Kyle Roth

This post was created as an assignment in Bang Liu’s IFT6289 course in winter 2022. The structure of the post follows the structure of the assignment: summarization followed by my own comments. The authors create a novel system for combining an LM and a knowledge graph by performing reasoning over a joint graph produced by the LM and the KG, thus solving the problem of irrelevant entities appearing in the knowledge graph and unifying the representations across the LM and KG.

This post was created as an assignment in Bang Liu’s IFT6289 course in winter 2022. The structure of the post follows the structure of the assignment: summarization followed by my own comments. To summarize, the authors create a unifying framework for describing message-passing neural networks, which they apply to the problem of predicting the structural properties of chemical compounds in the QM9 dataset. paper summarization permalink The authors first demonstrate that many of the recent works applying neural nets to this problem can fit into a message-passing neural network (MPNN) framework. Under the MPNN framework, at each time step \(t\) a message is computed for each vertex by summing the output of a learned function \(M_t\) over the vertex and all edges and vertices connected to it. Then the next state for each vertex is a learned function \(U_t\) of the previous state and the message. Finally, the “readout” function \(R\) is applied to all the vertices to compute the result.

This was a paper we presented about in Irina Rish’s neural scaling laws course (IFT6167) in winter 2022. You can view the slides we used here, and the recording here.

The unsurprising result here is that few-shot performance scales predictably with pre-training dataset size under traditional fine-tuning, matching network, and prototypical network approaches. The interesting result is that the exponents of these three approaches were substantially different (see Table 1 in the paper), which says to me that the few-shot inference approach matters a lot. The surprising result was that while more training on the “non-natural” Omniglot dataset did not improve few-shot accuracy on other datasets, training on “natural” datasets did improve accuracy on few-shot Omniglot.

The big idea here is to use the geometric mean instead of the arithmetic mean across samples in the batch when computing the gradient for SGD. This overcomes the situation where averaging produces optima that are not actually optimal for any individual samples, as demonstrated in their toy example below: In practice, the method the authors test is not exactly the geometric mean for numerical and performance reasons, but effectively accomplishes the same thing by avoiding optima that are “inconsistent” (meaning that gradients from relatively few samples actually point in that direction).