Collisions at high-energy particle colliders are a traditionally fruitful source of exotic particle discoveries. Finding these rare exotic particles requires solving difficult signal-versus-background classification problems, hence machine learning approaches are often used for this task. Standard approaches in the past have relied on 'shallow' machine learning models that have a limited capacity to learn complex non-linear functions of the inputs, and rely on a pain-staking search through manually constructed non-linear inputs. Progress on this problem has slowed, as a variety of techniques (neural networks, boosted decision trees, support vector machines) have shown equivalent performance. Recent advances in the field of deep learning, particularly with artificial neural networks, make it possible to learn more complex functions and better discriminate between signal and background classes. Using benchmark datasets, we show that deep learning methods need no manually constructed inputs and yet improve the AUC (Area Under the ROC Curve) classification metric by as much as 8% over the best current approaches. This is a large relative improvement and demonstrates that deep learning approaches can improve the power of collider searches for exotic particles. The field of high energy physics is devoted to the study of the elementary constituents of matter. By investigating the structure of matter and the laws that govern its interactions, this field strives to discover the fundamental properties of the physical universe. The primary tools of experimental high energy physicists are modern accelerators, which collide protons and/or anti-protons to create exotic particles that occur only at extremely high energy densities. Observing these particles and measuring their properties may yield critical insights about the very nature of matter [1] . Such discoveries require powerful statistical methods, and machine learning tools play a critical role. Given the limited quantity and expensive nature of the data, improvements in analytical tools directly boost particle discovery potential. To discover a new particle, physicists must isolate a subspace of their high-dimensional data in which the hypothesis of a new particle or force gives a significantly different prediction than the null hypothesis, allowing for an effective statistical test. For this reason, the critical element of the search for new particles and forces in high-energy physics is the computation of the relative likelihood of data under different hypotheses. Often this relative likelihood function cannot be expressed analytically, so simulated collision data generated with Monte Carlo methods are used as a basis for approximation of the likelihood function. The high dimensionality of data, referred to as the feature space, makes it intractable to generate enough simulated collisions to describe the relative likelihood in the full feature space, and machine learning tools are used for dimensionality reduction. Machine learning classifiers such as neural networks provide a powerful way to solve this learning problem, essentially by estimating the probability of membership in each class. In this paper, we show that the current techniques used in high-energy physics fail to capture all of the available information, even when boosted by manuallyconstructed physics-inspired features. This effectively reduces the power of the collider to discover new particles. We demonstrate that recent developments in deep learning tools can overcome these failings, providing significant boosts even without manual assistance. The relative likelihood function is a complicated function in a high-dimensional space. While any function can theoretically be represented by a 'shallow' classifier, such as a neural network with a single hidden layer [2] , an intractable number of hidden units may be required. Circuit complexity theory tells us that deep neural networks have the potential to compute complex functions much more efficiently (fewer hidden units), but in practice they are notoriously difficult to train due to the vanishing gradient problem [3, 4] ; the adjustments to the weights in the early layers of a deep network rapidly approach zero during training. A common approach is to combine shallow classifiers with high-level features that are derived manually from the raw features. These are generally non-linear functions of the input features that capture physical insights about the data. While helpful, this approach is labor-intensive and not necessarily optimal; a robust machine learning method would obviate the need for this additional step and capture all of the available classification power directly from the raw data. Recent successes in deep learning -e.g. neural networks with multiple hidden layers -have come from alleviating the gradient diffusion problem by a combination of factors, including: 1) speeding up the stochastic gradient descent algorithm with graphics processors; 2) using much larger training sets; 3) using new learning algorithms, including randomized algorithms such as dropout [5, 6] ; and 4) pre-training the initial layers of the network with unsupervised learning methods such arXiv:1402.4735v1 [hep-ph]
al. showed that deep neural networks could improve exotic particle searches and showed that learned high-level features outperform those engineered by physicists REF .
Searching for Exotic Particles in High-Energy Physics with Deep Learning
Nature communications
Nature communications
Physics Medicine