Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth2607.14018AuthorsKatie EverettAbstractWe investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank. We show that skip connections trade off rank collapse against ensemble-like behavior, controlled by the relative scales of the branch and the skip: skip connections route the gradient around the residual branch, where rank is lost, rather than along the long gradient paths that encourage the layers to compose. The placement of the normalization layer controls this same tradeoff by setting the branch-to-skip ratio across depth, unifying much of the normalization placement and depth scaling literature, in particular why rank collapses for Post-Norm but plateaus for Pre-Norm. Other aspects of the architecture, like the two-matrix structure that expands and contracts the width, use additional parameters to preserve the representation or branch Jacobian rank. The second matrix decorrelates a coherent mean spike that would grow across blocks with a single matrix and uncentered activation, preventing the residual representation from collapsing. The width expansion between the two matrices keeps the branch Jacobian full rank: applying the rank-reducing activation in this expanded space leaves enough directions to span the original, at a width that follows a Marchenko--Pastur law. The initialization rank of the input--output Jacobian predicts which networks train on CIFAR-10. Taken together, we recast architecture design for deep networks as navigating an intrinsic tradeoff among rank collapse, ensemble-like behavior, and parameter count.ResourcesView on Hugging FaceRead PDFArXiv
Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth
We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. ...
Related
ResearchLearning When to Trust via Selective Context Preference Optimization
Language models increasingly condition their answers on external signals, and a single misleading one can turn a correct answer wrong. The obvious remedy, training models to resist such signals, hides a failure mode: a model that ignores all context looks robust yet is useless when the context is worth trusting. We recast the problem as selective trust and introduce MIST, a human-annotated benchmark that renders each reasoning item under four matched conditions (clean, misleading, correct-context, and irrelevant-context), together with SC2W, a paired metric counting how often a misle
Learning When to Trust via Selective Context Preference Optimization
Language models increasingly condition their answers on external signals, and a single misleading one can turn a correct answer wrong. The obvious remedy, tr...
ResearchTracing the Heart: An Evidence-Linked Pipeline for Heart-Failure Feature Engineering
Electronic health record (EHR) feature engineering is a major bottleneck in clinical research and AI, accounting for 39-45% of data scientists' workload. This is especially pronounced in heart failure, which affects an estimated 6.7 million U.S. adults and requires integrating fragmented EHR data with disease-specific, guideline-based clinical reasoning. Existing rule-based and large language model (LLM)-based approaches offer only partial automation with limited maintainability and evidence traceability. We developed the Nimblemind Multi-Agent System (nMAS), an evidence-linked, rubr