💬 NLP

Fine-Tuning Improves Information Conveyance in Language Models

This paper introduces Canopy Entropy ( $\mathrm{CE}^\star$ ), a novel metric that accounts for output length to reveal that fine-tuning does not merely reduce uncertainty in language models but fundamentally reorganizes it to enhance information conveyance and semantic diversity.

Original authors: Yuwei Cheng, Weiyi Tian, Haifeng Xu

Published 2026-06-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yuwei Cheng, Weiyi Tian, Haifeng Xu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Why "Fine-Tuning" Changes How AI Thinks

Imagine a Large Language Model (LLM) as a very talented but slightly chaotic storyteller. Before you give it specific instructions (a process called fine-tuning), this storyteller might ramble, repeat themselves, or stop talking too soon. They have a lot of "uncertainty" in their head—they aren't sure what to say next, how long to talk, or if they should stop.

Many people thought that when we fine-tune these models to be more helpful, we were just "shutting down" their creativity, making them boring and robotic. This paper argues that's not quite true. Instead, fine-tuning doesn't just silence the noise; it reorganizes the noise into something much more useful.

To prove this, the authors invented a new way to measure how much "space" an AI has to explore when it writes. They call it Canopy Entropy.

The New Tool: The "Tree Canopy" Analogy

Imagine the AI's writing process as a giant tree growing from a seed (your prompt).

The Branches (Width): At every step, the AI has to choose the next word. Sometimes it has 100 options (wide branches), and sometimes it only has 2 (narrow branches).
The Height (Depth): The AI also has to decide when to stop. Does it write a short sentence or a whole novel?

Previous studies only looked at the width of the tree (how many word choices it had). They concluded that fine-tuning makes the tree narrower (less diverse).

The Problem: They ignored the height. Fine-tuned models often write longer stories. If you only look at how many branches there are, but ignore how tall the tree grows, you miss the whole picture.

The Solution (Canopy Entropy): The authors propose looking at the entire canopy—the total volume of the tree, combining both how wide the branches are and how deep the tree grows.

The Finding: When they measure the whole tree, they find that fine-tuning doesn't just shrink the tree. It changes the shape. The tree might have fewer branches at the bottom, but it grows much taller and more steadily.

Key Discovery 1: The "Longer is Better" Shift

The authors discovered a fascinating relationship between how long the AI talks and how interesting each new word is. They call this the Length-Entropy Correlation.

The "Base" Model (Before Fine-Tuning): Imagine a student who starts a story with great excitement but quickly runs out of ideas.
- Early words: Very creative and surprising.
- Later words: Boring, repetitive, and predictable.
- The Pattern: As the story gets longer, it gets less interesting. The correlation is negative. The student is just rambling to fill space.
The "Fine-Tuned" Model (After Fine-Tuning): Imagine a professional journalist.
- Early words: Clear and direct.
- Later words: Still informative, adding new details, facts, or plot points.
- The Pattern: As the story gets longer, it stays interesting. The correlation turns positive. The student is actually adding value the whole time.

What this means: Fine-tuning teaches the model that "longer" doesn't mean "repetitive." It teaches the model to keep the information density high, even in long responses.

Key Discovery 2: Turning "Confusion" into "Meaning"

The authors looked at how the AI's internal "uncertainty" (its confusion about what to say next) turns into semantic diversity (different meanings or ideas in the final output).

The Analogy: Think of uncertainty as a pile of raw clay.
- Base Models: They have a lot of clay (high uncertainty), but they often just make a messy lump. They don't know how to shape the clay into distinct, useful shapes.
- Fine-Tuned Models: They have less clay overall (lower uncertainty), but they are expert sculptors. They take that smaller amount of clay and shape it into distinct, meaningful statues.

The Result: The paper found that fine-tuning makes the model three times more efficient at turning its internal uncertainty into actual, meaningful variety. Even though the model is "less confused" about what to say, the things it does say are much more distinct from one another in terms of meaning.

Summary of Findings

It's not just about shrinking: Fine-tuning doesn't just make the AI less diverse. It changes how the diversity is distributed.
Length matters: Previous studies were fooled because fine-tuned models write longer. When you account for length, you see that fine-tuned models stay interesting much longer than base models.
Efficiency: Fine-tuned models are better at converting their "thinking process" into "useful variety." They don't just ramble; they elaborate.

The Bottom Line: Fine-tuning doesn't turn a creative AI into a boring robot. It turns a chaotic improviser into a structured storyteller who knows exactly how long to talk and how to keep the conversation interesting from start to finish.

Technical Summary: Fine-Tuning Improves Information Conveyance in Language Models

Problem Statement

Existing literature posits that fine-tuning (including instruction tuning and alignment) reduces the diversity and uncertainty of Large Language Models (LLMs), making them more deterministic. However, the paper identifies a critical limitation in these prior analyses: they largely fail to control for output length. Length is a major confounder in diversity measurement; metrics like type-token ratio or n-gram diversity are biased by text length, often making shorter responses appear artificially diverse. Furthermore, prior work treats diversity as a static property, failing to analyze how uncertainty evolves along generation trajectories or how it is allocated across different output lengths. Consequently, it remains unclear whether fine-tuning simply suppresses diversity or reorganizes it to produce more informative, semantically meaningful generations.

