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Entropy, Disagreement, and the Limits of Foundation Models in Genomics

This paper argues that the high entropy of genomic sequences fundamentally limits foundation models' ability to learn meaningful representations, leading to unstable predictions and a failure to capture inter-token relationships, which suggests that current self-supervised training methodologies may be unsuitable for genomic data.

Original authors: Maxime Rochkoulets, Lovro Vrček, Mile Šikić

Published 2026-04-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Maxime Rochkoulets, Lovro Vrček, Mile Šikić

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The Big Idea: Why AI is Great at Reading, But Bad at DNA

Imagine you have two students trying to learn a new language.

Student A is learning English. They read millions of books, learn that "The cat sat on the..." is almost always followed by "mat." They get very confident, and if you ask five different students to finish that sentence, they will all say "mat."
Student B is learning DNA. They read millions of genetic sequences. But DNA is weird. It's like a language where almost anything could come next. If you ask five different students to finish a DNA sentence, one might say "A," another "T," another "G," and another "C." They all guess differently.

This paper argues that Foundation Models (the super-smart AI brains we use for biology) are failing at DNA not because the AI is broken, but because DNA is fundamentally too chaotic for these models to learn the way they learn human language.

The Three Main Problems the Paper Found

The researchers trained groups of AI models (called "ensembles") on both English text and DNA. They kept everything else exactly the same (same brain size, same training time) to see what happened. Here is what they discovered:

1. The "Confused Crowd" Problem (High Entropy)

In the world of information, Entropy is a measure of chaos or surprise.

English has low entropy: If I say "I drink coffee in the morning," you are 99% sure the next word is "with" or "sugar." The AI is confident.
DNA has high entropy: If I give you a DNA sequence, the next letter is almost a coin toss. There is no strong pattern.

The Analogy: Imagine a game of "Telephone."

In the English version, everyone whispers the same clear message.
In the DNA version, everyone is shouting random letters. Because the "rules" of DNA are so loose, the AI models can't agree on what comes next. Even if you train 5 different models on the exact same data, they will all give you different answers. They are like a crowd of people guessing the weather in a storm; everyone is just guessing randomly.

2. The "Broken Dictionary" Problem (Unstable Embeddings)

AI models create a "dictionary" (called embeddings) where words that mean similar things are stored close together in their brain.

In English, the AI learns that "King" and "Queen" are close together, and "Cat" and "Dog" are close together. This is a stable, useful map.
In DNA, because the models are so confused by the randomness, their "dictionaries" are messy. One model might put "A" next to "T," while another puts "A" next to "G."

The Analogy: Imagine two cartographers trying to draw a map of a city.

The English cartographers draw the same map: The library is next to the park.
The DNA cartographers draw completely different maps. One puts the library in the ocean; another puts it in the sky. Because the data is so noisy, the AI can't build a reliable map of how DNA pieces relate to each other. This makes the AI's "knowledge" unreliable for real-world tasks.

3. The "Rote Memorizer" Problem (Fisher Information)

The researchers looked at where the AI was storing its knowledge.

English AI: It uses its "thinking layers" (the complex middle part of the brain) to understand how words relate to each other. It learns grammar.
DNA AI: It dumps all its knowledge into the "memory layer" (the very first part). It seems to be just memorizing specific letters rather than understanding the relationships between them.

The Analogy:

The English student is like a detective who understands clues and logic. They know why a suspect is guilty.
The DNA student is like a parrot. It can repeat a sequence of letters perfectly, but it doesn't understand the story or the connection between the letters. It's just memorizing the sound, not the meaning.

The Conclusion: What Does This Mean?

The paper concludes that the current method of training AI on DNA (just feeding it sequences and asking it to guess the next letter) might be a dead end.

The Problem: DNA is too random (high entropy) for the AI to learn "grammar" or "relationships" the way it does with human language.
The Result: The AI ends up just memorizing data, disagreeing with itself, and failing to build a useful "foundation" of biological knowledge.
The Future: We probably need to stop treating DNA exactly like English text. We need new ways to teach AI about biology that account for the fact that DNA is fundamentally different, chaotic, and full of noise.

In short: You can't teach a dog to speak French just by reading it French books; it needs a different approach. Similarly, you can't teach an AI to understand biology just by making it read DNA like it's a novel. The "language" of life is too different from the language of humans.

1. Problem Statement

Genomic Foundation Models (GFMs) have shown mixed success compared to their counterparts in Natural Language Processing (NLP). While NLP models (e.g., BERT, RoBERTa) successfully learn hidden grammatical structures and general knowledge from self-supervised training on text, GFMs trained on DNA sequences often underperform.

The Gap: Specialized, smaller models trained for specific tasks frequently outperform GFMs on downstream tasks, despite GFMs being trained on vast amounts of data.
The Unknown: There is currently no theoretical explanation for why GFMs fail to develop robust foundational capabilities from sequences alone.
Hypothesis: The authors propose that the fundamental difference lies in information entropy. They argue that DNA sequences possess higher entropy (lower information content regarding unseen token prediction) compared to human text, which prevents models from learning confident distributions and inter-token relationships.

