Parameter-efficient fine-tuning (PEFT) has emerged as a new paradigm for cost-efficient fine-tuning of large language models (LLMs), with low-rank adaptation (LoRA) being a widely adopted choice. However, fine-tuned LLMs often become overconfident especially when fine-tuned on small datasets. Bayesian methods, with their inherent ability to estimate uncertainty, serve as potent tools to mitigate overconfidence and enhance calibration. In this work, we introduce Laplace-LoRA, a straightforward yet effective Bayesian method, which applies the Laplace approximation to the LoRA parameters and, considerably boosts the calibration of fine-tuned LLMs.

Instruction tuning plays a crucial role in shaping the outputs of language models (LMs) to desired styles. In this work, we propose a simple yet effective method, Instruction Modelling (IM), which trains LMs by applying a loss function to the instruction and prompt part rather than solely to the output part. Through experiments across 21 diverse benchmarks, we show that, in many scenarios, IM can effectively improve the LM performance on both NLP tasks (*e.g.,* MMLU, TruthfulQA, and HumanEval) and open-ended generation benchmarks (*e.g.,* MT-Bench and AlpacaEval). Remarkably, in the most advantageous case, IM boosts model performance on AlpacaEval 1.0 by over 100%. We identify two key factors influencing the effectiveness of IM: (1) The ratio between instruction length and output length in the training data; and (2) The number of training examples. We observe that IM is especially beneficial when trained on datasets with lengthy instructions paired with brief outputs, or under the Superficial Alignment Hypothesis (SAH) where a small amount of training examples are used for instruction tuning. Further analysis substantiates our hypothesis that our improvement can be attributed to reduced overfitting to instruction tuning datasets. It is worth noting that we are not proposing \ours as a replacement for the current instruction tuning process. Instead, our work aims to provide practical guidance for instruction tuning LMs, especially in low-resource scenarios. Our code is available at https://github.com/ZhengxiangShi/InstructionModelling.

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

We define deep kernel processes in which positive definite Gram matrices are progressively transformed by nonlinear kernel functions and by sampling from (inverse) Wishart distributions. Remarkably, we find that deep Gaussian processes (DGPs), Bayesian neural networks (BNNs), infinite BNNs, and infinite BNNs with bottlenecks can all be written as deep kernel processes. For DGPs the equivalence arises because the Gram matrix formed by the inner product of features is Wishart distributed, and as we show, standard isotropic kernels can be written entirely in terms of this Gram matrix — we do not need knowledge of the underlying features. We define a tractable deep kernel process, the deep inverse Wishart process, and give a doubly-stochastic inducing-point variational inference scheme that operates on the Gram matrices, not on the features, as in DGPs. We show that the deep inverse Wishart process gives superior performance to DGPs and infinite BNNs on fully-connected baselines.