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David Balduzzi: dbalduzzi at gmail                               CV
I'm an applied mathematician working on theoretical neuroscience in Bernhard Schölkopf's department of Empirical Inference at the Max Planck Institute for Intelligent Systems. The focus of my research is distributed learning. Specifically: combining information theory, machine learning and techniques from algebraic geometry to better understand neuronal dynamics and synaptic plasticity.

My PhD was in algebraic geometry and representation theory with Victor Ginzburg at the University of Chicago. My thesis was on the Hamiltonian geometry of the moduli space of G-bundles on Riemann surfaces. After that, I was a postdoc in the Dept of Psychiatry at the University of Wisconsin-Madison with Giulio Tononi, where I developed tools for analyzing how information is differentiated and integrated in artificial neural networks.



A large fraction of my work is motivated by the following two questions:

How do neurons learn to cooperate?
The human brain contains about 100,000,000,000 neurons and 1,000,000,000,000,000 synapses. Most neurons do not interact directly with the environment but only with other neurons. All neurons "see" is patterns of activity on their 10,000 or so synapses, slices of about 0.00001% of total brain activity. All neurons do is output sequences of spikes through their single axons (each connecting to 10,000 or so other neurons), whilst having no idea how billions of other neurons reinterpret their outputs. Individual neurons are ignorant and ineffective. They do not know what their inputs mean, they do not know what they are communicating, to whom, or for what purpose, and in any case they have very little to say. How, then, can neurons possibly act in the interest of their brain?


What kind of language should inductive reasoners use to communicate?
The basis of scientific knowledge is induction: generalizing from observations. Vapnik and Chervonenkis proved necessary and sufficient conditions for consistency and fast convergence of induction via empirical risk minimization by suitably quantifying the complexity of learning algorithms, thereby laying the foundation for machine learning. However, there is more to scientific -- objective -- knowledge than generalizing from observations. According to Karl Popper, "a justification is objective if in principle it can be tested and understood by anybody". Thus, knowledge should be communicable and reproducible to count as objective. Whilst deduction and induction have been adequately formalized (Turing machines and statistical learning theory), communicability has not. The brain can be considered as a vast collection of inductive reasoners (i.e. neurons) that communicate what they learn via spikes. This suggests that the neural code may be a highly effective language for communicating generalizations.