numerical-stability

Leveraging network motifs to improve artificial neural networks

➗ This work presents a thorough analysis of a quadratic optimization model, confirming convexity, coercivity, and the exact global minimum. It compares gradient descent and Newton’s method, highlighting Newton’s superior efficiency when the Hessian is invertible.

Validate PyTorch model outputs across NVIDIA, AMD, Trainium, TPU, and Apple Silicon. Find numerical divergence before it reaches production.

Bilimsel Hesaplama ve Sayısal Analiz masterclass'ı. Hazır kütüphaneler yok; saf matematik ve NumPy var. Makine epsilonu analizi, güvenli hibrit kök bulma, pivotlu LU/Cholesky çözücüler, Chebyshev interpolasyonu, uyarlamalı Gauss kuadratürü ve katı (stiff) diferansiyel denklemlerin (ODE/BVP) sıfırdan inşası.

High-performance, branchless numerical stability kernels and compiler-optimized core infrastructure for advanced JAX/XLA deep learning architectures.

Research project analyzing stability and robustness of deep learning optimizers (SGD, Adam, SAM) under label noise and precision constraints.

How accurate is naive floating-point summation? Exact errors against the worst-case bound, the role of the condition number, and Kahan, pairwise, np.sum and math.fsum compared.

Certify that your top-k, argmin or threshold was determined by your data and not by the rounding of the kernel it ran on — or refuse, and name the boundary.

Detect numerical instability in ML applications using learned invariants (Soft Assertions) without modifying model logic. ACM FSE 2025.

Multi-Engine (PyTorch & JAX/XLA) Zero-Branching Geometric Acceleration Core. Enforces 0% Graph Breaks & Real-time Fault-Isolation via hardware-native bitwise MUX operations (torch.where / jax.lax.select) to permanently eliminate 'jmp' instructions and host-device synchronization fences.

Pre-registered experiment on differentiable EML-tree symbolic regression (Odrzywolek 2026, arXiv:2603.21852). Streamlit UI + headless reproducer + full results.

R package and replication code for the article “Numerical stability enhancements in beta autoregressive moving average model estimation” by Cribari-Neto, F., Costa, E., and Fonseca, R. V., published in the Brazilian Journal of Probability and Statistics (2025). DOI: 10.1214/25-BJPS645.

Makine Öğrenmesi için Lineer Cebir ve Matris Hesaplamaları masterclass'ı. Hazır kütüphaneler yok; saf geometrik sezgi ve NumPy var. Sıfırdan Gauss eleme, LU ve QR ayrıştırmaları, kararlı en küçük kareler, özdeğer iterasyonları ve doruk noktası olarak PCA ile uçtan uca SVD tabanlı boyut indirgeme mimarisi.

量測 LLM 推論的決定性：同一 prompt 重複執行時，輸出從第幾個 token 開始分歧。

The ZARQA NGVM Project is a paradigm shift in BCI technology: a closed-loop, 50-year implantable neural interface that actively modulates the neuro-glio-vascular ecosystem. It features mathematical inflammation suppression, quantum-resistant encryption, and hardware-agnostic deployment across x86, ARM, FPGA, and ASIC platforms.

Incremental corpus centroid with exact add/remove: compensated float64 accumulation and drift stats that separate rotation from diversity

Reproducible audit of finite-range failures in ONNX Normalizer implementations

A lightweight C++ tool that prices European call and put options using the Black–Scholes formula, computes all key Greeks (Δ, Γ, Θ, Vega, Rho), and lets you run quick ATM/ITM/OTM scenario checks—all via a simple command‑line interface.

A hands‑on, first‑principles guide to fitting logistic regression via the Iteratively Reweighted Least Squares (IRLS) algorithm complete with mathematical derivations, R code from scratch, and a real‑world S&P data case study to bring your statistical modeling skills to the next level.

This MATLAB function efficiently computes the inverse of a square matrix using LU factorization. By decomposing the matrix into lower and upper triangular matrices, the function solves for the inverse with improved numerical stability.