Evidence and Intervention: A Coupled Active-Inference Extension of Rational Speech Act Models

1. Introduction

• Active inference separates current-state inference and parameter learning from prospective policy evaluation and policy-prior learning in the proposed pragmatic architecture.Variational free energy characterizes inference about observations and model parameters; expected free energy evaluates policies by predicted epistemic and preferred-outcome consequences.Source: §1 · p. 2
• RSA models commonly fix states, utterance alternatives, semantics, utility, costs, and recursion depth before calculating production or interpretation distributions.Additional assumptions are needed to distinguish current-state inference from parameter learning, model how unexpected responses change later actions, and represent habits or longer-horizon policies.Source: §1 · p. 3
• The architecture is not itself a theory of pragmatics: explanatory predictions require specified linguistically and interactionally motivated states, observations, transitions, preferences, and policies.It is presented as a constrained process architecture, not a derivation of pragmatic theory from the free-energy principle alone.Source: §1 · p. 3
• Because discourse combines many possible referents, interpretations, goals, stances, and partner models, the account distinguishes exact model posteriors from tractable beliefs a bounded agent can compute.The distinction matters beyond experiments with small sets of states and utterance alternatives.Source: §1 · p. 4

1.1. The grammatical-pragmatic division of labor

• The model begins with structured utterance candidates already available and treats their communicative use as evidence about discourse-relevant causes, rather than explaining how linguistic objects are constructed.Its scope is communicative use, not deriving grammatical principles or the formal properties of human syntax.Source: §1 · p. 4, §1.1 · p. 4

1.2.1. Gricean and probabilistic pragmatics

• The model retains probabilistic pragmatics’ Gricean assumptions but changes its architecture by incorporating the partner’s choice distribution into the observer’s generative model and separating post-response updates.Those updates concern current pragmatic state, persistent partner parameters, policy evaluation, and habit.Source: §1.2.1 · p. 5

1.2.2. Relevance Theory

• Active inference has limited parallels with Relevance Theory, but cognitive effects, processing effort, and optimal relevance are not equivalent to information gain, VFE complexity, or arbitrary EFE minimization.The account is proposed as a possible process-level implementation space for making relevance-theoretic hypotheses explicit and comparable.Source: §1.2.2 · p. 5

1.2.3. Dynamic context, QUD, and commitments

• The model distinguishes interaction-level context—including QUD, commitments, turn position, and joint activity—from partners’ private referential, interpretive, goal, and stance variables.Participants may hold uncertain or divergent beliefs about the public record.Source: §1.2.3 · pp. 5–6

1.2.4. Grounding, repair, and sequence organization

• Grounding, repair, and closing provide graded evidence in organized sequences, so active-inference policies must extend across actions rather than reduce discourse moves to one-step utterances.Acknowledgment, relevant next actions, repair initiation, reformulation, and acceptance help establish whether a contribution has entered the interactional record.Source: §1.2.4 · p. 6

1.2.5. Audience design and partner adaptation

• Partner adaptation motivates separating a rapidly changing posterior over present state from slower partner-parameter learning, and testing whether adaptation is partner-specific, generalizes, or persists under task or time-pressure changes.The proposed distinctions address immediate effects as well as effects that persist across repeated interaction and become conventionalized within a dyad.Source: §1.2.5 · p. 6

1.2.6. Social meaning, indirectness, and noncooperation

• Communicative preferences can include task success, commitments, social consequences, and action coordination, allowing indirectness or noncooperation rather than assuming accurate transfer or alignment is always sought.The generative model may attribute different preferences, reliabilities, and degrees of cooperativity to different partners.Source: §1.2.6 · p. 6

1.3. Active inference, social coupling, and communication

• The proposed architecture embeds a partner’s policy distribution in the observer’s action likelihood, separates four update targets, specifies a restricted RSA correspondence, and distinguishes outcome values, temporal bias, and habit.The four targets are current-state inference, partner-model learning, policy evaluation, and habitual priors; the distinctions matter even when components are statically equivalent within a one-step RSA score.Source: §1.3 · p. 7

