Ontheotherhand,wefindthatstrong regularization is not necessary for learning high-quality feature representations.

In this paper, we present a convex optimization framework to compute guaranteed upper bounds on the Lipschitz constant of DNNs both accurately and efficiently.

We take integrating with a symbolic system further: we use its internal representation as input to the neural model.

Neural Information Processing Systems http://nips.cc/

NPI contributes structural biases in the form of modularity, hierarchy and recursion, which are helpful to reduce sample complexity, improve generalization and increase interpretability. AlphaZero contributes powerful neural network guided search algorithms, which we augment with recursion. AlphaNPI only assumes a hierarchical program specification with sparse rewards: 1 when the program execution satisfies the specification, and 0otherwise. This specification enables us to overcome the need for strong supervision in the form of execution traces andconsequently trainNPImodels effectivelywithreinforcement learning.

Neural Information Processing Systems http://nips.cc/

LSTMs are designed to help alleviate the issue of vanishing and exploding gradients commonly associatedwithtrainingRNNs[5].

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.