TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Claims from the fields of network neuroscience and connectomics suggest that topological models of the brain involving complex networks are of particular use and interest. The field of deep neural networks has mostly left inspiration from these claims out. In this paper, we propose three architectures and use each of them to explore the intersection of network neuroscience and deep learning in an attempt to bridge the gap between the two fields. Using the teachings from network neuroscience and connectomics, we show improvements over the ResNet architecture, we show a possible connection between early training and the spectral properties of the network, and we show the trainability of a DNN based on the neuronal network of C.Elegans.

SOLUTION: We explore the intersection of network neurosciences and deep learning.

PROBLEM: One of the most prevalent symptoms among the elderly population, dementia, can be detected by classifiers trained on linguistic features extracted from narrative transcripts. However, these linguistic features are impacted in a similar but different fashion by the normal aging process. Aging is therefore a confounding factor, whose effects have been hard for machine learning classifiers to isolate.

In this paper, we show that deep neural network (DNN) classifiers can infer ages from linguistic features, which is an entanglement that could lead to unfairness across age groups. We show this problem is caused by undesired activations of v-structures in causality diagrams, and it could be addressed with fair representation learning. We build neural network classifiers that learn low-dimensional representations reflecting the impacts of dementia yet discarding the effects of age. To evaluate these classifiers, we specify a model-agnostic score $\Delta_{eo}^{(N)}$ measuring how classifier results are disentangled from age. Our best models outperform baseline neural network classifiers in disentanglement, while compromising accuracy by as little as 2.56\% and 2.25\% on DementiaBank and the Famous People dataset respectively.

SOLUTION: Show that age confounds cognitive impairment detection + solve with fair representation learning + propose metrics and models.

PROBLEM: Motivated by applications to unsupervised learning, we consider the problem of measuring mutual information. Recent analysis has shown that naive kNN estimators of mutual information have serious statistical limitations motivating more refined methods. In this paper we prove that serious statistical limitations are inherent to any measurement method. More specifically, we show that any distribution-free high-confidence lower bound on mutual information cannot be larger than $O(\ln N)$ where $N$ is the size of the data sample. We also analyze the Donsker-Varadhan lower bound on KL divergence in particular and show that, when simple statistical considerations are taken into account, this bound can never produce a high-confidence value larger than $\ln N$. While large high-confidence lower bounds are impossible, in practice one can use estimators without formal guarantees. We suggest expressing mutual information as a difference of entropies and using cross entropy as an entropy estimator. We observe that, although cross entropy is only an upper bound on entropy, cross-entropy estimates converge to the true cross entropy at the rate of $1/\sqrt{N}$.

SOLUTION:
We give a theoretical analysis of the measurement and optimization of mutual information.