arXiv subjects

Antoine Groudiev

Publications and source records attributed to Antoine Groudiev.

3 recordsLinked to original sources

arXiv2026

Model Casting and Low-Parameter Gating: Towards More Sparsely Activated FFNs

This paper introduces model casting, a mid-training recipe that drastically sparsifies the activations within the Feed-Forward Network (FFN) layer. With this strategy, at inference time, we first compute the output of the gating matrix and, thanks to its high sparsity, we avoid computations with the two other matrices, reducing the FLOP count by up to 3x. While this theoretical speedup is an upper bound, model casting translates into significant speedups both on CPU and GPU. We then introduce LoPA Gating, a new FFN design that increases the maximum theoretical speedup. It is a low-FLOPs parameterization of the gating matrix that overcomes the 3x cap by allocating fewer FLOPs and parameters to the gating matrix, compared to the two other FFN matrices that are sparsely activated. We consider two cases: (i) we cast a pre-trained model with a sparsity inducing activation; (ii) we train with LoPA from scratch. In all settings, we significantly outperform existing pruning solutions and regular RELU-fication. For instance, at matched quality, we achieve a 3.2x FLOP speedup with LoPA Casting, against 1.6x at best for competing methods top-p and TEAL. Using dedicated kernels, we achieve an actual 3.31x speed-up on GPU at 90% sparsity, past the 3x ceiling of standard gating; RELU-fication, meanwhile, plateaus below 80% sparsity.

cs.LG↗

arXiv2026

Factorization-free Orthogonal Projection onto the Positive Semidefinite Cone with Composite Polynomial Filtering

We propose a factorization-free method for orthogonal projection onto the positive semidefinite (PSD) cone, leveraging composite polynomial filtering. Inspired by recent advances in homomorphic encryption, our approach approximates the PSD cone projection operator using a carefully optimized composite polynomial evaluated exclusively via matrix-matrix multiplications. This approach enables efficient GPU implementations with low-precision arithmetic, significantly outperforming the classical PSD cone projection using state-of-the-art GPU-based eigenvalue decomposition solvers. Specifically, our method achieves a consistent relative error of $10^{-3}$ in half-precision arithmetic with only 22 matrix-matrix multiplications, providing roughly a $10\times$ speed-up over NVIDIA's cuSOLVER routines on various large-scale matrices. In single-precision arithmetic with emulation on B200 GPUs, our approach maintains competitive accuracy while achieving up to a $2\times$ speed-up. Consequently, for a $10,000 \times 10,000$ dense symmetric matrix, our method requires approximately $55$ ms in half-precision and $400$ ms in single-precision arithmetic on B200 GPUs. Integration into a first-order semidefinite programming solver confirms that our low-precision projections reliably yield solutions of moderate accuracy.

math.OC↗

arXiv2026

Sampling-Based Global Optimal Control and Estimation via Semidefinite Programming

Global optimization has gained attraction over the past decades, thanks to the development of both theoretical foundations and efficient numerical routines. Among recent advances, Kernel Sum of Squares (KernelSOS) provides a powerful theoretical framework, combining the expressivity of kernel methods with the guarantees of SOS optimization. In this paper, we take KernelSOS from theory to practice and demonstrate its use on challenging control and robotics problems. We identify and address the practical considerations required to make the method work in applied settings: restarting strategies, systematic calibration of hyperparameters, methods for recovering minimizers, and the combination with fast local solvers. As a proof of concept, the application of KernelSOS to robot localization highlights its competitiveness with existing SOS approaches that rely on heuristics and handcrafted reformulations to render the problem polynomial. Even in the high-dimensional, non-parametric setting of trajectory optimization with simulators treated as black boxes, we demonstrate how KernelSOS can be combined with fast local solvers to uncover higher-quality solutions without compromising overall runtimes.

cs.RO↗