# Uncovering Scaling Laws for Large Language Models via Inverse Problems

arXiv: https://arxiv.org/abs/2509.07909 · HTML: https://mlsanity.com/paper/2509.07909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 73 of its 106 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Builds on (most cited first, 30 of 73)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [What Makes Good In-Context Examples for GPT-3?](https://mlsanity.com/paper/2101.06804/) (2021)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)

## Abstract (arXiv)

Large Language Models (LLMs) are large-scale pretrained models that have achieved remarkable success across diverse domains. These successes have been driven by unprecedented complexity and scale in both data and computations. However, due to the high costs of training such models, brute-force trial-and-error approaches to improve LLMs are not feasible. Inspired by the success of inverse problems in uncovering fundamental scientific laws, this position paper advocates that inverse problems can also efficiently uncover scaling laws that guide the building of LLMs to achieve the desirable performance with significantly better cost-effectiveness.