Surprisal Theory is Tautological (without Rational Grounding)

Surprisal theory is critiqued for being tautological without rational grounding, suggesting that its falsifiability requires restricting the language model to one grounded in non-empirically motivated cognitive principles.

The gist: For any observed pattern of processing difficulty, one can simply construct a language model whose surprisal is an affine function of it.

The Tautology Argument

Surprisal theory claims that processing difficulty is an affine function of the contextual surprisal under some language model q: d(utu<t) = −a log ⃗q(ut u<t) + b(u<t). The paper argues this is a tautology because for any non-negative difficulty measure d, one can construct a language model qd such that its surprisal is an affine function of d: ⃗qd(ut u<t) = exp(−d(ut u<t)). This construction yields the required affine form with a=1 and b(u<t) = − log Z(u<t), where Z is the partition function. This means any pattern of difficulty is consistent with some language model, making surprisal theory unfalsifiable without constraints on q.

The Problem of Grounding

To escape this tautology, the paper argues that one must restrict attention to a family of language models Q and select a q ∈ Q based on non-behavioral cognitive principles. The relevant constraint is the cognitivist assumption, which posits that q should approximate a theoretical construct pH derived from the comprehender’s internal language model, such as memory constraints or processing goals. This moves the grounding problem from selecting an arbitrary language model to choosing Q and q based on independently observable properties of the human mind, rather than reading-time data.

The Scaling Implication and Corpus Assumption

The corpus assumption identifies the target language model as pC, the distribution that generated the training corpus (q = pC). Under this assumption, maximizing a fitness measure M(q) predicts processing difficulty. The scaling implication states that as estimation improves (e.g., via maximum-likelihood estimation), a model q should asymptotically yield surprisal values that better correlate with processing difficulty. However, empirical work suggests this scaling implication is undermined by findings where contextual surprisal from larger models degrades as they become better approximations to pC, contradicting the prediction that pC maximizes M.

The Search for Rationalist Grounding

The paper identifies two main avenues for grounding Q:

1. Lossy-Context Surprisal: This involves replacing the full context u<t with a lossy compression m(u<t) derived from independently motivated assumptions about human memory decay or resource allocation policies, rather than fitting it to reading-time data.

2. Developmentally Plausible Corpora: This strategy restricts training data to corpora such as CHILDES, grounding the corpus choice in language acquisition research rather than reading-time correlations.

Technical Conditions and Consistency

The paper establishes technical conditions for the construction of qd: a non-negative difficulty measure d must satisfy certain properties related to its dependence on context (Proposition 1). Specifically, if d(EOS u) is bounded by a function f(u + 1) and P∞t=1 exp(−f(t)) = ∞, then qd is tight. Furthermore, if f is constant (i.e., d(EOS u) ≤ C), then qd has finite expected length, which is a necessary technical condition for the scaling implication to hold consistently across the family Q. The consistency of the Maximum Likelihood Estimator (MLE) convergence to the KL projection of pC onto Q is shown under compactness and uniform domination conditions.

Conclusion

The paper concludes that without further constraint on q, surprisal theory remains unfalsifiable. The empirical undermining of the scaling implication suggests that the corpus assumption is falsified, necessitating a rationalist intervention where q is grounded in cognitive aspects of the comprehender rather than behavioral data. This move mirrors the resolution found in evolutionary biology's propensity interpretation of fitness.

Limitations

The argument is conceptual and mathematical, not experimental. Limitations include: (1) The robustness of the falsification relies on specific empirical findings (Oh and Schuler, 2023). (2) The sufficient condition for Proposition 1 is mild and likely satisfied by many realistic measures but has not been empirically verified for specific datasets. (3) The grounding problem is identified but not solved, with proposed solutions like lossy-context surprisal remaining partial. (4) Theorem 1 assumes a perfect optimizer, which may be unattainable in practice due to non-convex optimization landscapes. (5) The analogy to evolutionary biology is structural rather than exhaustive.

Acknowledgements

The authors thank several individuals for helpful discussion and feedback on earlier drafts of the paper.

Based on the provided paper, here are specific improvements that can be made to AI systems by fundamentally re-grounding surprisal theory in cognitive constraints rather than purely empirical data.

The core improvement is shifting from an empirically validated but tautological framework (where any difficulty pattern can be explained by some model) to a constrained, falsifiable one based on the comprehender's internal architecture.

) 1. Shift from Empirically Driven Models to Cognitively Grounded Language Models (The Rationalist Intervention):

A key improvement is moving away from the implicit assumption that the relevant language model is simply the distribution that generated the training corpus (the corpus assumption, §1.3). Instead, AI systems should be guided by models derived from non-empirically motivated cognitive constraints, such as:

• Using models based on explicit memory constraints (e.g., Timkey and Linzen's work) to define context degradation rather than simply fitting the corpus statistics.

• Incorporating parsing strategies or working memory capacity directly into the model architecture (e.g., single self-attention heads mirroring cue-based retrieval theories).

) 2. Develop Lossy Context Architectures for Better Incremental Processing:

The paper suggests replacing full context with a lossy compression function, where the compression itself is motivated by human memory decay rather than just minimizing reading time error.

• AI systems can be designed with mechanisms that explicitly model context forgetting (deletion noise process, as proposed by Futrell et al., 2020).

• This allows the system to predict processing difficulty based on a rational analysis of the comprehender’s processing problem (resource allocation), leading to predictions that are fine-grained and cognitively plausible, even if they deviate from standard surprisal measures.

) 3. Implement Model Selection Based on Structural Commitments (Constraining Q):

The tautology arises because the set of possible language models, Q, is unconstrained. Improvements should involve selecting a specific family of models (Q) based on their structural commitments:

• If the system is intended to model syntax, restrict Q to Probabilistic Context-Free Grammars (PCFGs) or similar formalisms (Hale's Principle 1).

• If the system is intended for long-term dependency tracking, prioritize recurrent architectures (like LSTMs) over purely feed-forward transformers. This moves the choice of model from which architecture is in vogue to which architecture aligns with the cognitive mechanism.

) 4. Establish a Falsifiable Prediction via Model Evolution:

The scaling implication (Proposition 2), which predicts that better models should yield better fits, has been empirically contradicted by findings showing degradation as models approach the true distribution.

• AI development pipelines should include model fitness metrics that track this non-monotonic relationship. This forces researchers to ask: Is the degradation due to a mismatch between training data (corpus) and cognitive reality, or is it an artifact of model approximation?

• The goal becomes identifying the point where corpus fit degrades, signaling that the underlying cognitive assumption (the corpus assumption) is violated, thereby pinpointing the necessary rationalist intervention.

These improvements result in AI systems that are not just better at predicting reading times, but systems whose internal language modeling reflects a more accurate, constrained understanding of how human cognition actually processes language under resource limitations.