Large language models are usually fine-tuned to align with human preferences. However, fine-tuning a large language model can be challenging. In this work, we introduceweak-to-strong search, framing the alignment of a large language model as a test-time greedy search to maximize the log-probability difference between small tuned and untuned models while sampling from the frozen large model. This method serves both as (1) a compute-efficient model up-scaling strategy that avoids directly tuning the large model and as (2) an instance of weak-to-strong generalization thatenhances astrong model with weak test-time guidance.

The quadratic computational and memory complexities of the Transformer'sattention mechanism have limited its scalability for modeling long sequences.

These molecular properties were calculated using a hybrid quantum simulation (Gaussian 09) at the B3LYP/6-31G(2df,p) level of theory. In this study, we created a subset of the QM9 dataset with a limited number of atoms, M 14, per molecule, which we refer to as the "QM9under14atoms" dataset in the main text. As the learning/predicting targets, we selected three kinds of energy properties: atomization energy at 0 K, zero point vibrational energy, and enthalpy at 298.15 K. E RN is the bias vector in layer ℓ. The LCAO considers the normalization for the coefficients in Eq. (6) in the main text. Additionally, the normalization term in Eq. (7) in the main text is calculated as follows: Z(qn,ζn)=

However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT).