The Platonic Representation Hypothesis: Are AI Models Converging on Universal Representations? Nov 17, 2024

The Evidence for Convergence #

The researchers present several compelling pieces of evidence that AI representations are converging:

1. Cross-Model Alignment: Different neural networks, even when trained on different tasks and datasets, increasingly represent information in similar ways. As models get bigger and better, they tend to become more aligned with each other.

2. Cross-Modal Alignment: Perhaps most surprisingly, language models and vision models are developing similar internal representations. The better a language model gets at processing text, the more its representations align with those of vision models, and vice versa.

3. Brain Alignment: These AI representations are also increasingly aligning with how biological brains process information, suggesting they may be discovering fundamental principles about how to represent the world.

How Do You Measure “Similar”? #

“Represent information in similar ways” needs a number, and the paper makes it precise. The trick is to compare kernels, not features. Two models can use completely different coordinates, even different dimensions, and still agree on which inputs are close to which.

A representation is a function $f : \mathcal{X} \to \mathbb{R}^n$ that maps each input (an image, a sentence) to a feature vector. Its kernel records how it measures similarity between inputs:

$$K(x_i, x_j) = \langle f(x_i), f(x_j) \rangle .$$

A kernel-alignment metric $m(K_1, K_2)$ scores how similar two kernels are, for example those of a vision model and a language model evaluated on the same inputs (or on paired inputs, like an image and its caption). The paper’s main choice is the mutual $k$-nearest-neighbour metric. Take $n$ paired samples with features $\phi_i$ from the first model and $\psi_i$ from the second. Let $\mathcal{S}(\phi_i)$ be the set of indices of the $k$ nearest neighbours of $\phi_i$ among the other $\phi_j$, and define $\mathcal{S}(\psi_i)$ the same way. Then

$$m_{\mathrm{NN}} = \frac{1}{n} \sum_{i=1}^{n} \frac{1}{k}\, \big|\mathcal{S}(\phi_i) \cap \mathcal{S}(\psi_i)\big| \in [0, 1],$$

the average fraction of neighbours the two models agree on. The paper uses $k = 10$. A value of $1$ means both models induce the same neighbourhood structure. Two unrelated random embeddings score about $k/(n-1)$.

A popular alternative, which the paper also discusses, is centered kernel alignment (CKA). Let $K$ and $L$ be the $n \times n$ kernel matrices of the two models on the same inputs, and let $C = I - \frac{1}{n}\mathbf{1}\mathbf{1}^\top$ be the centering matrix. With the Hilbert-Schmidt independence criterion $\mathrm{HSIC}(K, L) = \operatorname{tr}(K C L C)/(n-1)^2$,

$$\mathrm{CKA}(K, L) = \frac{\mathrm{HSIC}(K, L)}{\sqrt{\mathrm{HSIC}(K, K)\,\mathrm{HSIC}(L, L)}} .$$

For linear kernels and column-centered feature matrices $A \in \mathbb{R}^{n \times p}$ and $B \in \mathbb{R}^{n \times q}$, this reduces to $\lVert B^\top A \rVert_F^2 / \big(\lVert A^\top A \rVert_F \,\lVert B^\top B \rVert_F\big)$. CKA is invariant to rotations and isotropic scaling of either feature space, which is exactly the freedom we want to ignore when asking whether two models “see” the same structure. The mutual-NN metric goes further and only looks at local neighbourhoods.

The paper also has a candidate for where the kernels converge. For a contrastive learner trained to tell co-occurring observations apart from independent ones, it argues that the learned kernel approaches the pointwise mutual information of co-occurrence, up to a constant: $\langle f(x_a), f(x_b) \rangle \approx \log \frac{P_{\text{coor}}(x_a, x_b)}{P(x_a)P(x_b)} + c$. That kernel depends on the world’s statistics, not on the modality, so it is a concrete version of the “ideal form” from the cave metaphor.

Why Is This Happening? #

The researchers propose three key mechanisms driving this convergence:

1. Task Generality: As models are trained on more diverse tasks, they’re forced to develop representations that capture fundamental aspects of reality that are useful across many different problems.

2. Model Capacity: Larger models have more flexibility to find optimal representations, making them more likely to converge on similar solutions.

3. Simplicity Bias: Neural networks naturally prefer simpler solutions, and as models get bigger, this bias toward simplicity actually gets stronger, pushing them toward shared, elegant representations.

What Does This Mean? #

If this hypothesis is correct, it has several important implications:

• Training data can be shared across modalities - images could help train better language models and vice versa
• Translation between different modalities (like text-to-image or image-to-text) should become easier
• As models scale up, they may naturally reduce problems like hallucination and bias
• We may be approaching a fundamental computational representation of reality. Wow!

This work suggests we may be witnessing the emergence of a universal way of representing knowledge - something akin to Plato’s concept of ideal forms, but discovered through machine learning.

The paper’s central metaphor draws from Plato’s Allegory of the Cave: just as Plato suggested there was an ideal reality behind our sensory experiences, these researchers suggest there may be an ideal computational representation of reality that different AI models are gradually discovering.

References #

• 13. Huh, B. Cheung, T. Wang, P. Isola (2024). The Platonic Representation Hypothesis. arXiv:2405.07987
• 19. Kornblith, M. Norouzi, H. Lee, G. Hinton (2019). Similarity of Neural Network Representations Revisited. ICML. arXiv:1905.00414