Dead-Direction Signatures provide closed-form spectral readings of dead directions in network activations and gradients that track rank deficits at singular minima, offering a cheap directional alternative to SGLD-based LLC.
arXiv preprint arXiv:2103.03404 , year=
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The normalized inverse-scale direction of LayerNorm's affine parameters is an exact algebraic kernel of the post-final-norm centred activation covariance for any input distribution in LayerNorm transformers.
Dead directions recover Watanabe's RLCT contribution and triple (λ, m, ν) from directional Fisher curvature decay rates in original parameter space for singular models, extended via K-FAC to networks and gauge-equivariant optimizers.
ASAP amortizes Sinkhorn-based doubly-stochastic attention by learning a parametric map from 1D potentials to the Sinkhorn dual and reconstructing the plan via two-sided entropic c-transform, delivering 5.3x faster inference at matched accuracy.
Induction heads, which implement pattern completion in attention, develop at the same training stage as a sudden rise in in-context learning, providing evidence they are the primary mechanism for in-context learning in transformers.
STS is a two-stage pruning framework that decouples structural diversity via repulsion sampling from semantic filtering via cross-attention to reduce redundancy in visual tokens for VLMs.
TOA augments attention with learnable sequence-space operators and stochastic regularization to enable signed temporal mixing, yielding gains on forecasting and related benchmarks when added to PatchTST and iTransformer.
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.
Sinkhorn-normalized doubly stochastic attention preserves rank more effectively than Softmax row-stochastic attention, with both showing doubly exponential rank decay to one with network depth.
citing papers explorer
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Dead-Direction Signatures: A Cheap Spectral Reading of Singular Complexity
Dead-Direction Signatures provide closed-form spectral readings of dead directions in network activations and gradients that track rank deficits at singular minima, offering a cheap directional alternative to SGLD-based LLC.
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Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale
The normalized inverse-scale direction of LayerNorm's affine parameters is an exact algebraic kernel of the post-final-norm centred activation covariance for any input distribution in LayerNorm transformers.
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Dead Directions: Geometric Singular Learning
Dead directions recover Watanabe's RLCT contribution and triple (λ, m, ν) from directional Fisher curvature decay rates in original parameter space for singular models, extended via K-FAC to networks and gauge-equivariant optimizers.
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ASAP: Amortized Doubly-Stochastic Attention via Sliced Dual Projection
ASAP amortizes Sinkhorn-based doubly-stochastic attention by learning a parametric map from 1D potentials to the Sinkhorn dual and reconstructing the plan via two-sided entropic c-transform, delivering 5.3x faster inference at matched accuracy.
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In-context Learning and Induction Heads
Induction heads, which implement pattern completion in attention, develop at the same training stage as a sudden rise in in-context learning, providing evidence they are the primary mechanism for in-context learning in transformers.
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When Attention Collapses: Stage-Aware Visual Token Pruning from Structure to Semantics
STS is a two-stage pruning framework that decouples structural diversity via repulsion sampling from semantic filtering via cross-attention to reduce redundancy in visual tokens for VLMs.
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Beyond Similarity: Temporal Operator Attention for Time Series Analysis
TOA augments attention with learnable sequence-space operators and stochastic regularization to enable signed temporal mixing, yielding gains on forecasting and related benchmarks when added to PatchTST and iTransformer.
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Dimension-Free Saddle-Point Escape in Muon
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.
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Sinkhorn doubly stochastic attention rank decay analysis
Sinkhorn-normalized doubly stochastic attention preserves rank more effectively than Softmax row-stochastic attention, with both showing doubly exponential rank decay to one with network depth.