We provide supplementary materials for the submission of Self-Weighted Contrastive Learning among Multiple Views for Mitigating Representation Degeneration. Specifically, Appendix A (Page1) shows all theoretical proofs and complexity analysis of SEM; Appendix B (Page-7) includes the settings in experiments; Appendix C (Page-8) lists additional experimental results and provides more experimental analysis, which are not shown in the paper due to space; Appendix D (Page-10) discusses the limitations and future work of this paper. The code implementation, trained models, and datasets used in our method are provided in https://github.com/SubmissionsIn/SEM. I(Xv;Hv), (8) where Wm,n > 0 as two views (v {m,n}) are with positive class mutual information. Therefore, if Hv is the tv-th layer's features (i.e., Hv(tv) act as the regularized hidden features), we have I(S;Zv) I(S;Xv) This design aims at separately maintaining different views' discriminative information by {Hv}Vv=1 and exploring their common semantic information by {Zv}Vv=1.

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dale's Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dale's Law is generally absent from RNNs because simply partitioning a standard network's units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dale's ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dale's Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dale's Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dale's ANNs. However, here we show the spectral properties of the recurrent weight matrix at initialisation are more impactful on network performance than sign constraints. We find that simple EI partitioning results in a singular value distribution that is multimodal and dispersed, whereas standard RNNs have an unimodal, more clustered singular value distribution, as do recurrent Dale's ANNs. We also show that the spectral properties and performance of partitioned EI networks are worse for small networks with fewer I units, and we present normalised SVD entropy as a measure of spectrum pathology that correlates with performance.

Location estimation is one of the most basic questions in parametric statistics. Suppose we have a known distribution density f, and we get ni.i.d.

Knowing what you know: valid and validated631 confidence sets in multiclass and multilabel prediction.