Many neural networks deployed in the real world scenarios are trained using cross entropy based loss functions. From the optimization perspective, it is known that the behavior of first order methods such as gradient descent crucially depend on the separability of datasets. In fact, even in the most simplest case of binary classification, the rate of convergence depends on two factors: (1) condition number of data matrix, and (2) separability of the dataset. With no further pre-processing techniques such as over-parametrization, data augmentation etc., separability is an intrinsic quantity of the data distribution under consideration. We focus on the landscape design of the logistic function and derive a novel sequence of {\em strictly} convex functions that are at least as strict as logistic loss. The minimizers of these functions coincide with those of the minimum norm solution wherever possible. The strict convexity of the derived function can be extended to finetune state-of-the-art models and applications. In empirical experimental analysis, we apply our proposed rooted logistic objective to multiple deep models, e.g., fully-connected neural networks and transformers, on various of classification benchmarks. Our results illustrate that training with rooted loss function is converged faster and gains performance improvements. Furthermore, we illustrate applications of our novel rooted loss function in generative modeling based downstream applications, such as finetuning StyleGAN model with the rooted loss. The code implementing our losses and models can be found here for open source software development purposes: https://anonymous.4open.science/r/rooted_loss.

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios $\in (0,1]$, and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

Score-based models have recently been introduced as a richer framework to model distributions in high dimensions and are generally more suitable for generative tasks. In score-based models, a generative task is formulated using a parametric model (such as a neural network) to directly learn the gradient of such high dimensional distributions, instead of the density functions themselves, as is done traditionally. From the mathematical point of view, such gradient information can be utilized in reverse by stochastic sampling to generate diverse samples. However, from a computational perspective, existing score-based models can be efficiently trained only if the forward or the corruption process can be computed in closed form. By using the relationship between the process and layers in a feed-forward network, we derive a backpropagation-based procedure which we call Intermediate Generator Optimization to utilize intermediate iterates of the process with negligible computational overhead. The main advantage of IGO is that it can be incorporated into any standard autoencoder pipeline for the generative task. We analyze the sample complexity properties of IGO to solve downstream tasks like Generative PCA. We show applications of the IGO on two dense predictive tasks viz., image extrapolation, and point cloud denoising. Our experiments indicate that obtaining an ensemble of generators for various time points is possible using first-order methods.