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Transformer Injectivity: Proving Input Recovery from Hidden States
Source: https://t.co/2whXzzCZfr
This extensive report challenges the common assumption that Transformer-based Large Language Models are inherently "lossy," arguing instead that the mapping from a discrete input prompt to its continuous internal representation in decoder-only architectures (like GPT) is almost-surely injective. The central thesis is supported by a rigorous mathematical proof demonstrating that the Transformer function is real-analytic, which confines potential information-collapsing events to a set of measure zero that standard training does not enter.
Empirical evidence further validates this by showing no collisions—where two distinct inputs yield the same hidden state—in billions of comparisons across state-of-the-art models. Crucially, this injectivity implies that the encoding is invertible, a property demonstrated by the SIPIT algorithm which can perfectly reconstruct the original input from the model's hidden states.
The findings have major implications for safety and privacy, as they establish that hidden states must be treated with the same security as raw personal data, though practical methods like quantization can break this lossless guarantee.
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By Benjamin Alloul 🗪 🅽🅾🆃🅴🅱🅾🅾🅺🅻🅼Source: https://t.co/2whXzzCZfr
This extensive report challenges the common assumption that Transformer-based Large Language Models are inherently "lossy," arguing instead that the mapping from a discrete input prompt to its continuous internal representation in decoder-only architectures (like GPT) is almost-surely injective. The central thesis is supported by a rigorous mathematical proof demonstrating that the Transformer function is real-analytic, which confines potential information-collapsing events to a set of measure zero that standard training does not enter.
Empirical evidence further validates this by showing no collisions—where two distinct inputs yield the same hidden state—in billions of comparisons across state-of-the-art models. Crucially, this injectivity implies that the encoding is invertible, a property demonstrated by the SIPIT algorithm which can perfectly reconstruct the original input from the model's hidden states.
The findings have major implications for safety and privacy, as they establish that hidden states must be treated with the same security as raw personal data, though practical methods like quantization can break this lossless guarantee.