We investigate the error surface of the XOR problem for a 2-2-1 network with sigmoid transfer functions. It is proved that all stationary points with finite weights are saddle points with positive error or absolute minima with error zero. So, for finite weights no local minima occur. The proof results from a careful analysis of the Taylor series expansion around the stationary points. For some points coefficients of third or even fourth order in the Taylor series expansion are used to complete the proof. The proofs give a deeper insight into the complexity of the error surface in the neighbourhood of saddle points. These results can guide the research in finding learning algorithms that can handle these kinds of saddle points.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1016/s0893-6080(98)00014-8 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Novel numerical and artificial neural computing with experimental validation towards unsteady micropolar nanofluid flow across a Riga plate.
Sci Rep
January 2025
Department of Mechanical Engineering, College of Engineering and Computer Sciences, Jazan University, P.O Box 45124, Jazan, Saudi Arabia.
Fluid flow across a Riga Plate is a specialized phenomenon studied in boundary layer flow and magnetohydrodynamic (MHD) applications. The Riga Plate is a magnetized surface used to manipulate boundary layer characteristics and control fluid flow properties. Understanding the behavior of fluid flow over a Riga Plate is critical in many applications, including aerodynamics, industrial, and heat transfer operations.
View Article and Find Full Text PDFShaping ability of NiTi reciprocating file systems R-motion and waveOne gold in mesial canals of mandibular molars; micro CT study.
Sci Rep
January 2025
Department of Endodontics, Faculty of Dentistry, King Abdulaziz University, Jeddah, Saudi Arabia.
The preservation of the original configurations of root canals during endodontic preparation is crucial for treatment success. Nickel-titanium (NiTi) rotary systems have been refined to optimize canal shaping while minimizing iatrogenic errors. This study aimed to evaluate and compare the shaping efficacy of the novel R-Motion (RM) and the established WaveOne Gold (WG) systems using micro-computed tomography (micro-CT).
View Article and Find Full Text PDFDeep eutectic solvent-based green extraction of Strychnos potatorum seed phenolics: Process optimization via response surface methodology and artificial neural network.
Talanta
December 2024
Department of Chemistry, Government College University, Lahore, Pakistan. Electronic address:
The current research focused on extraction optimization of bioactive compounds from Strychnos potatorum seeds (SPs) using an eco-friendly glycerol-sodium acetate based deep eutectic solvent (DES). The optimization was accomplished using response surface methodology (RSM) and artificial neural networking (ANN). The independent variables included shaking time (A), temperature (B), and solvent-to-feed ratio (C), and the responses were the extraction yield, total phenolic content (TPC), total flavonoid content (TFC), antioxidant activity (DPPH), and antidiabetic activity (α-amylase inhibitory activity).
View Article and Find Full Text PDFClinical Manifestations.
Alzheimers Dement
December 2024
WCG Clinical Endpoint Solutions, Princeton, NJ, USA.
Background: Clinical trials in Alzheimer's Disease (AD) suffer from high failure rates, in part due to imprecision in endpoint measurements that introduces noise. SIA is a quantitative approach that utilizes algorithms to identify inconsistencies in measurements that may be indicative of problematic scale administration and/or scoring errors. The CDR, a sole primary and key secondary endpoint in many AD trials, can be challenging to score, particularly in early symptomatic and mild diseases.
View Article and Find Full Text PDFClinical Manifestations.
Alzheimers Dement
December 2024
Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil.
Background: Language impairment manifestations in patients with the semantic variant of primary progressive aphasia (S-PPA) include surface dysgraphia. Word and pseudoword dictation helps characterize errors in these patients' writing to better conduct their therapeutic strategies. Few studies have addressed written language in patients with dementia, and even fewer have done so in PPA.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!