2. Methodology

To isolate the impact of data entropy from architectural or training differences, the authors conducted a controlled comparative experiment:

Model Architecture: They trained ensembles of BERT-style transformer encoders (90M parameters each).
Ensembles: Three ensembles were created, each containing N=5 models (total 15 models):
1. Text Ensemble: Trained on English text.
2. DNA (BPE) Ensemble: Trained on DNA sequences using Byte-Pair Encoding (BPE).
3. DNA (k-mer) Ensemble: Trained on DNA sequences using a non-overlapping k-mer tokenizer (standard in genomics).
Controlled Variables:
- All models used the exact same architecture and parameter count.
- All models were trained on the same number of tokens (5 billion).
- Vocabulary size was fixed to 4096 (matching a 6-mer scheme) for all models to ensure fair comparison.
- Data iteration order was deterministic and identical across models; only weight initialization was randomized.
Analysis Metrics:
- Output Distributions: Measured via Kullback-Leibler (KL) divergence against a uniform distribution and Jensen-Shannon (JS) distance between model pairs.
- Static Embeddings: Analyzed agreement in the first embedding layer using Top-k Jaccard overlap, Spearman correlation, Procrustes alignment (cosine similarity and disparity).
- Empirical Fisher Information: Calculated the diagonal of the Empirical Fisher Information Matrix (FIM) to determine where the model concentrates information (Embeddings vs. Transformer Layers vs. Head).

3. Key Results

A. High Entropy Leads to Uncertainty and Disagreement

KL Divergence: DNA models exhibited output distributions much closer to uniform (low KL divergence: ~3 bits for BPE, <1 bit for k-mer) compared to text models (>10 bits). This indicates DNA models are highly uncertain about predictions.
Ensemble Disagreement:
- When applying nucleus sampling (filtering for top probability mass), the distance between DNA models increased significantly as the probability mass threshold ( $p$ ) decreased.
- Text models remained stable and agreed on predictions even at low $p$ .
- Interpretation: DNA models do not agree on what the token is; they simply assign similar low probabilities to all tokens. This lack of consensus suggests the models fail to converge to a single "correct" solution due to the flat conditional distributions of DNA.

B. Instability in Static Embeddings

Embedding Space Disagreement: Even with identical training data and architecture, DNA models showed significantly lower agreement in their static word embeddings compared to text models.
- Metrics: Text models achieved higher Top-10 overlap (0.54 vs ~0.40) and higher Procrustes Cosine similarity (0.71 vs ~0.60).
- Implication: High data entropy combined with random initialization leads to poor robustness. Small changes in initialization cause DNA models to converge to vastly different embedding states, making static embedding-based analyses unreliable and reducing reproducibility.

C. Failure to Leverage Inter-Token Relationships (Fisher Information)

Information Concentration:
- Text Models: Fisher information was concentrated in the Transformer Layers, indicating the models successfully learned relationships between tokens via attention mechanisms.
- DNA Models: Fisher information was concentrated in the Static Embedding Layers.
Interpretation: DNA models appear to rely on memorizing token identities (static embeddings) rather than learning contextual relationships. They fail to utilize the attention mechanism effectively, suggesting they are not learning the "grammar" of the genome but rather treating tokens as isolated entities.

4. Key Contributions

Entropy as a Limiting Factor: The paper establishes that the high entropy of genomic sequences (from the perspective of next-token prediction) is a fundamental barrier to learning, distinct from architectural limitations.
Quantification of Model Instability: It provides empirical evidence that GFMs suffer from severe ensemble disagreement and embedding instability, making them less reliable than NLP models even under matched training conditions.
Fisher Information Analysis: It introduces a novel diagnostic using Empirical Fisher Information to show that GFMs fail to shift learning from static token identity to dynamic inter-token relationships.
Tokenization Independence: The results held true regardless of whether BPE or k-mer tokenization was used, suggesting the issue is intrinsic to the data distribution, not the tokenization scheme.

5. Significance and Conclusion

The paper challenges the prevailing assumption that self-supervised training on raw genomic sequences is sufficient to build foundational models.

Theoretical Implication: The "next-token prediction" objective, which works for language, may be fundamentally misaligned with genomic data due to entropy constraints.
Practical Impact: The instability of embeddings and the failure to learn relationships explain why specialized models often outperform GFMs. It suggests that current methodologies for training GFMs may need to be rethought, potentially requiring new objectives or incorporating biological priors beyond simple sequence prediction.
Reproducibility: The authors emphasize that their findings are fully reproducible, providing a source code repository to validate these limitations.

In summary, the authors argue that genomic foundation models are currently limited not by scale or architecture, but by the inherent information-theoretic properties of DNA, which prevent the models from developing the confident, relational understanding necessary for generalizable biological knowledge.