{"id":6088,"global_id":"www.ibs.re.kr\/bimag?id=6088","global_id_lineage":["www.ibs.re.kr\/bimag?id=6088"],"author":"3","status":"publish","date":"2022-06-13 07:00:00","date_utc":"2022-05-29 11:44:41","modified":"2022-05-29 20:46:27","modified_utc":"2022-05-29 11:46:27","url":"https:\/\/www.ibs.re.kr\/bimag\/event\/2022-06-13-sem\/","rest_url":"https:\/\/www.ibs.re.kr\/bimag\/wp-json\/tribe\/events\/v1\/events\/6088","title":"Dynamical System Perspective for Machine Learning","description":"
Abstract: The connection between deep neural networks and ordinary differential equations (ODEs) is an active field of research in machine learning. In this talk, we view the hidden states of a neural network as a continuous object governed by a dynamical system. The underlying vector field is written using a dictionary representation motivated by the equation discovery method. Within this framework, we develop models for two particular machine learning tasks: time-series classification and dimension reduction. We train the parameters in the models by minimizing a loss, which is defined using the solution to the governing ODE. To attain a regular vector field, we introduce a regularization term measuring the mean total kinetic energy of the flow, which is motivated by optimal transportation theory. We solve the optimization problem using a gradient-based method where the gradients are computed via the adjoint method from optimal control theory. Through various experiments on synthetic and real-world datasets, we demonstrate the performance of the proposed models. We also interpret the learned models by visualizing the phase plots of the underlying vector field and solution trajectories.\u00a0\u00a0<\/span><\/div>\n

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