1.4. Model overview and contributions

• Distinct updates within the architecture can produce conversational repair, partner adaptation, persistent misunderstanding, and discourse termination.The model treats these as consequences of different updates rather than a single undifferentiated pragmatic state.Source: §1.4 · p. 8
• Under explicit restrictions, the model recovers the RSA speaker and pragmatic listener distributions, embedding RSA without uniquely deriving it from the free-energy principle.The restrictions include a fixed finite state and utterance space, fixed partner model, exact inference, stable preferences and precision, and an RSA-matched expected-free-energy parameterization.Source: §1.4 · p. 8
• Outcome preferences, comprehension likelihood, context-sensitive temporal price, and learned habit receive distinct causal roles, although restricted one-step conditions let temporal price reproduce an RSA cost.Removing a deadline, changing partners, or repeatedly practicing a policy yields different immediate and carryover predictions.Source: §1.4 · pp. 9–10
• Interpretation and production form one coupled computation: an utterance is evidence about a partner’s policy and an intervention on the listener’s next move.The listener’s likelihood for an utterance is the choice rule it attributes to the speaker.Source: §1.4 · p. 10
• Pragmatic knowledge is organized by update target: reference, sense, and force resolve within turns; partner traits accumulate across turns; habits persist across conversations; deadlines set the price of time.Expected free energy is recomputed as beliefs and context change, while partner-model learning and habitual policy priors have more persistent characteristic timescales.Source: §1.4 · pp. 9–10

2. Active Inference Quantities

• A discrete partially observable Markov decision process distinguishes hidden states, observations, actions, model parameters, and policies.Given observations, an agent represents a tractable posterior over hidden states and minimizes variational free energy.Source: §2 · pp. 10–11
• Inference updates beliefs about hidden causes, whereas learning changes model parameters such as θ.The distinction is defined by the variable updated, not by a universal temporal boundary; state beliefs often change faster than partner-model parameters.Source: §2 · p. 11
• Expected free energy prospectively evaluates policies through expected information gain and predicted outcomes under prior preferences.Policies with greater information gain and more preferred predicted outcomes have lower expected free energy under the stated sign convention.Source: §2 · p. 11
• A policy posterior can combine a policy prior, evidence already available, and prospective expected free energy.Prior probability and prospective ranking remain distinct: a frequently selected policy can retain high prior probability even when it is no longer prospectively optimal.Source: §2 · pp. 11–12
• The policy prior is parameterized as a normalized product of a learned habitual baseline and a context-sensitive temporal factor.The habitual component is updated from policy history, whereas the temporal factor changes with the current deadline or opportunity context.Source: §2 · p. 12

3. Discourse as Coupled Active Inference

• An agent models a partner’s action likelihood as that partner’s policy posterior, embedding the partner’s expected free energy within its own variational and expected free-energy functionals.Source: §3 · p. 12

3.1. A coupled perception-action loop between two agents

• Turn-as-macro-action yields a one-step correspondence with RSA, while longer policies let agents evaluate communicative moves by their impact on common ground and task goals.Source: §3.1 · p. 13
• Dialogue forms a recursive perception-action loop in which each participant interprets the other’s action and conditions its next policy on the resulting posterior.Source: §3.1 · pp. 13–14

3.2. Inferring discourse states from another agent’s actions

• Rather than collapsing meaning into one intention, the model distinguishes linguistic form, interaction context, partner-private states, and parameters, creating a structured hypothesis space in which dependencies can be specified, learned, and tested.Source: §3.2 · pp. 14–15

3.3. Exact Bayesian inference and a tractable posterior 𝒒

• Natural discourse’s combinatorially large latent space makes exhaustive normalization implausible, so an agent may use a tractable posterior that reflects what it can represent or compute.Source: §3.3 · pp. 15–16
• Standard finite RSA updates are recovered when the variational family is sufficiently expressive and optimization sufficiently accurate, making exact and tractable posteriors effectively coincide.Source: §3.3 · p. 16
• The distinction between an exact posterior and the agent’s tractable posterior is essential.Source: §3.3 · p. 16

3.4. The basic correspondence with the RSA listener

• The model’s likelihood derives from the active-inference policy posterior attributed to the speaker, giving the pragmatic listener the same basic Bayesian structure as RSA.Source: §3.4 · p. 16

