Dumb question: Can inference be done in a reverse pass? Outputs predicting inputs?

Strictly speaking: no. The "forward pass" terminology does not imply that there exists a "reverse pass" that does the same kind of computation. Rather, it's describing two different kinds of computation, and the direction they occur in.

The forward pass is propagating from inputs to outputs, computing the thing the model was trained for. The reverse/backwards pass is propagating from outputs back to inputs, but it's calculating the gradients of parameters for training (rougly: how much changing each parameter in isolation affects the output, and whether it makes the output closer to the desired training output). The result of the "reverse pass" isn't a set of inputs, but a set of annotations on the model's parameters that guide their adjustment.

The computations of the forward pass are not trivially reversible (e.g. they include additions, which destroys information about the operand values). As a sibling thread points out, you can still probabilistically explore what inputs _could_ produce a given output, and get some information back that way, but it's a lossy process.

And of course, you could train a "reverse" model, one that predicts the prefix of a sequence given a suffix (trivially: it's the same suffix prediction problem, but you train it on reversed sequences). But that would be a separate model trained from scratch on that task, and in that model the prefix prediction would be its forward pass.

Not as trivially as the forwards direction, unsurprisingly information is lost, but better than you might expect. See for example https://arxiv.org/pdf/2405.15012

Sounds like a great premise for a sci-fi short story.