In-context learning (ICL) is a hallmark capability of transformers, through which trained models learn to adapt to new tasks by leveraging information from the input context. Prior work has shown that ICL emerges in transformers due to the presence of special circuits called induction heads. Given the equivalence between induction heads and conditional k-grams, a recent line of work modeling sequential inputs as Markov processes has revealed the fundamental impact of model depth on its ICL capabilities: while a two-layer transformer can efficiently represent a conditional 1-gram model, its single-layer counterpart cannot solve the task unless it is exponentially large. However, for higher order Markov sources, the best known constructions require at least three layers (each with a single attention head) -- leaving open the question: can a two-layer single-head transformer represent any kth-order Markov process? In this paper, we precisely address this and theoretically show that a two-layer transformer with one head per layer can indeed represent any conditional k-gram. Thus, our result provides the tightest known characterization of the interplay between transformer depth and Markov order for ICL. Building on this, we further analyze the learning dynamics of our two-layer construction, focusing on a simplified variant for first-order Markov chains, illustrating how effective in-context representations emerge during training. Together, these results deepen our current understanding of transformer-based ICL and illustrate how even shallow architectures can surprisingly exhibit strong ICL capabilities on structured sequence modeling tasks. Code is available at thelink.

Neural Information Processing Systems http://nips.cc/

This work presents xEEGNet, a novel, compact, and explainable neural network for EEG data analysis. It is fully interpretable and reduces overfitting through major parameter reduction. As an applicative use case, we focused on classifying common dementia conditions, Alzheimer's and frontotemporal dementia, versus controls. xEEGNet is broadly applicable to other neurological conditions involving spectral alterations. We initially used ShallowNet, a simple and popular model from the EEGNet-family. Its structure was analyzed and gradually modified to move from a "black box" to a more transparent model, without compromising performance. The learned kernels and weights were examined from a clinical standpoint to assess medical relevance. Model variants, including ShallowNet and the final xEEGNet, were evaluated using robust Nested-Leave-N-Subjects-Out cross-validation for unbiased performance estimates. Variability across data splits was explained using embedded EEG representations, grouped by class and set, with pairwise separability to quantify group distinction. Overfitting was assessed through training-validation loss correlation and training speed. xEEGNet uses only 168 parameters, 200 times fewer than ShallowNet, yet retains interpretability, resists overfitting, achieves comparable median performance (-1.5%), and reduces variability across splits. This variability is explained by embedded EEG representations: higher accuracy correlates with greater separation between test set controls and Alzheimer's cases, without significant influence from training data. xEEGNet's ability to filter specific EEG bands, learn band-specific topographies, and use relevant spectral features demonstrates its interpretability. While large deep learning models are often prioritized for performance, this study shows smaller architectures like xEEGNet can be equally effective in EEG pathology classification.