Combinatorial optimization problems are prevalent across a wide variety of domains. These problems are often nuanced, their optimal solutions might not be efficiently obtainable, and they may require lots of time and compute resources to solve (they are NP-hard). It follows that the best course of action for solving these problems is to use general optimization algorithm paradigms to quickly and easily develop algorithms that are customized to these problems and can produce good solutions in a reasonable amount of time. In this paper, we present optimizn, a Python library for developing customized optimization algorithms under general optimization algorithm paradigms (simulated annealing, branch and bound). Additionally, optimizn offers continuous training, with which users can run their algorithms on a regular cadence, retain the salient aspects of previous runs, and use them in subsequent runs to potentially produce solutions that get closer and closer to optimality. An earlier version of this paper was peer reviewed and published internally at Microsoft.

A text generation model is a machine learning model that uses neural networks, especially transformers architecture to generate contextually relevant text based on linguistic patterns learned from extensive corpora. The models are trained on a huge amount of textual data so that they can model and learn complex concepts of any language like its grammar, vocabulary, phrases, and styles. Text generation models can increase the productivity of humans in their current business processes. These models are already automating the process of content creation across industries for the generation of reports, summaries, and emails among others. These models are also allowing for a greater level of personalization in communications between businesses and their customers.

We present a novel framework for generating photorealistic Editing capabilities for 3D-aware GANs have also been 3D human head and subsequently manipulating achieved through latent space auto-decoding, altering a 2D and reposing them with remarkable flexibility. The proposed semantic segmentation [62, 63], or modifying the underlying approach leverages an implicit function representation geometry scaffold [64]. However, generation and editing of 3D human heads, employing 3D Gaussians anchored quality tends to be unstable and less diversified due to on a parametric face model. To enhance representational the inherent limitation of GANs, and detailed-level editing capabilities and encode spatial information, we is not well supported due to feature entanglement in the embed a lightweight tri-plane payload within each Gaussian compact latent space or tri-plane representations.

Abstract--Azure (the cloud service provided by Microsoft) is composed of physical computing units which are called nodes. These nodes are controlled by a software component called Fabric Controller (FC), which can consider the nodes to be in one of many different states such as Ready, Unhealthy, Booting, etc. Some of these states correspond to a node being unresponsive to FCs requests. When a node goes unresponsive for more than a set threshold, FC intervenes and reboots the node. We minimized the downtime caused by the intervention threshold when a node switches to Unhealthy state by fitting various heavy-tail probability distributions. We consider using features of the node to customize the organic recovery model to the individual nodes that go unhealthy. This regression approach allows us to use information about the node like hardware, software versions, historical performance indicators, etc. to inform the organic recovery model and hence the optimal threshold. In another direction, we consider generalizing this to an arbitrary number of thresholds within the node state machine (or Markov chain). When the states become intertwined in ways that different thresholds start affecting each other, we cant simply optimize each of them in isolation. For best results, we must consider this as an optimization problem in many variables (the number of thresholds). We no longer have a nice closed form solution for this more complex problem like we did with one threshold, but we can still use numerical techniques (gradient descent) to solve it. Section 2 will briefly go over the architecture of Azure and the data we use for modeling. Sections 3 and 4 will formulate the problem mathematically. In section 5, we will discuss extending the model to multiple thresholds and in section 6, we will explore ways to use regression, so we can leverage features to customize our recovery models.