Generalization in Large Models
Yes— large models can achieve strong generalization , and PAC Bayes helps explain how . In the paper, the authors argue that generalization phenomena seen in deep learning (including benign overfitting and double desc...
Yes— large models can achieve strong generalization , and PAC Bayes helps explain how . In the paper, the authors argue that generalization phenomena seen in deep learning (including benign overfitting and double descent) can be “rigorously characterized… using long standing generalization frameworks such as PAC Bayes” .[:cite[1]{ln=4}] They also state that these frameworks show generalization behavior that is not distinct/mysterious for neural networks.[:cite[2]{ln=1}] Why PAC Bayes matters for large model generalization The paper frames PAC Bayes/countable hypothesis style bounds in terms of empirical risk plus compressibility : Generalization is upper bounded by empirical risk and “compressibility” of a hypothesis.[:cite[3]{ln=1}] “Compressibility” can be linked to Kolmogorov complexity and further upper bounded by a model’s filesize .[:cite[3]{ln=2}] The authors conclude: “Large models fit the data well, and can be effectively compressed to small filesizes.” [:cite[3]{ln=3}] Importantly, these bounds do not penalize the model for having a hypothesis class that can fit noise, and thus “describe benign overfitting, double descent, and overparametrization.” [:cite[3]{ln=4}] The mechanism: soft inductive biases (preference, not hard restriction) They propose that large hypothesis spaces work because of soft preference toward simpler, consistent solutions: With no preference among equally fitting solutions, training “will often lead to overfit solutions that generalize poorly.”[:cite[4]{ln=3}] With soft inductive biases , training is guided toward solutions that generalize well, even though the hypothesis space is flexible.[:cite[4]{ln=4}] They explicitly connect this “preference for certain solutions over others” to PAC Bayes style thinking: soft inductive biases can be implemented via mechanisms like Bayesian priors and regularization.[:cite[5]{ln=1}] So, from this perspective, large models generalize strongly when they are biased toward compressible/simple solutions consistent with data , and PAC Bayes provides formal bounds that incorporate that compressibility rather than punishing raw hypothesis space size.[:cite[3]{ln=1}], [:cite[3]{ln=3}], [:cite[3]{ln=4}], [:cite[4]{ln=4}]