When constructing random forests, it is of prime importance to ensure high accuracy and low correlation of individual tree classifiers for good performance. Nevertheless, it is typically difficult for existing random forest methods to strike a good balance between these conflicting factors. In this work, we propose a generalized convolutional forest networks to learn a feature space to maximize the strength of individual tree classifiers while minimizing the respective correlation. The feature space is iteratively constructed by a probabilistic triplet sampling method based on the distribution obtained from the splits of the random forest. The sampling process is designed to pull the data of the same label together for higher strength and push away the data frequently falling to the same leaf nodes. We perform extensive experiments on five image classification and two domain generalization datasets with ResNet-18, ResNet-50 and DenseNet-161 backbone networks. Experimental results show that the proposed algorithm performs favorably against state-of-the-art methods.
The paper proposes a scheme to learn representations and a random
forest model in a closely coupled manner, where the representations
are learned to simultaneously improve the predictive performance of
the individual trees in the random forest and reduce the correlation
between these trees. This is achieved via a novel triplet sampling
scheme where the positive samples are used to improve the predictive
performance of the individual trees, while the negative samples are
used to reduce the correlation between the trees. The empirical
results indicate the improvement of the proposed scheme over random
forests learned over the original representations across various
datasets. 
The manuscript is well presented and I am leaning towards accept, one
major issue with this manuscript is the number of pages which crosses
the 8 page recommended limit in the ICLR CfP. Given that higher
standard, I feel that there are multiple minor issues which should be
addressed. 
- It is not clear why the proposed scheme is especially well suited
  for "domain generalization" and "visual recognition" and not for
  general supervised classification tasks (like those on CIFAR, SVHN,
  etc). This needs to be clarified.
- The theoretical results for random forest rely on the independence
  of the individual trees. Given that the trees in the random forest
  are no longer independent in the proposed scheme, the upper bound in
  Equation (1) may no longer be valid. While this does not affect the
  empirical performance, it might be good to discuss the theoretical
  implications of the proposed scheme.
- It is not clear why the curves for the canonical features in Figure
  3 not improving with the number of iterations (which corresponds to
  number of trees to the best of my understanding). The results in
  Table 1 do indicate improvement in the performance with canonical
  features, putting Figure 3 and Table 1 at odds.
Minor:
- The individual trees in a random forest are supposed to have low
  bias but high variance, and the heterogeneity between the trees is
  supposed to squash the variance with the bagging. The introduction
  mentions that the individual trees in the forest are "less
  biased". Maybe this is because of our different definitions of bias
  but any clarification here would be helpful.