Timezone: »
Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed as the cardinality of the sets under consideration increases. However, we demonstrate that the analysis leading to this conjecture requires mappings which are highly discontinuous and argue that this is only of limited practical use. Motivated by this observation, we prove that an implementation of this model via continuous mappings (as provided by e.g. neural networks or Gaussian processes) actually imposes a constraint on the dimensionality of the latent space. Practical universal function representation for set inputs can only be achieved with a latent dimension at least the size of the maximum number of input elements.
Author Information
Ed Wagstaff (University of Oxford)
Fabian Fuchs (Oxford Robotics Insitute)
Martin Engelcke (University of Oxford)
Ingmar Posner (University of Oxford)
Michael A Osborne (U Oxford)
Related Events (a corresponding poster, oral, or spotlight)
-
2019 Oral: On the Limitations of Representing Functions on Sets »
Thu Jun 13th 07:15 -- 07:20 PM Room Grand Ballroom
More from the Same Authors
-
2020 Poster: Knowing The What But Not The Where in Bayesian Optimization »
Vu Nguyen · Michael A Osborne -
2020 Poster: Bayesian Optimisation over Multiple Continuous and Categorical Inputs »
Binxin Ru · Ahsan Alvi · Vu Nguyen · Michael A Osborne · Stephen Roberts -
2019 Workshop: Workshop on AI for autonomous driving »
Anna Choromanska · Larry Jackel · Li Erran Li · Juan Carlos Niebles · Adrien Gaidon · Wei-Lun Chao · Ingmar Posner · Wei-Lun (Harry) Chao -
2019 Poster: Automated Model Selection with Bayesian Quadrature »
Henry Chai · Jean-Francois Ton · Michael A Osborne · Roman Garnett -
2019 Poster: AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs »
Gabriele Abbati · Philippe Wenk · Michael A Osborne · Andreas Krause · Bernhard Schölkopf · Stefan Bauer -
2019 Poster: Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation »
Ahsan Alvi · Binxin Ru · Jan-Peter Calliess · Stephen Roberts · Michael A Osborne -
2019 Oral: Automated Model Selection with Bayesian Quadrature »
Henry Chai · Jean-Francois Ton · Michael A Osborne · Roman Garnett -
2019 Oral: AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs »
Gabriele Abbati · Philippe Wenk · Michael A Osborne · Andreas Krause · Bernhard Schölkopf · Stefan Bauer -
2019 Oral: Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation »
Ahsan Alvi · Binxin Ru · Jan-Peter Calliess · Stephen Roberts · Michael A Osborne -
2019 Poster: Fingerprint Policy Optimisation for Robust Reinforcement Learning »
Supratik Paul · Michael A Osborne · Shimon Whiteson -
2019 Oral: Fingerprint Policy Optimisation for Robust Reinforcement Learning »
Supratik Paul · Michael A Osborne · Shimon Whiteson -
2018 Poster: Fast Information-theoretic Bayesian Optimisation »
Binxin Ru · Michael A Osborne · Mark Mcleod · Diego Granziol -
2018 Poster: Optimization, fast and slow: optimally switching between local and Bayesian optimization »
Mark McLeod · Stephen Roberts · Michael A Osborne -
2018 Oral: Optimization, fast and slow: optimally switching between local and Bayesian optimization »
Mark McLeod · Stephen Roberts · Michael A Osborne -
2018 Oral: Fast Information-theoretic Bayesian Optimisation »
Binxin Ru · Michael A Osborne · Mark Mcleod · Diego Granziol -
2018 Poster: TACO: Learning Task Decomposition via Temporal Alignment for Control »
Kyriacos Shiarlis · Markus Wulfmeier · Sasha Salter · Shimon Whiteson · Ingmar Posner -
2018 Oral: TACO: Learning Task Decomposition via Temporal Alignment for Control »
Kyriacos Shiarlis · Markus Wulfmeier · Sasha Salter · Shimon Whiteson · Ingmar Posner