3.5. Learning a partner-specific generative model

• Current partner-state inference and learning persistent partner-model parameters are distinct updates within a common coupled generative model.The learned parameters can govern partner-specific likelihoods, transitions, reliability, preferences, policy precision, conventions, and habitual policy propensities.Source: §3.5 · p. 18
• The model retains one normalized policy prior, combining a learned habitual baseline with a context-sensitive factor that changes with deadline or opportunity conditions.The context-sensitive factor is not itself a persistent partner parameter or a second independently learned prior.Source: §3.5 · p. 18

3.6. The speaker B’s policy posterior as listener A’s likelihood

• The listener’s likelihood for an observed action is induced by the policy distribution attributed to the speaker, marginalizing over temporally extended policies compatible with that action.When a whole conversational turn is identified with a one-step policy, this reduces to a useful limiting case for comparison with RSA.Source: §3.6 · pp. 18–19
• To avoid circular explanation, the attributed policy must be constructed from information available before the action; observing it then updates the partner model and future policy evaluation.Source: §3.6 · p. 19

3.7. The listener A’s variational free energy contains the speaker B’s expected free energy

• The listener’s variational free energy contains the expected free energy attributed to the speaker through the likelihood of the speaker’s action, not through joint minimization of both agents’ free energies.The state-dependent normalization term compares the action’s score with alternative policies and is not a removable constant.Source: §3.7 · pp. 20–21
• The same utterance can be interpreted differently across turns because the listener can revise beliefs about what the speaker believes, learns, and values relative to alternatives.These are quantities the listener may be wrong about, unlike the fixed recursion-depth assumptions and absent information-gain term described for an RSA listener.Source: §3.7 · p. 21

3.8. Expanding the attributed information gain and pragmatic value

• An agent’s attributed evaluation of its partner’s action depends on how the partner is believed to have interpreted the agent’s preceding action, as well as the partner’s expected information gain and preferred outcomes.The evaluation embeds the partner’s expected free energy in the agent’s interpretation of the observed action.Source: §3.8 · pp. 22–23

3.9. Separating A’s predictive and counterfactual posterior beliefs

• For each candidate policy, the agent forms a predictive belief and constructs a counterfactual posterior for each possible future outcome, using exact Bayesian updating or a variational projection.The counterfactual update uses the predictive belief as its prior; expected information gain compares the resulting posterior with that belief.Source: §3.9 · p. 24
• Expected free energy ranks policies by averaging epistemic and preference consequences of hypothetical updates; it is distinct from retrospective variational free energy and its naive expected counterfactual counterpart.Under exact inner inference, the counterfactual divergence vanishes and the counterfactual variational free energy reduces to predictive surprisal, whose average is predictive-outcome entropy.Source: §3.9 · pp. 25–26

3.10. Generating B’s response recursively inside A’s EFE

• The response likelihood is generated recursively: the agent models how its partner reads its action and then models the partner’s response, without treating the attributed posterior as the partner’s objective mental state.The agent’s candidate model of the partner’s response policy generates a predictive belief about the agent’s subsequent state.Source: §3.10 · p. 26
• A evaluates candidate policies under its own EFE using a recursively generated response distribution that preserves uncertainty about what B observes and which policy B selects.A’s action shapes B’s possible observation; the attributed observation and policy posterior shape B’s response, which enters A’s prospective evaluation.Source: §3.10 · p. 28

3.11 Recursive interdependence without an alignment objective

• Recursive interdependence is a dependency between generative processes, not an alignment objective: compatible models and preferences can stabilize interaction, while conflict or model misspecification can sustain disagreement or divergence.Source: §3.11 · p. 29

