Here's the context on both, verified against the arXiv abstracts:
Idea A's source: A Simple Neural Network Module for Relational Reasoning (Santoro et al., NeurIPS 2017)
The motivating problem: standard neural nets (CNNs, MLPs) are surprisingly bad at questions that require relating things to each other — "what shape is the object closest to the blue thing?" — even when they're great at questions about single objects ("what color is the square?").
Their fix, the Relation Network (RN), is almost embarrassingly simple, which was the selling point. You take the set of "objects" in a scene (in practice, just the cells of a CNN feature map — no explicit object detection), form every possible pair of them, run each pair (plus an embedding of the question) through a small shared MLP that outputs a "relation score" vector, sum all of those up, and decode the answer from the sum. That's it. The architecture forces the network to consider pairwise relations, which a plain CNN+MLP never quite learns to do on its own.
Results were striking for the time: superhuman, state-of-the-art performance on CLEVR (a visual question-answering benchmark built around relational questions), plus strong results on the bAbI text reasoning tasks and a physics-prediction task. They also built Sort-of-CLEVR — a deliberately simple diagnostic dataset of 2D scenes with colored squares and circles, with questions split into "relational" and "non-relational" — and showed a plain CNN+MLP handles the non-relational questions fine but fails the relational ones, while the RN aces both. That's the dataset design I'd replicate (generating our own version).
The riff: the RN's magic ingredient is that exhaustive all-pairs sum — O(n²) pair evaluations, most of which are presumably irrelevant to any given question. Nobody at the time asked how much of that is necessary. Can the network learn to pick out the ~few relevant pairs? Does forcing it to hurt accuracy, or actually help generalization by acting as a bottleneck? That's a question that would have fit right into 2018-era NeurIPS.
Idea C's source: Cognitive Psychology for Deep Neural Networks: A Shape Bias Case Study (Ritter, Barrett, Santoro & Botvinick, ICML 2017)
This one is a methods-borrowing paper. Developmental psychologists established decades ago that toddlers learning a new word ("this is a dax") assume it refers to the object's shape, not its color or texture — the "shape bias." It's a classic probe of inductive bias: given ambiguous evidence, what does the learner assume?
The authors' move: treat a trained neural network as a psych-experiment subject. They took one-shot image-classification models trained on ImageNet, showed them a novel labeled object, then asked whether the model extends that label to a shape-match or a color-match — exactly the stimuli structure used with children.
Findings: the networks showed a strong human-like shape bias — but the bias varied a lot between identically-trained models that differed only in random seed, and fluctuated over the course of training, even while classification accuracy stayed flat. The headline point: models with indistinguishable benchmark scores can have very different underlying inductive biases, and psychology-style probes reveal properties that accuracy metrics hide.
The riff would be porting that probe logic to LLMs via the API (novel-word learning in text). But as I said, "run psych experiments on LLMs" has become a busy genre since ~2022, so it's harder to stake out something that feels novel without a proper literature dig.
My recommendation stands with A — it has the cleaner "nobody asked this specific question" shape, and everything stays under our control (synthetic data, small models, CPU). But C is genuinely cheaper and faster if you'd rather burn API credits than CPU-hours. Your call.