Understanding Intention Collapse

• Intention collapse is the irreversible reduction of rich, multidimensional internal states—such as intentions, concepts, and latent knowledge—into a singular external output.
• It is quantified using model-agnostic metrics like intention entropy, effective dimensionality, and latent knowledge recoverability to assess the extent of information loss.
• This phenomenon spans multiple domains including neural language generation, decision theory, requirements engineering, and quantum measurement, influencing both theoretical models and practical applications.

Intention collapse refers to the irreversible compression of a rich, high-dimensional set of internal states—intentions, concepts, latent knowledge—into a single observable or externalized behavior, answer, or output. This phenomenon is observed across domains: in neural language generation, human-computer interaction, decision-making theory, requirements engineering, quantum measurement, and formal logic. Intention collapse is both a technical and philosophical construct: it captures the unavoidable loss of nuance and latent structure that occurs when internal reasoning, desire, or knowledge must be externalized in a way that is verifiable or communicable (Vera, 3 Jan 2026, Khaitovich et al., 27 Nov 2025, Jureta, 2017, Kremnizer et al., 2014, Ilboudo et al., 29 Dec 2025).

1. Formalization of Intention Collapse in LLMs

Intention collapse in LLMs is mathematically described as a many-to-one projection from a high-dimensional intention space $\mathcal{J}$ to an external language space $\mathcal{L}$ (Vera, 3 Jan 2026). The process is formalized by the function

$$\kappa : \mathcal{J} \times C \rightarrow \mathcal{L}$$

or, for deterministic mapping,

$$f : \mathcal{J} \rightarrow \mathcal{L}, \quad f(I) = y_{1:T}$$

where $I \in \mathcal{J}$ is the internal state and $y_{1:T}$ is the emitted token sequence. The mapping $f$ is not invertible—multiple distinct internal intentions may project to the same external output, guaranteeing the loss of internal nuance, alternatives, and latent knowledge.

To quantify the severity of intention collapse, (Vera, 3 Jan 2026) introduces three orthogonal, model-agnostic metrics:

• Intention Entropy ($H_{\text{int}}$): The entropy of the output distribution immediately before emission, defined as $$H_{\text{int}}(I) = -\sum_k p(y_1=k|I, x) \log p(y_1=k|I, x)$$. High $H_{\text{int}}$ indicates many plausible continuations; low $H_{\text{int}}$ signals a committed plan.
• Effective Dimensionality ($d_{\text{eff}}$): The minimal $k$ such that the top $k$ principal components account for $90\%$ variance in hidden activations during reasoning. High $d_{\text{eff}}$ reflects multifaceted intentions.
• Latent Knowledge Recoverability ($\text{Recov}$): The accuracy/AUROC of a linear probe on $I$ to predict downstream targets $Z$ (e.g., answer correctness). High $\text{Recov}$ means critical knowledge is encoded but may be lost in collapse.

For empirical context, chain-of-thought (CoT) regimes induce lower intention entropy ($H_{\text{int}}$ fell from $1.42$ to $0.37$ bits), higher effective dimensionality ($d_{\text{eff}}$ rose to $2.85$), and improved probe AUROC beyond verbalized accuracy, indicating richer and more decisive internal states that outstrip what is spoken (Vera, 3 Jan 2026).

2. Decision Theory: Collapse as Mode-Seeking Inference

In hierarchical decision models, intention collapse is formalized as the selection of a unimodal approximation to a multimodal underlying intent–action distribution (Ilboudo et al., 29 Dec 2025). Let $p(x)$ be the mixture over decision regions; the agent must commit to a single intent–action pair by minimizing a weighted sum of reverse vs. forward KL divergences:

$$\mathcal{F}[q] = (1-\lambda) D_{\text{KL}}[q(x)\|p(x)] + \lambda D_{\text{KL}}[p(x)\|q(x)]$$

with $\lambda\in[0,1]$. Setting $\lambda=0$ (reverse KL, mode-seeking) yields rapid intention collapse: $q^*$ collapses onto one mixture component. Setting $\lambda=1$ (forward KL, mode-covering) means indecision persists, as $q^*$ covers all modes and may fail to select an option.

Dynamic drift–diffusion models show that when option values are similar (intent or affordance saturation), mode-covering inference produces extremely slow or failed commitment—empirically modeling decision inertia and shutdown (Ilboudo et al., 29 Dec 2025). Thus, intention collapse in this setting is governed by the relative weights of exploration versus exploitation in probabilistic inference, with sharp commitment representing rapid collapse.