3.12. A restricted correspondence with RSA

• The coupled architecture recovers RSA speaker and pragmatic-listener calculations in a restricted one-step, exact-inference limit, without claiming that active inference uniquely derives RSA.Source: §3.12 · p. 30
• Under a restricted one-step parameter mapping, softmax normalization recovers the RSA speaker and Bayes’ rule yields the RSA pragmatic listener.The correspondence fixes temporal, learning, and recursion variables; it establishes equality of normalized distributions, not a unique causal allocation of RSA terms.Source: §3.12 · p. 32
• Unlike RSA, the model assigns the speaker information gain from a listener’s reply, which varies across alternatives when the speaker is uncertain about the partner.In the restricted correspondence, this information gain is common across alternatives; outside that condition, it can affect choice.Source: §3.12 · p. 32
• The RSA correspondence is restricted and static, and does not identify a unique causal location for each reduced-form RSA term.The parameter mapping is for the RSA comparison, not a claim that the identities hold for active inference in general.Source: §3.12 · pp. 31–32

3.13. Linguistic interpretation of the architecture

• The architecture assigns linguistic distinctions to variables with different update targets, transition structures, and temporal signatures.Reference hypotheses, lexical interpretations, speech-act force, QUD, commitments, stance, and partner reliability are treated as distinct sources of uncertainty.Source: §3.13 · pp. 32–33
• Reference beliefs can update rapidly and need not persist, while speech-act interpretation, relevance, and public commitments depend on activity, discourse questions, and uptake.Indirect-act value can vary with social preferences at fixed literal informativeness; uptake can change the public record despite private uncertainty.Source: §3.13 · p. 33
• Clarification targets the latent factor whose resolution most changes future action, repair depends on mismatch type and location, and partner-learning effects can persist across turns.Partner-specific evidence can also produce persistent stance expectations.Source: §3.13 · p. 33
• Repeatedly successful forms can gain persistent policy-prior support, while politeness and indirectness vary with social stakes and deception can yield low free energy without belief alignment.Whether convention produces shorter expressions depends on the policy set and temporal assumptions.Source: §3.13 · p. 33
• The proposal gains empirical support if selective persistence, partner specificity, factor-targeted clarification, and policy reversal follow targeted manipulations rather than static RSA predictions.If outcome-value, capacity, time-pressure, and policy-history manipulations have indistinguishable immediate and carryover effects, or static RSA predicts responses without added terms, the richer machinery may be unnecessary.Source: §3.13 · pp. 33–34

4.1 Static reparameterization of E and PV

• Reweighting E and compensating PV leaves the policy posterior unchanged, so cross-sectional choices cannot identify the bias source; longitudinal data, transfer, and interventions can distinguish them.Although E and PV are generatively different, their causal sources are not identifiable from a single choice distribution.Source: §4.1 · p. 35

4.2. Outcome-valued factors represented through PV

• Factorized prior preferences let PV add values for task completion, partner response, effort, fatigue, or acceptance; interacting outcome dimensions require retaining joint preferences.Additivity depends on the stated factorization of prior preferences.Source: §4.2 · pp. 35–36
• Listener capacity and channel noise affect likelihood, uncertainty resolution belongs to IG, and production difficulty may enter PV, action likelihood, or policy duration as rival causal models.These influences should not be collapsed merely because they can yield similar behavior.Source: §4.2 · p. 36
• Although elapsed time could be represented as a PV outcome, this model reserves PV for terminal consequences and assigns residual how-fast policy bias to a contextual temporal factor.The temporal factor modulates policy bias concerning how quickly matched consequences are reached.Source: §4.2 · p. 36

4.3. Terminal equivalence and the residual temporal difference

• Under strong terminal-equivalence conditions, short and full policies have equal terminal information gain and pragmatic value yet may differ in duration, which a contextual temporal factor can represent.The separation makes explicit whether an effect changes immediately with a deadline or persists because a policy has been learned.Source: §4.3 · pp. 36–37

4.4. Separating communicative benefit from the price of time

• With equal habitual priors and positive temporal price, the shorter policy is preferred; in a restricted one-step comparison, the temporal factor can match an RSA temporal cost without identifying its cause.The causal interpretations diverge when temporal context or policy history is manipulated.Source: §4.4 · p. 38

4.5. Contextual temporal policy factors and learned habitual priors

• Contextual temporal factors change immediately with deadlines or opportunity costs, whereas learned habitual policy priors reflect accumulated selections and may persist.The two influences entering the policy prior have different causal sources and update rules.Source: §4.5 · pp. 38–39
• Temporal context transiently shifts policy selection, whereas repeated selections can build a habitual bias that persists after a one-off deadline is removed.The two contributions to a current policy prior are not identifiable from cross-sectional choice alone; their distinction becomes meaningful under intervention and learning.Source: §4.5 · p. 39

