The Implicit Bias of Structured State Space Models Can Be Poisoned With Clean Labels

Abstract: Neural networks are powered by an implicit bias: a tendency of gradient descent to fit training data in a way that generalizes to unseen data. A recent class of neural network models gaining increasing popularity is structured state space models (SSMs), regarded as an efficient alternative to transformers. Prior work argued that the implicit bias of SSMs leads to generalization in a setting where data is generated by a low dimensional teacher. In this paper, we revisit the latter setting, and formally establish a phenomenon entirely undetected by prior work on the implicit bias of SSMs. Namely, we prove that while implicit bias leads to generalization under many choices of training data, there exist special examples whose inclusion in training completely distorts the implicit bias, to a point where generalization fails. This failure occurs despite the special training examples being labeled by the teacher, i.e. having clean labels! We empirically demonstrate the phenomenon, with SSMs trained independently and as part of non-linear neural networks. In the area of adversarial machine learning, disrupting generalization with cleanly labeled training examples is known as clean-label poisoning. Given the proliferation of SSMs, particularly in LLMs, we believe significant efforts should be invested in further delineating their susceptibility to clean-label poisoning, and in developing methods for overcoming this susceptibility.