arXiv subjects

Joel Andersson

Publications and source records attributed to Joel Andersson.

5 recordsLinked to original sources

arXiv2026

Engineering Compressed Matrix Multiplication with the Fast Walsh-Hadamard Transform

We present an implementation of Pagh's compressed matrix multiplication algorithm, a randomized algorithm that constructs sketches of matrices to compute an unbiased estimate of their product. By leveraging fast polynomial multiplication via the FFT, the algorithm achieves high performance when the product matrix is sparse or contains only a small number of entries with magnitudes significantly larger than the rest. We show empirically that the algorithm is practical and can outperform state-of-the-art DGEMM implementations when the product matrix has few nonzero entries or is otherwise dominated by a small subset of elements with large magnitude. As a minor theoretical contribution, we replace the FFT with the Fast Walsh-Hadamard Transform (FWHT) in sketched multiplication, preserving all correctness and variance guarantees of the original algorithm. Experiments with our carefully engineered multithreaded CPU implementation for dense double-precision matrices on 64-core CPU nodes across a range of synthetic benchmarks, exhibiting variable sparsity patterns, show that the FWHT variant is up to 4 times faster than the FFT-based version. Under favorable sparsity and magnitude patterns in the product matrix, our FWHT-based implementation achieves a speedup of up to 40 over DGEMM from Intel MKL, with low probability of error in the estimates. Our implementation is released as free software and comes with NumPy-compatible Python bindings.

cs.DS↗

arXiv2023

Learning for CasADi: Data-driven Models in Numerical Optimization

While real-world problems are often challenging to analyze analytically, deep learning excels in modeling complex processes from data. Existing optimization frameworks like CasADi facilitate seamless usage of solvers but face challenges when integrating learned process models into numerical optimizations. To address this gap, we present the Learning for CasADi (L4CasADi) framework, enabling the seamless integration of PyTorch-learned models with CasADi for efficient and potentially hardware-accelerated numerical optimization. The applicability of L4CasADi is demonstrated with two tutorial examples: First, we optimize a fish's trajectory in a turbulent river for energy efficiency where the turbulent flow is represented by a PyTorch model. Second, we demonstrate how an implicit Neural Radiance Field environment representation can be easily leveraged for optimal control with L4CasADi. L4CasADi, along with examples and documentation, is available under MIT license at https://github.com/Tim-Salzmann/l4casadi

eess.SY↗

arXiv2016

Stability for a magnetic Schrödinger operator on a Riemann surface with boundary

We consider a magnetic Schrödinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the assumption that they satisfy appropriate a priori bounds. We also give a similar stability result for the holonomy of the connection 1-form $X$.

math.AP↗

arXiv2014

Stability estimates with a priori bound for the inverse local Radon transform

We consider the inverse problem for the $2$-dimensional weighted local Radon transform $R_m[f]$, where $f$ is supported in $y\geq x^2$ and $R_m[f](ξ,η)=\int f(x, ξx + η) m(ξ, η, x)\,\text{d} x$ is defined near $(ξ,η)=(0,0)$. For weight functions satisfying a certain differential equation we give weak estimates of $f$ in terms of $R_m[f]$ for functions $f$ that satisfies an a priori bound.

math.AP↗

arXiv2013

On the Theorem of Uniform Recovery of Random Sampling Matrices

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements (with high probability) is known to be $m\gtrsim s(\ln s)^3\ln N$. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of $m\times N$-matrices, by considering what we call \emph{low entropy}. We also present an improved condition on the so-called restricted isometry constants, $δ_s$, ensuring sparse recovery via $\ell^1$-minimization. We show that $δ_{2s}<4/\sqrt{41}$ is sufficient and that this can be improved further to almost allow for a sufficient condition of the type $δ_{2s}<2/3$.

cs.IT↗