Hyungjoon Soh

Hyungjoon Soh, Junghyo Jo

We formulate an attention mechanism for continuous and ordered sequences that explicitly functions as an alignment model, which serves as the core of many sequence-to-sequence tasks. Standard scaled dot-product attention relies on positional encodings and masks but does not enforce continuity or monotonicity, which are crucial for frame-synchronous targets. We propose learned nonnegative \emph{clocks} to source and target and model attention as the meeting probability of these clocks; a path-integral derivation yields a closed-form, Gaussian-like scoring rule with an intrinsic bias toward causal, smooth, near-diagonal alignments, without external positional regularizers. The framework supports two complementary regimes: normalized clocks for parallel decoding when a global length is available, and unnormalized clocks for autoregressive decoding -- both nearly-parameter-free, drop-in replacements. In a Transformer text-to-speech testbed, this construction produces more stable alignments and improved robustness to global time-scaling while matching or improving accuracy over scaled dot-product baselines. We hypothesize applicability to other continuous targets, including video and temporal signal modeling.

Hyungjoon Soh, Dongha Lee, Vipul Periwal et al.

Selecting key variables from high-dimensional data is increasingly important in the era of big data. Sparse regression serves as a powerful tool for this purpose by promoting model simplicity and explainability. In this work, we revisit a valuable yet underutilized method, the statistical physics-based Variational Garrote (VG), which introduces explicit feature selection spin variables and leverages variational inference to derive a tractable loss function. We enhance VG by incorporating modern automatic differentiation techniques, enabling scalable and efficient optimization. We evaluate VG on both fully controllable synthetic datasets and complex real-world datasets. Our results demonstrate that VG performs especially well in highly sparse regimes, offering more consistent and robust variable selection than Ridge and LASSO regression across varying levels of sparsity. We also uncover a sharp transition: as superfluous variables are admitted, generalization degrades abruptly and the uncertainty of the selection variables increases. This transition point provides a practical signal for estimating the correct number of relevant variables, an insight we successfully apply to identify key predictors in real-world data. We expect that VG offers strong potential for sparse modeling across a wide range of applications, including compressed sensing and model pruning in machine learning.