4.6. Listener capacity and over-compression

• Communicative efficiency is partner-relative: a policy can be too short to resolve its target, too dense for the listener to process, or too long for its marginal benefit.Listener capacity changes the policy-to-outcome likelihood rather than adding a separate utterance cost.Source: §4.6 · p. 40

4.7. Evidence arrival and the speed of variational updating

• Policies that supply the same sufficient statistics may reach the same posterior at different clock-time speeds, while diagnostic information unique to a longer policy can yield unequal terminal posteriors.This proposed link between linguistic evidence arrival and belief-updating dynamics is an additional process hypothesis, not a consequence of the free-energy principle alone.Source: §4.7 · pp. 40–41

4.8. Experimental identification and stopping

• Clarification can be rejected despite positive information gain and lower expected free energy when its expected improvement per unit time falls below the current temporal opportunity rate.The section proposes testing this causal allocation through manipulations of outcome values, deadlines, repeated deadline training, listener capacity, and terminal-equivalent policies.Source: §4.8 · pp. 41–42
• Static policy scores can yield the same one-step utterance distribution under different allocations, but the proposed causal account predicts responses to temporal intervention, repeated selection, partner change, and transfer.It assigns outcome-valued consequences to pragmatic value, uncertainty resolution to information gain, outcome-generation constraints to the likelihood, learned policy propensity to habit, and residual duration context to the temporal factor.Source: §4.8 · p. 42
• The proposed allocation places outcome value in pragmatic value, uncertainty resolution in information gain, generation constraints in the likelihood, learned propensity in habit, and residual duration context in the temporal factor.The allocation is a causal modeling commitment, not a unique or exhaustive decomposition of static RSA terms.Source: §4.8 · pp. 42–43

6. Linguistic and Empirical Implications

• A conversational move is both evidence about its producer and an intervention on the interaction, so pragmatic competence extends beyond inferring speaker meaning.The resulting posterior should shape predictions about uptake, repair, commitment, and action.Source: §6 · p. 59
• Active inference separates current-state inference, parameter learning, prospective policy evaluation, and habit while keeping these processes coupled.The section argues that the framework should be judged by whether this integration yields predictions unavailable from a simpler model.Source: §6 · p. 59

6.1. Empirical dissociations

• A factorial research program can match manipulations on immediate utterance probability while testing different learning, persistence, and interaction signatures.This program draws on dialogue research about grounding, turn-taking, repair, and closing, and audience-design research about partner-specific learning and convention formation.Source: §6.1 · p. 59, §6 · p. 59

1. One-off deadline

• Increasing the current temporal opportunity rate should shift probability toward shorter policies when terminal consequences and habitual support are matched.Source: §1 · p. 60
• Removing the deadline before substantial repeated selection has accumulated should return the temporal factor toward unity.Source: §1 · p. 60
• Under that early-removal condition, the compression bias should largely disappear.Source: §1 · p. 60

2. Repeated deadline training

• Repeated temporal pressure repeatedly favors shorter policies.Source: §2 · p. 60
• Repeated realized selection of the same short policy gradually increases its habitual prior support.Source: §2 · p. 60
• The temporal factor itself is not learned into the habitual prior; realized policy selections supply the history for habit updates and forgetting.Source: §2 · p. 60

3. Listener divided attention

• High local processing load should make policies less likely to support successful comprehension, favoring forms that distribute or reduce that load.The predicted effect depends on the current listener’s capacity and local information density, with little carryover to a new attentive listener.Source: §3 · p. 60

4. Listener familiarity with a partner-specific convention

• Shorthand should be favored when the current partner is believed to be familiar with it.The relevant variable is the relatively persistent partner-model variable m+ and likelihoods conditioned on it.Source: §4 · p. 60
• Unexpected clarification after shorthand should lower inferred familiarity and may reverse the policy ranking.This prediction holds even when current policy evidence and the expected policy prior are held fixed.Source: §4 · p. 60
• The resulting adaptation should preferentially persist for the same partner rather than transfer indiscriminately to another shorthand-familiar partner.Source: §4 · p. 60

