Recent studies on deep forests have shown that deep learning frameworks can be built on non-differentiable modules without a backpropagation training process. However, the feature representations of deep forests only consist of predicted class probabilities. The information these class probabilities deliver is very limited and lacks diversity, especially when the number of output labels is far less than the number of input features. Besides, the prediction-based representations require us to save multiple layers of random forests to use them during testing, which is high-memory and high-time cost. In this paper, we propose a novel deep forest model that utilizes high-order interactions of input features to generate more informative and diverse feature representations. Specifically, we design a generalized version of Random Intersection Trees (gRIT) to discover stable high-order interactions and apply Activated Linear Combination (ALC) to transform them into hierarchical distributed representations. These interaction-based representations obviate the need to store random forests in the front layers, thus greatly improving the computational efficiency. Our experiments show that our method achieves highly competitive predictive performance with significantly reduced time and memory cost.