3. Collapse of Intentional Concepts in Requirements Engineering

In requirements engineering, intention collapse arises from the epistemic impossibility of verifying stakeholders’ internal intentional states (Jureta, 2017). The Non-Verifiability Proposition (NVP):

$$\forall s \in \text{Stakeholders}, \forall t \in \text{Time}: \neg K(I_s(t))$$

holds for all agents $s$ at all times $t$: actual intentions can be believed but never known. This undermines the use of goal, intention, desire, and belief as meaningful requirements artifacts. Six pathologies follow:

1. Non-verifiable intentionality: Goals are representations but unverifiable.
2. Uncertain intentionality: Future-oriented requirements reference unknowable states.
3. Speculative intentionality: Novel systems induce guesswork about future intentions.
4. Expiring intentionality: Intentions evolve, invalidating requirements.
5. Distorted intentionality: Strategic communication masks genuine states.
6. Incomplete intentionality: Critical aspects are omitted or forgotten.

The resulting collapse shifts requirements engineering toward a hypothesis-driven discipline: requirements become falsifiable empirical claims with time-stamping, observable verification, and continuous risk monitoring. Intentional concepts are deprioritized in favor of persistent evidence-based practices (Jureta, 2017).

4. Logical Collapse in Intention Formalism

Standard modal logics of intention validate closure principles (closure under entailment or equivalence): if $\phi \leftrightarrow \psi$, then $I\phi \leftrightarrow I\psi$. This forces agents to intend all logical consequences and side-effects, resulting in intention collapse—agents cannot differentiate intended from unintended, but necessary, side-effects (Khaitovich et al., 27 Nov 2025).

The hyperintensional logic of intention addresses this by introducing an atomic semilattice of decision problems $(P, \oplus)$ and a solution map $s: \text{CPL} \to \mathcal{P}(P)$. The modal semantics demand:

$$M, w \models I\alpha \iff (\forall v: wRv \Rightarrow M,v\models \alpha) \quad \text{and} \quad f(w)\in s(\alpha)$$

Axioms block collapse under both entailment and equivalence, preserving restricted closure, consistency, and agglomeration, and allowing agents to intend $\phi$ without necessarily intending all $\psi$ such that $\phi \leftrightarrow \psi$. Strong completeness and soundness are established for problem-sensitive models (Khaitovich et al., 27 Nov 2025).

5. Intention Collapse in Quantum Measurement

Integrated information-induced collapse models replace physical size as the driver of quantum collapse with quantum Integrated Information (QII) (Kremnizer et al., 2014). QII, for a state $\rho$, is

$$\Phi(\rho) = \inf_{\text{partitions }\varphi} S\left( \rho \, \| \, \bigotimes_{i=1}^N \rho_i \right)$$

where $S$ is quantum relative entropy. Collapse rate $\lambda \equiv \lambda(\Phi(\rho))$ increases with QII, capturing the system’s capacity to act as an observer. Systems with high QII self-induce collapse; low QII systems remain unitary. This formalizes observer-driven, non-subjective intention collapse in physical theory.

Experimentally, deviations from quantum theory occur for systems with large $\Delta\Phi$, regardless of mass. Systems with equal mass but different QII exhibit different collapse rates, distinguishing this framework from mass-dependent collapse models (Kremnizer et al., 2014).

6. Empirical and Practical Implications

Intention collapse is both theoretically inevitable and empirically partial: in neural models, chain-of-thought increases internal richness but still fails to externalize all latent knowledge; in quantum models, collapse is a function of informational structure; in decision theory, mode-seeking yields crisp commitment but discards alternatives; in requirements engineering, unfalsifiable goals are replaced by verifiable hypotheses.

Limitations of current metrics and proxies are acknowledged: intention entropy, effective dimensionality, and recoverability do not capture fine-grained modalities or all circuits relevant to reasoning (Vera, 3 Jan 2026). Broad empirical agendas include assessing intention collapse across architectures, learning state-dependent decoding policies, and exploring mitigations such as structured internal scratchpads, all to make intention collapse more observable, controllable, and interpretable.

The unifying theme is the transformation of rich, irreducibly multidimensional internal states into constrained, externalizable forms, delimiting what is recoverable, knowable, or actionable in any system where intention must be collapsed for communication, action, or measurement.