5. Social risk or politeness stakes

• Greater face, relationship, or strategic risk should favor more indirect, face-preserving, or deniable policies, even at matched informativeness and duration.The policy prior reflects preferences over predicted social outcomes and hence PV.Source: §5 · p. 60
• The effect should generalize across policies with similar predicted social consequences, not merely policies of similar length.Source: §5 · p. 61

6. Production difficulty

• Difficult forms are predicted to be avoided, but persistence and transfer depend on whether difficulty arises from action or observation likelihoods, valued consequences, or time cost.Articulatory difficulty, lexical retrieval difficulty, duration, and listener burden should be manipulated separately rather than collapsed into one effort cost.Source: §6 · p. 61

7. Uncertainty about one latent factor

• Clarification should target the uncertain latent factor, and question form is predicted to reveal uncertainty about reference, force, QUD, or reliability.Source: §7 · p. 61

8. Unexpected partner response

• An unexpected response may reorganize the next policy through revised current state, interaction context, or persistent partner-model hypotheses, with different predicted carryover.Current-state changes should remain episode-local, interaction-level changes track discourse or task, and partner-model changes persist preferentially for that partner.Source: §8 · p. 61

9. Persistent misunderstanding

• Responses can be well predicted by both agents while their referential beliefs remain sharply divergent; conversational fluency alone does not establish shared reference.Diagnostic evidence that distinguishes competing referents should reduce divergence, whereas nondiagnostic uptake may leave it unchanged.Source: §9 · p. 61

10. Conversation stopping.

• Conversation may stop when prospective EFE improvement per unit time falls below the current temporal opportunity rate, even if continuation has lower EFE than stopping.Termination need not mean residual uncertainty or all prospective benefit from clarification has disappeared.Source: §10 · pp. 61–62

6.2. Model-comparison requirements

• A single contemporaneous policy distribution cannot generally identify habitual and temporal components separately, motivating temporal interventions, transfer tests, and parameter-recovery checks.Model comparisons should establish predictive improvement beyond history, using held-out performance, posterior predictive checks, recovery simulations, and intervention-based validation.Source: §6.2 · p. 62

6.3. Relation to Relevance Theory and efficiency accounts

• Target-evidence rate is a descriptive measure, not the general policy-selection score or a direct input to policy prior; brevity is not intrinsically efficient.The same shorthand may yield different target-evidence gain per unit time for familiar and unfamiliar partners.Source: §6.3 · p. 63

6.4. Relation to bounded and amortized pragmatics

• Amortization can approximate several levels of coupled inference, bounding nested social reasoning without exhaustive recursion; the empirical question is which approximations generalize under which histories.A learned amortized mapping differs from a habitual policy prior, which contributes prior support and updates from realized policy history.Source: §6.4 · pp. 63–64

Conclusion

• Placing the speaker’s choice rule inside the listener’s generative model makes production and interpretation one computation, with each conversational move serving as evidence about a partner and an intervention on discourse.A posterior about intended meaning changes the expected consequences of the next move, including clarification, acknowledgment, reformulation, gesture, or closing.Source: §7 · p. 64
• The proposed architecture separates inference about a partner’s current state, learning partner-specific parameters, prospective expected free energy, and policy priors.Temporal pressure changes with the opportunity structure, while habitual policy components change through accumulated selections, allowing pressure to leave longer-term traces indirectly.Source: §7 · p. 64
• Under a restricted one-step construction, the familiar RSA speaker and listener distributions are recovered, but a static match cannot identify the causal allocation behind behavior.The decomposition instead predicts distinct intervention, learning, persistence, and transfer signatures.Source: §7 · pp. 64–65
• Speaking also samples evidence for the speaker’s model of the hearer: predicted replies support that representation, while dialogue can reinforce partner models that are wrong.Dialogue therefore certifies an agent’s internal representation of the other, not the other person themselves.Source: §7 · p. 65
• Richer latent structure risks non-identifiability and post hoc explanation, and multi-agent recursion requires finite depth, factorization, support restriction, or learned approximation.Coupling also does not guarantee truth, shared reference, or belief convergence; agents may maintain divergent referential beliefs despite low free energy.Source: §7 · p. 65
• Discourse may end before certainty when a continuation’s prospective benefit is too small relative to its duration and the current temporal opportunity rate.The numerical examples illustrate this possibility rather than establishing it empirically.Source: §7 · p. 65
• The framework’s central empirical contribution is to generate testable differences in adaptation, persistence, transfer, misunderstanding, and stopping, which future work must compare against behavioral data.Proposed tests include selective interventions on temporal pressure, partner familiarity, processing load, social risk, unexpected feedback, and repair or closing uptake.Source: §7 · pp. 65–66
• The framework treats grammar and compositional semantics as making structured forms available for downstream communication, so language can serve communication without being reducible to it.Communicative efficiency of linguistic outputs alone does not identify the mechanism that produced them.Source: §7 · p. 66

