Technical Summary: Convergence Without Understanding

Problem Statement

The Platonic Representation Hypothesis (PRH) posits that large language models (LLMs) trained on diverse objectives and architectures converge toward a shared statistical model of reality, developing increasingly similar internal representations as they scale. While empirical evidence supports representational convergence using aggregate similarity metrics like Centered Kernel Alignment (CKA), it remains untested whether this convergence extends to the reasoning processes that operate over these representations. Existing similarity metrics often fail to condition on what models do with representations, potentially conflating shared input processing constraints with shared reasoning strategies. This paper investigates the phenomenon of "convergence without understanding": whether models agree on representations while disagreeing on the causal reasoning that leads to predictions.

Methodology

The study evaluates 16 instruction-tuned language models spanning 8 architectural families (ranging from 1.5B to 72B parameters) on 800 reasoning problems across four domains: mathematics (GSM8K), science (ARC-Challenge), truthfulness (TruthfulQA), and commonsense (HellaSwag).

The methodology employs a stratified analysis along three axes previously unexamined jointly:

1. Problem Difficulty: Stratifying problems by the fraction of models solving them (Hard: 0–4/14 correct; Medium: 5–9; Easy: 10–14).
2. Computational Stage: Splitting model layers into pre-decision (input encoding) and post-decision (output generation) stages, defined by the layer where a correctness probe first exceeds chance accuracy.
3. Causal Relevance: Distinguishing between information that is merely encoded in shared representations versus information that causally drives predictions.

Key Metrics and Techniques:

• Centered Kernel Alignment (CKA): The primary metric for linear representational similarity, computed on mean-centered activations at the last input token.
• Mutual Nearest Neighbors (MNN): Used as a topological complement to validate CKA findings.
• Transfer Probes: Linear probes trained on one model's representations to predict correctness, then evaluated on other models to test information transferability.
• Causal Ablation: Projections of activations onto the orthogonal complement of the correctness-predictive subspace to measure "flip rates" (changes in predictions).
• Attention Entropy: Analysis of Shannon entropy in attention weights to explain mechanisms behind convergence patterns.

Key Contributions and Results

1. Difficulty Inversion

Contrary to the PRH, which predicts maximal convergence where models successfully represent reality, the study finds a difficulty inversion: models are more representationally similar on problems they collectively fail than on those they solve.

• Hard Problems (0–4 correct): Mean CKA = 0.897.
• Easy Problems (10–14 correct): Mean CKA = 0.830.
• Mechanism: This inversion is driven by attention entropy. Hard problems induce diffuse, high-entropy attention patterns that homogenize representations across architectures, whereas solvable problems allow for focused, model-specific strategies.
• Domain Specificity: The inversion holds for science, truthfulness, and commonsense reasoning but reverses for mathematics (GSM8K), where algorithmic constraints force successful models into similar strategies.

2. The Generation Gap

Representational convergence is primarily a property of input encoding, not output computation.

• Pre-decision Layers: High convergence (CKA = 0.875).
• Post-decision Layers: Significant divergence (CKA = 0.274).
• Implication: Models agree on how to encode inputs but disagree fundamentally on how to generate outputs. This explains why model stitching succeeds in early layers but degrades in late layers.

3. Epiphenomenal Correctness

Shared representations encode task-relevant information but do not causally deploy it for prediction.

• Transfer Accuracy: A probe trained on one model achieves 66% accuracy on another, confirming shared encoding.
• Causal Flip Rate: Ablating the shared correctness subspace changes only 1.5% of predictions (rising to 5.5% on easier subsets).
• Conclusion: Correctness information is present in the shared representation space but is largely epiphenomenal to the actual reasoning process.

4. Baselines and Mechanisms

• Architectural vs. Learned: Randomly initialized (untrained) models exhibit higher CKA (0.864) than trained models (0.612), indicating that a substantial component of observed convergence is architectural rather than learned. Training actively differentiates representations.
• Base Models: The difficulty inversion is stronger in base (non-instruction-tuned) models, ruling out alignment training as the source.
• Head-Level Causality: While global ablation shows low flip rates, individual attention head ablation reveals higher causal importance (up to 63% in MHA models), suggesting that global CKA masks architectural differences in computational granularity.

Significance and Claims

The paper argues that representational convergence in LLMs reflects shared input processing constraints (driven by natural language statistics and transformer inductive biases) rather than shared reasoning strategies.

• Reinterpreting PRH: The PRH correctly identifies convergence in perceptual representations (input encoding) but fails to account for the divergence in computational processes (reasoning and output generation). Learning actively differentiates models from a shared architectural starting point.
• Ensemble Design: Selecting models for ensembles based on representational dissimilarity (low CKA) is suboptimal. Since models are most behaviorally diverse on problems they solve (where CKA is low) and most redundant on problems they fail (where CKA is high), ensembles should target reasoning diversity and output-level behavioral diversity.
• Interpretability Transfer: Mechanistic interpretability findings regarding input processing (e.g., induction heads) are likely to generalize across architectures due to high pre-decision CKA. However, findings regarding reasoning circuits in late layers are unlikely to transfer due to the generation gap and architectural dependencies (e.g., MHA vs. GQA differences invisible to global CKA).
• Safety Implications: The assumption that model convergence implies convergence toward truthful representations is unsupported. Convergence may reflect shared failure modes rather than shared truth, necessitating caution in safety evaluations that rely on representational similarity as a proxy for reliability.

The study concludes that diverse language models converge on a shared perceptual representation of inputs but maintain divergent cognitive processes for reasoning, challenging the notion that high representational similarity equates to shared understanding.