# When can isotropy help adapt LLMs' next word prediction to numerical domains?

arXiv: https://arxiv.org/abs/2505.17135 · HTML: https://mlsanity.com/paper/2505.17135/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 15 of 15)

- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Language Models are Realistic Tabular Data Generators](https://mlsanity.com/paper/2210.06280/) (2022)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [The Lipschitz Constant of Self-Attention](https://mlsanity.com/paper/2006.04710/) (2020)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [LIFT: Language-Interfaced Fine-Tuning for Non-Language Machine Learning Tasks](https://mlsanity.com/paper/2206.06565/) (2022)
- [Why Do Pretrained Language Models Help in Downstream Tasks? An Analysis of Head and Prompt Tuning](https://mlsanity.com/paper/2106.09226/) (2021)
- [Temporal Data Meets LLM -- Explainable Financial Time Series Forecasting](https://mlsanity.com/paper/2306.11025/) (2023)
- [Inducing High Energy-Latency of Large Vision-Language Models with Verbose Images](https://mlsanity.com/paper/2401.11170/) (2024)
- [LLM4CP: Adapting Large Language Models for Channel Prediction](https://mlsanity.com/paper/2406.14440/) (2024)
- [Large Multi-Modal Models (LMMs) as Universal Foundation Models for AI-Native Wireless Systems](https://mlsanity.com/paper/2402.01748/) (2024)

## Abstract (arXiv)

Vector representations of contextual embeddings learned by pre-trained large language models (LLMs) are effective in various downstream tasks in numerical domains such as time series forecasting. Despite their significant benefits, the tendency of LLMs to hallucinate in such domains can have severe consequences in applications such as energy, nature, finance, healthcare, retail and transportation, among others. To guarantee prediction reliability and accuracy in numerical domains, it is necessary to open the black box behind the LLM and provide performance guarantees through explanation. However, there is little theoretical understanding of when pre-trained language models help solve numerical downstream tasks. This paper seeks to bridge this gap by understanding when the next-word prediction capability of LLMs can be adapted to numerical domains through a novel analysis based on the concept of isotropy in the contextual embedding space. Specifically, a log-linear model for LLMs is considered in which numerical data can be predicted from its context through a network with softmax in the output layer of LLMs (i.e., language model head in self-attention). For this model, it is demonstrated that, in order to achieve state-of-the-art performance in numerical domains, the hidden representations of the LLM embeddings must possess a structure that accounts for the shift-invariance of the softmax function. By formulating a gradient structure of self-attention in pre-trained models, it is shown how the isotropic property of LLM embeddings in contextual embedding space preserves the underlying structure of representations, thereby resolving the shift-invariance problem and providing a performance guarantee. Experiments show that different characteristics of numerical data and model architectures have different impacts on isotropy, and this variability directly affects the performances.