Methodology

Canopy Entropy ( $CE^\star$ )

To address these gaps, the authors propose Canopy Entropy ( $CE^\star$ ), an information-theoretic measure that views language generation from a tree perspective.

Concept: The "canopy" represents the set of all possible finished rollouts (leaves) available to the model. $CE^\star$ quantifies the effective volume of this generation space by jointly accounting for local branching width (token-level uncertainty) and trajectory depth (stopping time variability).
Formal Definition: $CE^\star$ is defined as the expected sum of local entropies along generation trajectories:
$CE^\star := \mathbb{E}\left[\sum_{t=1}^{N(x)} \tilde{H}(g_t | x)\right]$
where $N(x)$ is the random stopping time (length), $g_t$ is the generation history, and $\tilde{H}$ is the local entropy of the next token (including the EOS token).
Theoretical Equivalence: The authors prove that $CE^\star$ is exactly equivalent to the total Shannon entropy of the generation process:
$CE^\star = H(N, Y_{1:N} | X)$
This decomposes total uncertainty into length uncertainty $H(N|X)$ (predictability of stopping time) and content uncertainty $H(Y_{1:N}|N, X)$ (diversity of sequences given a fixed length).

Derived Metrics

To make $CE^\star$ interpretable, two normalized variants are introduced:

Generation Perplexity (GenPPL): A token-level normalization of $CE^\star$ , reflecting the diversity of a typical token.
Branching Factor (BF): A trajectory-level normalization (expectation of entropy rate), reflecting the diversity of a typical trajectory.

Length–Entropy Correlation ( $\rho(N, r_N)$ )

The paper introduces a novel metric to study how uncertainty evolves with generation length: the correlation between output length $N$ and entropy rate $r_N$ (per-token content uncertainty).

Definition: $\rho(N, r_N)$ measures whether longer generations remain informative (positive correlation) or become increasingly redundant/predictable (negative correlation).
Significance: This metric addresses the confounding effect of length, distinguishing between genuine information gain and statistical artifacts in longer texts.

Estimation

Since computing $CE^\star$ over the exponential space of all rollouts is intractable, the authors develop Monte Carlo estimators. They establish the consistency of these estimators under conditions of diminishing truncation bias (as the maximum length $T_{max} \to \infty$ ) and modest truncation length. The error bounds decompose into Monte Carlo sampling error and truncation bias.

Key Results

The authors evaluated three model families (LLaMA-3.1-8B, Qwen3-8B, Gemma-3-12B) across four tasks (Math, Coding, Sentence Completion, Story Generation), comparing base models against instruction-tuned variants.

Reduction in Normalized Uncertainty:
Fine-tuning consistently reduces both token-level (GenPPL) and trajectory-level (BF) normalized uncertainty across nearly all models and tasks. The magnitude of reduction varies significantly by task (e.g., ~5% in Math for Qwen vs. ~80% in Sentence Completion), suggesting alignment compresses the generation space but does so heterogeneously depending on task structure.
Task-Dependent Effects on Total Uncertainty ( $CE^\star$ ):
- In structured tasks (Math, Coding, Sentence Completion), $CE^\star$ decreases significantly after fine-tuning, as the valid generation space is pruned to a small set of correct trajectories.
- In open-ended tasks (Story Generation), $CE^\star$ can increase. Fine-tuned models generate longer, more elaborate sequences. While local branching diversity decreases, the increase in trajectory depth (stopping time uncertainty) can mathematically outweigh the reduction in local entropy, leading to a larger total generation space volume.
Shift in Length–Entropy Correlation:
A pivotal finding is that fine-tuning systematically shifts the correlation $\rho(N, r_N)$ from negative to positive.
- Base Models: Exhibit negative correlation; longer outputs tend to have lower entropy rates, implying later tokens are redundant.
- Fine-Tuned Models: Exhibit positive correlation; longer generations maintain higher entropy rates, indicating that additional tokens remain informative rather than collapsing into repetition.
Efficiency in Semantic Diversity:
Using a Beta mixed-effects regression framework, the authors found that while fine-tuning reduces baseline semantic diversity at a fixed entropy rate, it nearly triples the sensitivity of semantic diversity to entropy rate. This implies that aligned models utilize token-level uncertainty more efficiently, converting it into meaningful semantic variation more effectively than base models.

Significance and Claims

The paper claims that the prevailing view—that fine-tuning merely reduces diversity—is incomplete. Instead, the results demonstrate that fine-tuning fundamentally reorganizes uncertainty.

Reorganization, Not Just Reduction: Fine-tuning does not simply shrink the generation space; it restructures how uncertainty is allocated across generation trajectories.
Information Efficiency: Aligned models produce outputs that are more organized and semantically meaningful. They sustain information density over longer trajectories, avoiding the "completion traps" and redundancy often seen in base models.
Methodological Contribution: By introducing $CE^\star$ and the length–entropy correlation, the paper provides a principled, length-aware framework for evaluating generation diversity that overcomes the confounding effects of output length inherent in previous metrics.

The authors conclude that fine-tuning improves the information conveyance of language models, making them more effective at translating uncertainty into semantically diverse and task-appropriate generations.