The Blessing of Dimensionality: How Near-Orthogonality in High-Dimensional Spaces Explains Temporal Portability
This paper explores how a method called PortLLM can help large language models adapt to new information over time without needing to be retrained frequently. It shows that this method works well even as the models are updated with new data.
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- 1 We aim to perform continual pretraining that updates outdated information with new temporal knowledge.
- 2 We continually pretrain Mistral on eight sections of Cosmopedia to investigate temporal portability under heterogeneous data.
- 3 Direction fine-tuning of all base model parameters is infeasible for resource-constrained developers due to LLM scale.
- 4 The update for a fully connected layer is restricted to be low-rank using learnable matrices A and B.
Introduction
The two-stage process of pretraining and fine-tuning facilitates the success and growth of large language models (LLMs). AI companies allocate massive compute budgets to pretrain large models.
Downstream developers with constrained resources often fine-tune these pretrained models.
Companies with substantial resources perform continual pretraining while smaller companies with limited resources perform downstream fine-tuning.
Companies with substantial resources perform continual pretraining while smaller companies with limited resources perform downstream fine-tuning.
Limited access to private data in domains like medicine or finance often motivates data-free methods.
Research Question
We aim to perform continual pretraining that updates outdated information with new temporal knowledge. We continually pretrain Mistral on eight sections of Cosmopedia to investigate temporal portability under heterogeneous data.
Methodology
We propose two theoretical analysis methods using a 1-D loss landscape slice and iterative relations of continual pretraining steps. These analysis methods apply to broader use cases like CAR-LoRA and other LoRA variants.
Study Design
Our analysis considers three deployment strategies for the PortLLM example.
We propose a method to mathematically compare patching strategies based on a 1-D slice of the fine-tuning loss landscape.
While our analysis above focuses on the PortLLM scenario, it is not limited to this scenario.
Future work may consider how the mathematical device of near-orthogonality may be generally applicable to other other scenarios, e.g., improving analysis of fine-tuning strategies or considering how different LoRA patches for different tasks can be jointly used.
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Results & Findings
Unsupervised pretraining on a huge corpus enables a model to learn general knowledge and language understanding. Supervised downstream fine-tuning on a smaller data set allows the model to excel at domain-specific tasks.
- Unsupervised pretraining on a huge corpus enables a model to learn general knowledge and language understanding.
- Supervised downstream fine-tuning on a smaller data set allows the model to excel at domain-specific tasks.
- Direction fine-tuning of all base model parameters is infeasible for resource-constrained developers due to LLM scale.
- Parameter efficient fine-tuning (PEFT) methods reduce trainable parameters during fine-tuning to address this problem.
- Low-rank adaptation (LoRA) restricts the rank of update matrices to achieve parameter efficiency.
We leave it for future work to estimate a smaller range for \u03b1 \u2032 to mitigate this limitation.
Practical Applications
Developers may choose stepwise fine-tuning or plan for a performance drop if there is a substantial decline. Limited access to computational resources or logistical costs may motivate training-free methods.
One may expect the displaced-gradient-displacement product to be large because the gradient points away from the optimal point.
Remark 5 notes that the bound in Theorem 4 may be loose.
Limited access to computational resources or logistical costs may motivate training-free methods.
Motivating Experimental Study of Long-Term Temporal Portability
The section outlines the motivation for studying the long-term performance of PortLLM and sets the stage for the experimental analysis presented in the following sections.
Experimental Setup
This section details the experimental design, including the base models used, the datasets for continual pretraining, and the benchmarks for evaluating temporal portability. It describes the methodology for assessing the performance of PortLLM across different model architectures.
Frequently Asked Questions
We aim to perform continual pretraining that updates outdated information with new temporal knowledge. We continually pretrain Mistral on eight sections of Cosmopedia to investigate temporal portability under heterogeneous data.
Low-rank adaptation is a widely-used PEFT method of particular interest to our work. We propose two approaches for theoretical analysis to explain the empirical results observed in Section 3.
Direction fine-tuning of all base model parameters is infeasible for resource-constrained developers due to LLM scale. The update for a fully connected layer is restricted to be low-rank using learnable matrices A and B.
Remark 15 Gradient clipping, which is common in practical scenarios, could replace Assumption 3 on pretraining stability to bound the distance between iterates. While the sum of singular values may be quite large, both \u03b7 2 and e 2 are expected to.
Limited access to computational resources or logistical costs may motivate training-free methods. We leave it for future work to estimate a smaller range for \u03b1 \u2032 to mitigate this limitation.
This paper explores how a method called PortLLM can help large language models adapt to new information over time without needing to be retrained frequently. It shows that this method works well even as the models are updated with new data.