  `Double descent' delineates the generalization behaviour of models depending
on the regime they belong to: under- or over-parameterized. The current
theoretical understanding behind the occurrence of this phenomenon is primarily
based on linear and kernel regression models -- with informal parallels to
neural networks via the Neural Tangent Kernel. Therefore such analyses do not
adequately capture the mechanisms behind double descent in finite-width neural
networks, as well as, disregard crucial components -- such as the choice of the
loss function. We address these shortcomings by leveraging influence functions
in order to derive suitable expressions of the population loss and its lower
bound, while imposing minimal assumptions on the form of the parametric model.
Our derived bounds bear an intimate connection with the spectrum of the Hessian
at the optimum, and importantly, exhibit a double descent behaviour at the
interpolation threshold. Building on our analysis, we further investigate how
the loss function affects double descent -- and thus uncover interesting
properties of neural networks and their Hessian spectra near the interpolation
threshold.
