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Yayın Evaluating the efficiency of latent spaces via the coupling-matrix(Cornell Univ, 2025-09-08) Yavuz, Mehmet Can; Yanıkoğlu, BerrinA central challenge in representation learning is constructing latent embeddings that are both expressive and efficient. In practice, deep networks often produce redundant latent spaces where multiple coordinates encode overlapping information, reducing effective capacity and hindering generalization. Standard metrics such as accuracy or reconstruction loss provide only indirect evidence of such redundancy and cannot isolate it as a failure mode. We introduce a redundancy index, denoted ρ(C), that directly quantifies inter-dimensional dependencies by analyzing coupling matrices derived from latent representations and comparing their off-diagonal statistics against a normal distribution via energy distance. The result is a compact, interpretable, and statistically grounded measure of representational quality. We validate ρ(C) across discriminative and generative settings on MNIST variants, Fashion-MNIST, CIFAR-10, and CIFAR-100, spanning multiple architectures and hyperparameter optimization strategies. Empirically, low ρ(C) reliably predicts high classification accuracy or low reconstruction error, while elevated redundancy is associated with performance collapse. Estimator reliability grows with latent dimension, yielding natural lower bounds for reliable analysis. We further show that Treestructured Parzen Estimators (TPE) preferentially explore lowρ regions, suggesting that ρ(C) can guide neural architecture search and serve as a redundancy-aware regularization target. By exposing redundancy as a universal bottleneck across models and tasks, ρ(C) offers both a theoretical lens and a practical tool for evaluating and improving the efficiency of learned representations.Yayın Variational self-supervised learning(Cornell Univ, 2025-04-06) Yavuz, Mehmet Can; Yanıkoğlu, BerrinWe present Variational Self-Supervised Learning (VSSL), a novel framework that combines variational inference with self-supervised learning to enable efficient, decoder-free representation learning. Unlike traditional VAEs that rely on input reconstruction via a decoder, VSSL symmetrically couples two encoders with Gaussian outputs. A momentum-updated teacher network defines a dynamic, data-dependent prior, while the student encoder produces an approximate posterior from augmented views. The reconstruction term in the ELBO is replaced with a cross-view denoising objective, preserving the analytical tractability of Gaussian KL divergence. We further introduce cosine-based formulations of KL and log-likelihood terms to enhance semantic alignment in high-dimensional latent spaces. Experiments on CIFAR-10, CIFAR-100, and ImageNet-100 show that VSSL achieves competitive or superior performance to leading self-supervised methods, including BYOL and MoCo V3. VSSL offers a scalable, probabilistically grounded approach to learning transferable representations without generative reconstruction, bridging the gap between variational modeling and modern self-supervised techniques.Yayın Multivariate variational autoencoder(Cornell Univ, 2025-11-08) Yavuz, Mehmet CanLearning latent representations that are simultaneously expressive, geometrically well-structured, and reliably calibrated remains a central challenge for Variational Autoencoders (VAEs). Standard VAEs typically assume a diagonal Gaussian posterior, which simplifies optimization but rules out correlated uncertainty and often yields entangled or redundant latent dimensions. We introduce the Multivariate Variational Autoencoder (MVAE), a tractable full-covariance extension of the VAE that augments the encoder with sample-specific diagonal scales and a global coupling matrix. This induces a multivariate Gaussian posterior of the form N (µϕ(x), C diag(σ2ϕ(x))C⊤), enabling correlated latent factors while preserving a closedform KL divergence and a simple reparameterization path. Beyond likelihood, we propose a multi-criterion evaluation protocol that jointly assesses reconstruction quality (MSE, ELBO), downstream discrimination (linear probes), probabilistic calibration (NLL, Brier, ECE), and unsupervised structure (NMI, ARI). Across Larochelle-style MNIST variants, Fashion-MNIST, and CIFAR-10/100, MVAE consistently matches or outperforms diagonal-covariance VAEs of comparable capacity, with particularly notable gains in calibration and clustering metrics at both low and high latent dimensions. Qualitative analyses further show smoother, more semantically coherent latent traversals and sharper reconstructions. All code, dataset splits, and evaluation utilities are released to facilitate reproducible comparison and future extensions of multivariate posterior models.
