Neural architecture search tries to shift the manual design of neural network (NN) architectures to algorithmic design. In these cases, the NN architecture itself can be viewed as data and needs to be modeled. A better modeling could help explore novel architectures automatically and open the black box of automated architecture design. To this end, this work proposes a new encoding scheme for neural architectures, the Training-Analogous Graph-based ArchiTecture Encoding Scheme (TA-GATES). TA-GATES encodes an NN architecture in a way that is analogous to its training. Extensive experiments demonstrate that the flexibility and discriminative power of TA-GATES lead to better modeling of NN architectures. We expect our methodology of explicitly modeling the NN training process to benefit broader automated deep learning systems.

Neural architecture search tries to shift the manual design of neural network (NN) architectures to algorithmic design. In these cases, the NN architecture itself can be viewed as data and needs to be modeled. A better modeling could help explore novel architectures automatically and open the black box of automated architecture design. To this end, this work proposes a new encoding scheme for neural architectures, the Training-Analogous Graph-based ArchiTecture Encoding Scheme (TA-GATES). TA-GATES encodes an NN architecture in a way that is analogous to its training.

Quantum machine learning uses principles from quantum mechanics to process data, offering potential advances in speed and performance. However, previous work has shown that these models are susceptible to attacks that manipulate input data or exploit noise in quantum circuits. Following this, various studies have explored the robustness of these models. These works focus on the robustness certification of manipulations of the quantum states. We extend this line of research by investigating the robustness against perturbations in the classical data for a general class of data encoding schemes. We show that for such schemes, the addition of suitable noise channels is equivalent to evaluating the mean value of the noiseless classifier at the smoothed data, akin to Randomized Smoothing from classical machine learning. Using our general framework, we show that suitable additions of phase-damping noise channels improve empirical and provable robustness for the considered class of encoding schemes.

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants for scalable projection-free optimization. We first propose 1-SFW, the first projection-free method that requires only one sample per iteration to update the optimization variable and yet achieves the best known complexity bounds for convex, non-convex, and monotone DR-submodular settings. Then we move forward to the distributed setting, and develop Quantized Frank-Wolfe (QFW), a general communication-efficient distributed FW framework for both convex and non-convex objective functions. We study the performance of QFW in two widely recognized settings: 1) stochastic optimization and 2) finite-sum optimization. Finally, we propose Black-Box Continuous Greedy, a derivative-free and projection-free algorithm, that maximizes a monotone continuous DR-submodular function over a bounded convex body in Euclidean space.

How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this paper, we propose Quantized Frank-Wolfe (QFW), the first projection-free and communication-efficient algorithm for solving constrained optimization problems at scale. We consider both convex and non-convex objective functions, expressed as a finite-sum or more generally a stochastic optimization problem, and provide strong theoretical guarantees on the convergence rate of QFW. This is done by proposing quantization schemes that efficiently compress gradients while controlling the variance introduced during this process. Finally, we empirically validate the efficiency of QFW in terms of communication and the quality of returned solution against natural baselines.