Mehran Shakerinava

Doctorat - McGill

Superviseur⋅e principal⋅e

Siamak Ravanbakhsh

Sujets de recherche

Théorie de l'apprentissage automatique

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Publications

Parity Requires Unified Input Dependence and Negative Eigenvalues in SSMs

Jayesh Khullar

Franccois Rivest

Recent work has shown that LRNN models such as S4D, Mamba, and DeltaNet lack state-tracking capability due to either time-invariant transiti… (voir plus)on matrices or restricted eigenvalue ranges. To address this, input-dependent transition matrices, particularly those that are complex or non-triangular, have been proposed to enhance SSM performance on such tasks. While existing theorems demonstrate that both input-independent and non-negative SSMs are incapable of solving simple state-tracking tasks, such as parity, regardless of depth, they do not explore whether combining these two types in a multilayer SSM could help. We investigate this question for efficient SSMs with diagonal transition matrices and show that such combinations still fail to solve parity. This implies that a recurrence layer must both be input-dependent and include negative eigenvalues. Our experiments support this conclusion by analyzing an SSM model that combines S4D and Mamba layers.

2025-08-10

ArXiv (prépublication)

arxiv.org