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1. Adversarially trained neural representations may already be as robust as corresponding biological neural representations

   Guo, Chong ; Lee, Michael J. ; Leclerc, Guillaume ; Dapello, Joel ; Rao, Yug ; Madry, Aleksander ; DiCarlo, James J. ( January 2022 , Proceedings of the 38th International Conference on Machine Learning)
2. Representation via Representations: Domain Generalization via Adversarially Learned Invariant Representations

   Deng, Zhun ; Ding, Frances ; Dwork, Cynthia ; Hong, Rachel ; Parmigiani, Giovanni ; Patil, Prasad ; Sur, Pragya ( June 2020 , ArXivorg)

   We investigate the power of censoring techniques, first developed for learning {\em fair representations}, to address domain generalization. We examine {\em adversarial} censoring techniques for learning invariant representations from multiple "studies" (or domains), where each study is drawn according to a distribution on domains. The mapping is used at test time to classify instances from a new domain. In many contexts, such as medical forecasting, domain generalization from studies in populous areas (where data are plentiful), to geographically remote populations (for which no training data exist) provides fairness of a different flavor, not anticipated in previous work on algorithmic fairness. We study an adversarial loss function for k domains and precisely characterize its limiting behavior as k grows, formalizing and proving the intuition, backed by experiments, that observing data from a larger number of domains helps. The limiting results are accompanied by non-asymptotic learning-theoretic bounds. Furthermore, we obtain sufficient conditions for good worst-case prediction performance of our algorithm on previously unseen domains. Finally, we decompose our mappings into two components and provide a complete characterization of invariance in terms of this decomposition. To our knowledge, our results provide the first formal guarantees of these kinds for adversarial invariant domain generalization. 

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3. Generically free representations I: Large representations

   https://doi.org/doi.org/10.2140/ant.2020.14.1577  

   Garibaldi, S. ; Guralnick, R. ( January 2020 , Algebra and number theory)

   This paper concerns a faithful representation V of a simple linear algebraic group G. Under mild assumptions, we show that if V is large enough, then the Lie algebra of G acts generically freely on V. That is, the stabilizer in Lie.G/ of a generic vector in V is zero. The bound on dim V grows like the square of the rank and holds with only mild hypotheses on the characteristic of the underlying field. The proof relies on results on generation of Lie algebras by conjugates of an element that may be of independent interest. We use the bound in subsequent works to determine which irreducible faithful representations are generically free, with no hypothesis on the characteristic of the field. This in turn has applications to the question of which representations have a stabilizer in general position. 

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4. GENERICALLY FREE REPRESENTATIONS II: IRREDUCIBLE REPRESENTATIONS

   https://doi.org/10.1007/s00031-020-09591-3  

   Garibaldi, S. ; Guralnick, R. ( January 2020 , Transformation groups)

   We determine which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose stabilizer in Lie(G) is zero. This relies on bounds on dim V obtained in prior work (part I), which reduce the problem to a finite number of possibilities for G and highest weights for V , but still infinitely many characteristics. The remaining cases are handled individually, some by computer calculation. These results were previously known for fields of characteristic zero, although new phenomena appear in prime characteristic; we provide a shorter proof that gives the result with very mild hypotheses on the characteristic. (The few characteristics not treated here are settled in part III.) These results are related to questions about invariants and the existence of a stabilizer in general position. 

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5. Learning V1 simple cells with vector representations of local contents and matrix representations of local motions.

   https://doi.org/10.1609/aaai.v36i6.20622  

   Gao, R. ; Xie, J. ; Huang, S. ; Ren, Y. ; Zhu, S.-C. ; Wu, Y. N. ( January 2022 , The Thirty-Sixth AAAI Conference on Artificial Intelligence (AAAI) 2022.)

   This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of local contents of images and (2) the matrix representations of local pixel displacements caused by the relative motions between the agent and the objects in the 3D scene. When the image frame undergoes changes due to local pixel displacements, the vectors are multiplied by the matrices that represent the local displacements. Thus the vector representation is equivariant as it varies according to the local displacements. Our experiments show that our model can learn Gabor-like filter pairs of quadrature phases. The profiles of the learned filters match those of simple cells in Macaque V1. Moreover, we demonstrate that the model can learn to infer local motions in either a supervised or unsupervised manner. With such a simple model, we achieve competitive results on optical flow estimation. 

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