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Trajectory Geometry of Transformer Representations Across Layers

arXiv:2606.09287v2 Announce Type: replace Abstract: Understanding how transformer representations evolve across layers, not merely what they encode, remains an open problem in mechanistic interpretability. We recast the transformer forward pass as a discrete population trajectory through a high-dimensional representation manifold, drawing on geometric tools from computational neuroscience. Rather than probing for pre-specified features, we characterize trajectory geometry using five metrics computed directly in the ambient space: trajectory length, curvature, a semantic convergence index, layerwise cosine similarity, and representational stability. Across three model families (GPT-2, TinyLlama, Qwen2.5) and five controlled prompt families, we report four findings. First, semantically related prompts converge significantly in middle-to-late layers (peak CI 0.41–0.58, p

The Target ALS Global Natural History Study: Cross-platform proteomics to accelerate biofluid biomarker and drug target discovery in amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a fatal, rapidly progressive neurodegenerative disease of motor neurons for which therapeutics are limited. Improved biomarkers are imperative to improve patient care and therapeutic development. Here, we employed 35-plex isobaric tandem mass tag labeling based on isobutyl-proline reporter group (TMTpro) to perform unbiased proteomic analysis of cerebrospinal fluid (CSF) and plasma from control (n= 28, n= 31) and sporadic ALS (sALS) (n= 39, n= 41), from the Target ALS Global Natural History Study (TALS GNHS). We identified 2,875 proteins in CSF and 1,118 proteins in plasma and identified known and novel differentially expressed proteins (DEPs) between controls and sALS, some of which were orthogonally validated using immunoassay. Comparison of TMTpro-MS and Olink proximity extension assay proteomics revealed common and non-overlapping differentially expressed proteins illustrating strengths unique to each platform. This initial cross-sectional proteomic study of biofluids from the TALS GNHS, with unrestricted availability of study results to the research community, highlights the potential of this resource as a potent platform for ALS biomarker discovery.