41 research outputs found
Deep equilibrium networks are sensitive to initialization statistics
Deep equilibrium networks (DEQs) are a promising way to construct models
which trade off memory for compute. However, theoretical understanding of these
models is still lacking compared to traditional networks, in part because of
the repeated application of a single set of weights. We show that DEQs are
sensitive to the higher order statistics of the matrix families from which they
are initialized. In particular, initializing with orthogonal or symmetric
matrices allows for greater stability in training. This gives us a practical
prescription for initializations which allow for training with a broader range
of initial weight scales
Understanding plastic deformation in thermal glasses from single-soft-spot dynamics
By considering the low-frequency vibrational modes of amorphous solids,
Manning and Liu [Phys. Rev. Lett. 107, 108302 (2011)] showed that a population
of "soft spots" can be identified that are intimately related to plasticity at
zero temperature under quasistatic shear. In this work we track individual soft
spots with time in a two-dimensional sheared thermal Lennard Jones glass at
temperatures ranging from deep in the glassy regime to above the glass
transition temperature. We show that the lifetimes of individual soft spots are
correlated with the timescale for structural relaxation. We additionally
calculate the number of rearrangements required to destroy soft spots, and show
that most soft spots can survive many rearrangements. Finally, we show that
soft spots are robust predictors of rearrangements at temperatures well into
the super-cooled regime. Altogether, these results pave the way for mesoscopic
theories of plasticity of amorphous solids based on dynamical behavior of
individual soft spots.Comment: 9 pages, 6 figure