Deep-Learning the Landscape

Machine learning has played an important role in the analysis of high-energy physics data for decades. The emergence of deep learning in 2012 allowed for machine learning tools which could adeptly handle higher-dimensional and more complex problems than previously feasible. This review is aimed at the reader who is familiar with high energy physics but not machine learning. The connections between machine learning and high energy physics data analysis are explored, followed b...

Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification accuracy. In this paper we focus on deriving good initial weights by modeling the error function of a deep neural network as a high-dimensional landscape. We observe that due to the inherent complexity in its algebraic structure, such an error...

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to arrive at accurate and predictive models. It is hitherto unknown why are deep neural networks easily optimizable. We analyze the energy landscape of a spin glass model of deep neural networks using random matrix theory and algebraic geometry. ...

Deep neural networks exhibit a fascinating spectrum of phenomena ranging from predictable scaling laws to the unpredictable emergence of new capabilities as a function of training time, dataset size and network size. Analysis of these phenomena has revealed the existence of concepts and algorithms encoded within the learned representations of these networks. While significant strides have been made in explaining observed phenomena separately, a unified framework for understan...

In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and error than on theory. While still far behind the application forefront, the theoretical study of DNNs has recently made important advancements in analyzing the highly over-parameterized regime where some exact results have been obtained. Leve...

We revisit the question of predicting both Hodge numbers $h^{1,1}$ and $h^{2,1}$ of complete intersection Calabi-Yau (CICY) 3-folds using machine learning (ML), considering both the old and new datasets built respectively by Candelas-Dale-Lutken-Schimmrigk / Green-H\"ubsch-Lutken and by Anderson-Gao-Gray-Lee. In real world applications, implementing a ML system rarely reduces to feed the brute data to the algorithm. Instead, the typical workflow starts with an exploratory dat...

We present a statistical approach for the discovery of relationships between mathematical entities that is based on linear regression and deep learning with fully connected artificial neural networks. The strategy is applied to computational knot data and empirical connections between combinatorial and hyperbolic knot invariants are revealed.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the pro...

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as natural language processing and computer vision, largely attributed to deep learning, a special class of machine learning models. Deep learning arguably surpasses traditional approaches by learning the relevant features from raw data through a s...

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly modeling the interactions between sets of parameters and the overall quality of the solutions discovered. We demonstrate a novel method, based on learning deep networks, to model the global landscapes of optimization problems. To represent the ...