3 research outputs found
Cardinality-Minimal Explanations for Monotonic Neural Networks
In recent years, there has been increasing interest in explanation methods
for neural model predictions that offer precise formal guarantees. These
include abductive (respectively, contrastive) methods, which aim to compute
minimal subsets of input features that are sufficient for a given prediction to
hold (respectively, to change a given prediction). The corresponding decision
problems are, however, known to be intractable. In this paper, we investigate
whether tractability can be regained by focusing on neural models implementing
a monotonic function. Although the relevant decision problems remain
intractable, we can show that they become solvable in polynomial time by means
of greedy algorithms if we additionally assume that the activation functions
are continuous everywhere and differentiable almost everywhere. Our experiments
suggest favourable performance of our algorithms
Double-descent curves in neural networks: a new perspective using Gaussian processes
Double-descent curves in neural networks describe the phenomenon that the
generalisation error initially descends with increasing parameters, then grows
after reaching an optimal number of parameters which is less than the number of
data points, but then descends again in the overparameterised regime. Here we
use a neural network Gaussian process (NNGP) which maps exactly to a fully
connected network (FCN) in the infinite width limit, combined with techniques
from random matrix theory, to calculate this generalisation behaviour, with a
particular focus on the overparameterised regime. An advantage of our NNGP
approach is that the analytical calculations are easier to interpret. We argue
that neural network generalization performance improves in the
overparameterised regime precisely because that is where they converge to their
equivalent Gaussian process