Branching Program Lower Bounds

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Two Topics: I am proposing two quite independent topics: Branching program lower bounds and machine learning. I have 30 years of experience and a great deal of success in the first and the last six months I have taken a few courses and read a few books in the second. In today's job market, students tend to be drawn to Machine Learning rather than Logic (such as Lower Bounds).There is also a large job market for HQP with Machine Learning expertise. In addition to already existing expertise in AI and Deep Learning, York U is starting a new program dedicated to Machine Learning to address this need. My plan is to include training students in this discipline in the future. Lower Bounds in Branching Programs: For both practical and theoretical reasons, we would like to know the minimum amount of time (or space) needed to solve a given computational problem on an input of a given size. An upper bound provides an algorithm that achieves some time bound. A lower bound proves that no algorithm correctly solves the problem faster no matter how clever. Proving lower bounds on general models of computation (eg. in JAVA or a Turing Machine) is beyond our reach. For this reason, researchers often prove lower bounds on weaker modes of computation. The most powerful model of computation measuring the amount of space used by an algorithm is branching programs. We will continue in this important area of fundamental research in order to understand more about the limits of computation. Machine Learning: Computers can now drive cars and find cancer in x-rays. For better or worse, this will change the world (and the job market). Strangely, designing these algorithms is not done by telling the computer what to do or even by understanding what the computer does. The computers learn themselves from lots and lots of data and lots of trial and error. This learning process is more analogous to how brains evolved over billions of years of learning. The machine itself is a neural network which models both the brain circuits, which are great for computing. The only difference with neural networks is that what they compute is determined by weights and small changes in these weights give you small changes in the result of the computation. The process for finding an optimal setting of these weights is analogous to finding the bottom of a valley. If a machine can give the correct answers on randomly chosen training data without simply memorizing, then we can prove that with high probability the same machine will also work well on never seen before instances.