Encoding and Understanding Astrophysical Information in Large Language Model-Generated Summaries

Conference: NeurIPS 2025 arXiv: 2511.14685 Code: None Area: Physics / LLM Scientific Reasoning Keywords: LLM embeddings, astrophysics, sparse autoencoders, X-ray astronomy, physical encoding

TL;DR

This work investigates whether LLM embeddings encode physically meaningful quantities derived from X-ray astronomical observations—specifically hardness ratios, power-law indices, and variability indices. Results show that structured prompt design improves clustering purity of physical attributes by 5.9%–57.5%, and sparse autoencoders reveal that LLMs infer physical parameters not explicitly stated by recognizing object types.

Background & Motivation

Background: LLMs have demonstrated cross-domain generalization capabilities, yet it remains unclear whether their embeddings encode physical attributes directly measured from scientific observations—rather than merely textual descriptions. Astrophysics provides an ideal testbed: X-ray sources are characterized by precise physical measurements (from the Chandra Source Catalog) and rich literature descriptions.

Limitations of Prior Work: (a) The scientific reasoning capabilities of LLMs are difficult to quantitatively assess; (b) it is unclear how prompt design affects the encoding of physical information; (c) the semantic pathways through which physical concepts are represented in LLM internal representations remain opaque.

Key Challenge: Do LLMs genuinely "understand" physics, or have they merely learned statistical correlations? How can physical information be disentangled from embedding spaces?

Goal: (1) Does prompt design affect how LLMs encode physical quantities? (2) Which aspects of language are most important for encoding physical information?

Key Insight: GPT-4o-mini is used to generate textual summaries for 4,000 X-ray sources from NASA ADS papers; ada-002 is used to produce embeddings; the clustering quality of physical attributes in embedding space is then measured.

Core Idea: KNN purity is used to measure the encoding quality of physical attributes in embeddings, while sparse autoencoders are employed to trace semantic pathways—revealing that LLMs infer physical parameters through object-type recognition.

Method

Overall Architecture

A three-step pipeline: (1) structured source descriptions are generated from astronomical papers using GPT-4o-mini; (2) embeddings are encoded via ada-002; (3) physical attribute clustering is evaluated using KNN purity, and semantic features are analyzed using a sparse autoencoder (SAE).

Key Designs

1. Prompt Engineering (Baseline vs. Optimized):

   • Function: Compare the effect of different prompt designs on physical encoding.
   • Mechanism: The baseline prompt simply requests a summary of physical attributes; the optimized prompt includes structured formatting instructions, rules for handling missing information, and explicit guidance to avoid uninformative text.
   • Design Motivation: Different prompts direct the LLM's attention to different information, directly influencing the physical content encoded in the resulting embeddings.

2. KNN Purity Evaluation:

   • Function: Quantify the clustering quality of physical attributes in embedding space.
   • Mechanism: For each source, \(K=10\) nearest neighbors are identified, and the proportion of neighbors sharing similar physical attributes is computed. Higher purity indicates better encoding of physical attributes.
   • Design Motivation: Directly measures whether physical information is preserved in the embeddings.

3. Sparse Autoencoder (SAE) Feature Analysis:

   • Function: Reveal the semantic pathways through which physical information is encoded in LLM embeddings.
   • Mechanism: A pretrained SAE extracts monosemantic features from ada-002 embeddings; the analysis identifies which tokens activate which features; Claude/Gemini is used to annotate the semantic meaning of the most strongly activated features.
   • Design Motivation: SAE provides an interpretable feature decomposition that exposes the physical reasoning mechanisms of LLMs.

Loss & Training

The SAE is trained with standard sparsity constraints. The main experiments involve no model training—the pipeline is purely evaluative.

Key Experimental Results

Main Results

Physical Quantity	Baseline Prompt Purity	Optimized Prompt Purity	Gain
Hardness Ratio	0.7998	0.8468	+5.9%
Power-Law Index \(\gamma\)	0.8185	0.9418	+15.1%
Variability Index	0.6346	0.9994	+57.5%

SAE Feature Analysis

SAE Feature ID	Semantic Label	Associated Physical Quantity
Feature 1212	"Scientific inference and likelihood"	Source classification
Feature 839	"X-ray binary burst periodicity"	Variability
Feature 2047	"Non-thermal emission spectrum"	Power-law index

Key Findings

• Physical encoding without explicit numerical values: The high clustering purity of the power-law index \(\gamma\) (0.94) arises from object-type descriptions rather than numerical values—the model encodes physical properties through a causal reasoning chain of "QSO-type → non-thermal spectrum → specific \(\gamma\) range."
• Substantial impact of prompt design: The variability index purity increases from 0.63 to 0.9994 (+57.5%), demonstrating that the degree of prompt structuring directly controls the retention of physical information.
• SAE reveals compositional reasoning: Rather than directly memorizing physical values, the model infers them indirectly through semantic pathways such as object-type recognition and spectral feature association.

Highlights & Insights

• Semantic pathways for physical encoding: LLMs encode physical information through hierarchical reasoning of the form "object type → physical characteristics → parameter inference," which goes beyond simple statistical correlation.
• Prompts as physical information selectors: Structured prompt design is equivalent to selecting which physical dimensions the LLM "attends to."
• SAE as a tool for scientific interpretability: This work introduces a new instrument for understanding the scientific reasoning processes of LLMs.

Limitations & Future Work

• The study is limited to X-ray astrophysics; generalization to other scientific domains (e.g., particle physics, chemistry) has not been validated.
• It is not possible to definitively distinguish between "understanding physics" and "learning statistical correlations present in training data."
• Evaluation relies on a single embedding model (ada-002); other models may exhibit different behavior.

Related Work & Insights

• vs. Traditional Scientific ML: Conventional approaches directly model physical equations, whereas this work explores the implicit physical encoding capabilities of LLMs.
• Insights: The SAE + KNN evaluation framework is generalizable to assessing domain-specific knowledge encoding in LLMs across any scientific field.

Rating

• Novelty: ⭐⭐⭐⭐ First systematic evaluation of astrophysical information encoding in LLM embeddings; SAE-based analysis is novel.
• Experimental Thoroughness: ⭐⭐⭐ Dataset of 4,000 sources is moderate in scale, but limited to a single scientific domain.
• Writing Quality: ⭐⭐⭐⭐ Cross-disciplinary exposition is clear; figures and tables are intuitive.
• Value: ⭐⭐⭐⭐ Introduces a new methodology for evaluating LLM knowledge encoding in the context of AI for Science.

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