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.

Example Input: The softmax function is widely used to train deep neural networks for multi-class classification. Despite its outstanding performance in classification tasks, the features derived from the supervision of softmax are usually sub-optimal in some scenarios where Euclidean distances apply in feature spaces. To address this issue, we propose a new loss, dubbed the isotropic loss, in the sense that the overall distribution of data points is regularized to approach the isotropic normal one. Combined with the vanilla softmax, we formalize a novel criterion called the isotropic softmax, or isomax for short, for supervised learning of deep neural networks. By virtue of the isomax, the intra-class features are penalized by the isotropic loss while inter-class distances are well kept by the original softmax loss. Moreover, the isomax loss does not require any additional modifications to the network, mini-batches or the training process. Extensive experiments on classification and clustering are performed to demonstrate the superiority and robustness of the isomax loss.
Example Output: The discriminative capability of softmax for learning feature vectors of objects is effectively enhanced by virture of isotropic normalization on global distribution of data points.

Example Input: Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions.
 In particular, we propose the use of $k$-determinantal point processes in  hyperparameter optimization via random search. Compared to conventional uniform random search where hyperparameter settings are sampled independently, a $k$-DPP promotes diversity.   We describe an approach that transforms hyperparameter search spaces for efficient use with a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from $k$-DPPs defined over spaces with a mixture of discrete and continuous dimensions. Our experiments show significant benefits over uniform random search  in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel.
Example Output: Driven by the need for parallelizable, open-loop hyperparameter optimization methods, we propose the use of $k$-determinantal point processes in  hyperparameter optimization via random search.

Example Input: Current practice in machine learning is to employ deep nets in an overparametrized limit, with the nominal number of parameters typically exceeding the number of measurements. This resembles the situation in compressed sensing, or in sparse regression with $l_1$ penalty terms, and provides a theoretical avenue for understanding phenomena that arise in the context of deep nets. One such phenonemon is the success of deep nets in providing good generalization in an interpolating regime with zero training error. Traditional statistical practice calls for regularization or smoothing to prevent "overfitting" (poor generalization performance). However, recent work shows that there exist data interpolation procedures which are statistically consistent and provide good generalization performance\cite{belkin2018overfitting} ("perfect fitting"). In this context, it has been suggested that "classical" and "modern" regimes for machine learning are separated by a peak in the generalization error ("risk") curve, a phenomenon dubbed "double descent"\cite{belkin2019reconciling}. While such overfitting peaks do exist and arise from ill-conditioned design matrices, here we challenge the interpretation of the overfitting peak as demarcating the regime where good generalization occurs under overparametrization. 

 We propose a model of Misparamatrized Sparse Regression (MiSpaR) and analytically compute the GE curves for $l_2$ and $l_1$ penalties. We show that the overfitting peak arising in the interpolation limit is dissociated from the regime of good generalization. The analytical expressions are obtained in the so called "thermodynamic" limit. We find an additional interesting phenomenon: increasing overparametrization in the fitting model increases sparsity, which should intuitively improve performance of $l_1$ penalized regression. However, at the same time, the relative number of measurements decrease compared to the number of fitting parameters, and eventually overparametrization does lead to poor generalization. Nevertheless, $l_1$ penalized regression can show good generalization performance under conditions of data interpolation even with a large amount of overparametrization. These results provide a theoretical avenue into studying inverse problems in the interpolating regime using overparametrized fitting functions such as deep nets.
Example Output:
Proposes an analytically tractable model and inference procedure (misparametrized sparse regression, inferred using L_1 penalty and studied in the data-interpolation limit) to study deep-net related phenomena in the context of inverse problems.