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This paper revisits pruning for recurrent networks, using poset and lattice theory to decide which weights to keep. Its main contribution is a correction: the authors show the earlier criterion retained everything or nothing, and they replace it with a strongly-connected-components approach. In their matched-sparsity LSTM tests on sequential MNIST, the order-based score performs no better than simple baselines like degree, PageRank, or weight magnitude, so readers should treat the theory as promising but not yet a practical pruning gain.
Lattice-Based Pruning of Recurrent Neural Networks via Poset Modeling: A Corrected Theory and a Matched-Sparsity Evaluation
arXiv:2502.16525v2 Announce Type: replace-cross Abstract: Magnitude pruning of recurrent neural networks (RNNs) ignores how information flows between neurons. An earlier version proposed to model RNN dependencies as a partially ordered set (poset) and to retain the meet-irreducible elements of its dependency lattice. By Birkhoff's representation theorem, the meet-irreducible ideals of a finite poset are in bijection with its elements, so retaining them retains everything; the critical-set criterion used earlier selects precisely the elements comparable to all others, of which a dense recurrent layer has none. Condensing a thresholded dependency graph into strongly connected components yields a well-defined dependency order, a graded order score and an acyclic pruning rule; for Cohen-Grossberg networks and LSTMs, acyclic pruning makes local stability decompose over modules. For a 128-unit LSTM pruned at matched sparsity on row-wise and chunked sequential MNIST (three seeds, equal training budgets), the original rules remove every recurrent weight or equal random column pruning; the order score is no better than degree, PageRank or norm; trained weights show little directional bias; and imposing acyclicity from initialisation costs 2.1 and 10.5 percentage points at 50% and 90% sparsity. In the networks studied, order structure must be imposed rather than discovered.
Abstract:Magnitude pruning of recurrent neural networks (RNNs) ignores how information flows between neurons. An earlier version proposed to model RNN dependencies as a partially ordered set (poset) and to retain the meet-irreducible elements of its dependency lattice. By Birkhoff's representation theorem, the meet-irreducible ideals of a finite poset are in bijection with its elements, so retaining them retains everything; the critical-set criterion used earlier selects precisely the elements comparable to all others, of which a dense recurrent layer has none. Condensing a thresholded dependency graph into strongly connected components yields a well-defined dependency order, a graded order score and an acyclic pruning rule; for Cohen-Grossberg networks and LSTMs, acyclic pruning makes local stability decompose over modules. For a 128-unit LSTM pruned at matched sparsity on row-wise and chunked sequential MNIST (three seeds, equal training budgets), the original rules remove every recurrent weight or equal random column pruning; the order score is no better than degree, PageRank or norm; trained weights show little directional bias; and imposing acyclicity from initialisation costs 2.1 and 10.5 percentage points at 50% and 90% sparsity. In the networks studied, order structure must be imposed rather than discovered.
v2: substantially revised. The Transformer extension of v1 is withdrawn. 29 pages, 4 figures, 6 tables
Neurons and Cognition (q-bio.NC); Machine Learning (cs.LG)
arXiv:2502.16525 [q-bio.NC]
(or arXiv:2502.16525v2 [q-bio.NC] for this version)
https://doi.org/10.48550/arXiv.2502.16525 Focus to learn more arXiv-issued DOI via DataCite
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