Komposisi Fungsi Nonlinier Antar Ruang Vektor Berdimensi Tinggi Dalam Arsitektur Neural Network
DOI:
https://doi.org/10.30605/proximal.v8i2.6538Keywords:
neural network, transformasi non linear, geometri data, ruang vektor berdimensi tinggi, interpretabilitas modelAbstract
Penelitian ini menyajikan pendekatan konseptual dan eksperimental dalam memodelkan jaringan saraf tiruan (neural network) sebagai suatu transformasi nonlinier berlapis antar ruang vektor berdimensi tinggi. Dengan mendasarkan pada kerangka matematis komposisi fungsi linier dan aktivasi nonlinier, studi ini memetakan bagaimana representasi data secara spasial berubah melalui setiap lapisan jaringan. Menggunakan data sintetis berdimensi tinggi dan arsitektur multilayer perceptron (MLP), transformasi internal jaringan dianalisis baik secara visual melalui proyeksi PCA dan t-SNE, maupun secara kuantitatif melalui pengukuran perubahan metrik spasial. Hasil eksperimen menunjukkan bahwa jaringan saraf tidak hanya berfungsi sebagai aproksimator fungsi, tetapi juga secara aktif membentuk ulang geometri manifold data untuk meningkatkan keterpisahan antar kelas. Fungsi aktivasi seperti ReLU dan tanh terbukti memiliki dampak signifikan terhadap struktur representasi, dengan ReLU menghasilkan sparsifikasi spasial yang lebih kuat. Temuan ini mendemonstrasikan bahwa pemahaman terhadap dinamika spasial dalam neural network dapat memberikan fondasi yang lebih transparan dalam interpretasi model, serta membuka arah baru dalam riset interpretabilitas deep learning berbasis pendekatan matematis dan geometris.
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