Transformers can optimally learn regression mixture models
Reese Pathak, Rajat Sen, Weihao Kong, Abhimanyu Das
TL;DR
This paper demonstrates that transformers can effectively learn and implement optimal predictors for mixture of regressions, achieving low error and robustness in a sample-efficient manner, supported by theoretical proofs.
Contribution
It shows that transformers can learn the decision-theoretic optimal predictor for mixture of regressions, combining empirical results with constructive theoretical proof.
Findings
Transformers achieve low mean-squared error on mixture regression data.
Transformers' predictions are close to the optimal predictor.
Transformers are sample-efficient and robust to distribution shifts.
Abstract
Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close…
Peer Reviews
Decision·ICLR 2024 poster
* The idea of the paper is original and novel. * The paper is written well. The illustration of the proof adds to the clarity of it and gives a good intuition. * In general, the experiment section is good (although I think it misses some things; but more on that in the next section). * Code was provided and the results seem to be reproducible.
* I am not convinced about the significance of this work. To clarify that, I would like the authors to address the following questions, how and when can one use the observation in the paper? In the introduction, federated learning is mentioned as a possible application. But, federated learning systems do not use linear models and if they do the number of components is known in advance (which is arguably the biggest advantage of the proposed viewpoint in the paper). I acknowledge though that this
It is a simply presented, well-articulated problem and solution. The presentation is clear and more or less self-contained.
I'm not sure that the new work really address limitations in the existing literature. The main motivation is that existing methods are potentially brittle and that their theoretical guarantees do not extend to the model misspecification setting. It isn't clear that this work really demonstrates much of an improvement in that regard. As a result, it isn't clear to me what this approach really offers (other than perhaps simplicity?). It too does not come with any guarantees more generally -- o
The paper makes an interesting contribution in the recently popular literature on using transformers for in-context learning regression models. The posterior mean in eq.(4) is particularly interesting as a desired goal, as it requires a more complex transformer architecture than related papers, which combines both in-context algorithmic operations, and some "knowledge" from the data distribution, in the form of the $w_i^*$ vectors. The experiments seem to give promising evidence that this targ
Two points would significantly strengthen the paper: * while empirical results suggest the transformer might be related to the posterior mean, it would be good to have some interpretability results to assess whether this is true in practice, and if your construction in Theorem 1 is practically relevant: is there any evidence that the blocks shown in Figure 1 are actually being learned by the pre-trained transformer? Where are the $w_i^*$ being stored in the weights? Is it necessary to have at l
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Taxonomy
TopicsGenerative Adversarial Networks and Image Synthesis · Neural Networks and Applications · Bayesian Methods and Mixture Models
MethodsSparse Evolutionary Training