A Note On The Dai-Singleton Canonical Representation Of Affine Term Structure Models

Dai and Singleton (2000) study a class of term structure models for interest rates that specify the short rate as an affine combination of the components of an N-dimensional affine diffusion process. Observable quantities in such models are invariant under regular affine transformations of the underlying diffusion process. In their canonical form, the models in Dai and Singleton (2000) are based on diffusion processes with diagonal diffusion matrices. This motivates the following question: Can the diffusion matrix of an affine diffusion process always be diagonalized by means of a regular affine transformation? We show that if the state space of the diffusion is of the form D = R-+(m) x RN-m for integers 0

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

A Note On The Dai-Singleton Canonical Representation Of Affine Term Structure Models

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A generic diffusion-based approach for 3D human pose prediction in the wild

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

A generic diffusion-based approach for 3D human pose prediction in the wild

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances