Intention Collapse: Intention-Level Metrics for Reasoning in Language Models

TL;DR

This paper introduces intention collapse as a formal two-stage process in language generation, separating rich internal intention formation from an irreversible linguistic collapse. It defines three model-agnostic metrics—Intention Entropy $H_{int}(I)$, Effective Intention Dimensionality $ ext{dim}_{eff}(I)$, and Latent Knowledge Recoverability $ ext{Recov}(I;Z)$—to quantify the pre-collapse state and proposes an empirical program to validate these metrics across inference regimes. An initial GSM8K study shows chain-of-thought substantially improves accuracy while reducing pre-collapse entropy and increasing global dimensionality, and demonstrates latent information about success can be recovered from pre-collapse representations. The work argues that intention-focused metrics can diagnose and guide inference-time computation, bridging cognitive science concepts with scalable AI techniques, while outlining limitations and a roadmap for larger-scale, multi-domain validation.

Abstract

Every act of language generation compresses a rich internal state into a single token sequence. We call this process intention collapse: a many-to-one projection from a high dimensional intention space I into an external language space L. We formalize intention collapse for contemporary language models, define three simple, model agnostic intention metrics (intention entropy Hint, effective dimensionality dimeff, and latent knowledge recoverability Recov), and propose an empirical agenda for studying how inference time computation shapes internal intentions before they are verbalized. We also report a first small scale experiment. Using a 4 bit Mistral 7B model on 200 GSM8K problems, we compare a direct answer baseline, a chain of thought (CoT) regime, and a babble control. CoT raises accuracy from 5.5 percent to 53 percent, sharply reduces pre collapse intention entropy (from 1.42 to 0.37 bits), and shows higher global effective dimensionality than the other regimes despite producing fewer tokens than babble. At the same time, Hint has little item level predictive power, and a linear probe on I achieves AUROC 0.65 in the CoT regime but only about chance in the baseline regime, where it collapses to the majority class. These preliminary results indicate that intention level metrics can distinguish inference regimes and expose latent information that is partly lost during collapse, while also revealing important limitations of our current proxies

Figures (4)

• Figure 1: Conceptual overview of intention collapse. An internal intention state $I = f_{\theta}(x, H)$ aggregates parameters, long-context caches, retrieved memories, and control signals before any token is emitted. A collapse operator $\kappa_{\theta}$ then maps $I$ into a single linguistic trajectory $y_{1:T}$, discarding most of the richness present in $I$. The three intention metrics---entropy $H_{\text{int}}(I)$, effective dimensionality $\text{dim}_{\text{eff}}(I)$, and latent recoverability $\text{Recov}(I;Z)$---quantify different aspects of this pre-collapse state.
• Figure 2: Per-layer effective dimensionality $\text{dim}_{\text{eff}}(I)$ across layers 27--31 for the three inference regimes. The Baseline regime exhibits the largest within-layer dimensionality (approximately 104--110), followed by Babble (78--89) and CoT (68--78). This pattern contrasts with global dimensionality results and suggests a distinction between richness (high per-layer dimensions) and sprawl (unstructured variance that does not aid reasoning).
• Figure 3: Pre-collapse intention entropy $H_{\text{int}}(I)$ distributions stratified by answer correctness for the Baseline and Enhanced (CoT) regimes. In both regimes, entropy shows minimal separation between correct and incorrect answers (Pearson $|r| \approx 0.06$), indicating that $H_{\text{int}}(I)$ is more informative as a regime-level signature than as a per-instance predictor of success.
• Figure 4: Verbalized answer accuracy vs. linear probe accuracy on the pre-collapse intention state $I$ for the Baseline and CoT regimes. In the Baseline regime, the probe attains 93.5% accuracy but simply matches a trivial majority-class baseline (94.5% incorrect answers). In the CoT regime, the same probe reaches 66.0% accuracy compared to 53.0% verbalized accuracy on the same items, indicating that $I$ contains systematically recoverable information about success that is partially lost during collapse.