# Predictable Confabulations: Factual Recall by LLMs Scales with Model Size and Topic Frequency

arXiv: https://arxiv.org/abs/2605.18732 · HTML: https://mlsanity.com/paper/2605.18732/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 18 of 18)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Large Language Models Struggle to Learn Long-Tail Knowledge](https://mlsanity.com/paper/2211.08411/) (2022)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Head-to-Tail: How Knowledgeable are Large Language Models (LLMs)? A.K.A. Will LLMs Replace Knowledge Graphs?](https://mlsanity.com/paper/2308.10168/) (2023)
- [Scaling Laws and Interpretability of Learning from Repeated Data](https://mlsanity.com/paper/2205.10487/) (2022)
- [Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Laws](https://mlsanity.com/paper/2404.05405/) (2024)
- [The Quantization Model of Neural Scaling](https://mlsanity.com/paper/2303.13506/) (2023)
- [Scaling Laws for Fact Memorization of Large Language Models](https://mlsanity.com/paper/2406.15720/) (2024)
- [Superposition Yields Robust Neural Scaling](https://mlsanity.com/paper/2505.10465/) (2025)
- [The Law of Knowledge Overshadowing: Towards Understanding, Predicting, and Preventing LLM Hallucination](https://mlsanity.com/paper/2502.16143/) (2025)
- [The Landscape of Memorization in LLMs: Mechanisms, Measurement, and Mitigation](https://mlsanity.com/paper/2507.05578/) (2025)
- [Towards a Holistic Evaluation of LLMs on Factual Knowledge Recall](https://mlsanity.com/paper/2404.16164/) (2024)
- [Superposition as Lossy Compression: Measure with Sparse Autoencoders and Connect to Adversarial Vulnerability](https://mlsanity.com/paper/2512.13568/) (2025)

## Built on by (most cited first, 1 of 1)

- [Memory vs. Context? Influential Factors of Factual Recall in Language Models](https://mlsanity.com/paper/2609.24238/) (2026)

## Abstract (arXiv)

While scaling laws govern aggregate large language model performance, no scaling law has linked factual recall to both model size and training-data composition. We evaluated 38 models on over 8,900 scholarly references evaluated by an automated reference verification system. Recall quality follows a sigmoid in the log-linear combination of model parameter count and topic representation in training data. These two variables alone explain 60% of the variance across 16 dense models from four families, rising to 74-94% within individual families. The form matches a superposition-inspired account in which recall is gated by a signal-to-noise ratio: signal strength scales with concept frequency and the noise floor with model capacity.