Robin Labryga

Hanna Herasimchyk, Robin Labryga, Tomislav Prusina et al.

Transformer models systematically favor certain token positions, yet the architectural origins of this position bias remain poorly understood. Under causal masking at infinite depth, prior theoretical analyses of attention rollout predict an inevitable collapse of attention onto the first token. Such collapse, however, does not occur in practice. We resolve this discrepancy with a residual-aware theory of cumulative attention rollout. By incorporating residual connections, we show that this architectural component prevents collapse under realistic conditions. At finite depth, we prove that causal Transformers induce a U-shaped position bias, with attention concentrating on early and late tokens. This result provides a principled architectural explanation for the Lost-in-the-Middle phenomenon.

Robin Labryga, Tomislav Prusina, Sören Laue

Line search is a fundamental part of iterative optimization methods for unconstrained and bound-constrained optimization problems to determine suitable step lengths that provide sufficient improvement in each iteration. Traditional line search methods are based on iterative interval refinement, where valuable information about function value and gradient is discarded in each iteration. We propose a line search method via Bayesian optimization, preserving and utilizing otherwise discarded information to improve step-length choices. Our approach is guaranteed to converge and shows superior performance compared to state-of-the-art methods based on empirical tests on the challenging unconstrained and bound-constrained optimization problems from the CUTEst test set.