> "Faith and Fate: Limits of Transformers on Compositionality" - We investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that Transformers solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills.
Or recognize that you're not confident in the answer and throw something else and see if it sticks.
Here's an example while learning linear algebra where I tried to throw it off:
I say> So I'll say A_{M x N} to mean a matrix of size M x N. Similarly, I'll also say x_{M x 1} to mean a vector of a certain length. The result of A_{M x N} x_{N x 1} is a linear combination of the columns in A. A has N columns. The result is a M x 1 matrix (or vector) in M dimensional space. Please be very brief, only confirming whether I am correct or incorrect until I explicitly ask for more details.
GPT4 says> Yes, your understanding is correct. The product of an M x N matrix A and an N x 1 vector x is indeed an M x 1 vector, and it is a linear combination of the columns of A. <end quote>
But then I try to trick it, just for fun, and I very subtly change my prompt. See if you can spot the difference.
I say> So I'll say A_{M x N} to mean a matrix of size M x N. Similarly, I'll also say x_{M x 1} to mean a vector of a certain length. The result of A_{M x N} x_{N x 1} is a linear combination of the columns in A. A has N columns. The result is a N x 1 matrix (or vector) in N dimensional space. Please be very brief, only confirming whether I am correct or incorrect until I explicitly ask for more details.
GPT says> Almost correct. The result of A_{M x N} x_{N x 1} is actually an M x 1 vector (or matrix), not N x 1. The resulting vector lives in the column space of A, which is a subspace of R^M, not R^N. <end quote>
I mentioned elsewhere that I use GPT4 as a math tutor. It is quick to call out my mistakes. It is more than a smiling mirror.