floating-point formula as a series of optimization problems in three stages of…
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets…
This paper reports on a novel method for LiDAR odometry estimation, which completely parameterizes the system with dual quaternions. To accomplish this, the features derived from the point cloud, including edges, surfaces, and Stable…
We experimentally demonstrate a hybrid reservoir computing system consisting of an electro-optic modulator and field programmable gate array (FPGA). It implements delay lines and filters digitally for flexible dynamics and high…
Probabilistic cataloging (PCAT) outperforms traditional cataloging methods on single-band optical data in crowded fields (Portillo et al. 2017). We extend our work to multiple bands, achieving greater sensitivity ($\sim$ 0.4 mag) and…
Statically reasoning in the presence of exceptions and about the effects of exceptions is challenging: exception-flows are mutually determined by traditional control-flow and points-to analyses. We tackle the challenge of analyzing…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…
Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…
Many numerical problems with input $x$ and output $y$ can be formulated as a system of equations $F(x, y) = 0$ where the goal is to solve for $y$. The condition number measures the change of $y$ for small perturbations to $x$. From this…
Conventional hardware-friendly quantization methods, such as fixed-point or integer, tend to perform poorly at very low word sizes as their shrinking dynamic ranges cannot adequately capture the wide data distributions commonly seen in…
Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
In this paper, we establish for the first time the oracle complexity of a Riemannian inexact augmented Lagrangian (RiAL) method with the classical dual update for solving a class of Riemannian nonsmooth composite problems. By using the…
With streaming floating-point numbers being increasingly prevalent, effective and efficient compression of such data is critical. Compression schemes must be able to exploit the similarity, or smoothness, of consecutive numbers and must be…
We present DeFlow, a decoupled offline RL framework that leverages flow matching to faithfully capture complex behavior manifolds. Optimizing generative policies is computationally prohibitive, typically necessitating backpropagation…
The combination of a number of correlated estimates of a given observable is frequently performed using the Best Linear Unbiased Estimate (BLUE) method. Most features of such a combination can already be seen by analysing the special case…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…