• Linguistic structure constrains the objects available for interpretation, while dialogue determines how those objects become evidence and action.Source: §7 · p. 67
• The proposed common causal architecture connects interpretation, production, learning, and repair.Source: §7 · p. 67
• Successful coordination need not imply perfect mental alignment, and each utterance both changes another mind and tests the speaker’s model of it.Source: §7 · p. 67

Appendix A: Active-inference definitions and derivations

• Variational free energy evaluates current or past observations, whereas expected free energy evaluates possible future outcomes under candidate policies.Both quantities are defined relative to an agent’s generative model, but serve distinct formal roles.Source: Appendix A · p. 67

A.1. Generative models and inverse inference

• A generative model factors hidden-state priors and observation likelihoods; inference uses observations to estimate hidden states, while learning changes persistent model parameters.The represented belief q changes through inference, while parameters θ determine the prior, likelihood, and, in temporal models, state transitions.Source: §A.1 · pp. 67–69
• When exact inference is impractical, variational inference uses a tractable approximate posterior that may not represent the model posterior exactly.Exact inference becomes difficult with high-dimensional, interacting, deep, or complex hidden states; even an exact posterior is relative to the model and need not reflect an objective external state.Source: §A.1 · p. 69

Appendix Equation (A10) can first be written as an energy-entropy decomposition:

• The energy-entropy decomposition of variational free energy balances the improbability of state-observation combinations against the entropy of q.The terms cannot be optimized independently: a diffuse q can have high entropy yet still assign probability to states that poorly explain the observation.Source: Appendix Equation (A10) can first be… · p. 70

A.2.1. Posterior-divergence form

• For a fixed observation and model, variational free energy bounds observation surprisal, and minimizing it over q minimizes divergence from the model posterior.The bound is tight if the variational family contains the exact posterior; a restricted family leaves a residual approximation gap.Source: §A.2.1 · pp. 70–71

A.2.2. Inaccuracy-complexity form

• The inaccuracy-complexity form balances expected negative log likelihood against the information-theoretic difference between posterior belief and prior.Belief revision can increase complexity but lower total free energy when its gain in accuracy is larger; minimization regulates the trade-off rather than either term alone.Source: §A.2.2 · p. 71
• Variational complexity should not automatically be equated with reaction time, subjective difficulty, conscious effort, neural firing, metabolic expenditure, or computational operations.Connecting it to psychological or neurobiological cost requires a process theory specifying how relevant probability distributions are represented and updated.Source: §A.2.2 · p. 71
• VFE is the negative evidence lower bound, so minimizing VFE is equivalent to maximizing the ELBO.With Gaussian likelihoods and a Laplace approximation, free energy may reduce to precision-weighted prediction errors.Source: §A.2.2 · pp. 71–72
• In general, VFE is not raw prediction error alone: it includes expected log likelihood and divergence between posterior and prior beliefs.Source: §A.2.2 · p. 72

A.3. Inference, learning, and action as distinct updates

• Inference updates current beliefs about hidden states, learning updates the model parameters that define them, and action changes the observations available to the agent.These processes can be formulated in relation to free-energy minimization, but optimize different variables.Source: §A.3 · p. 72, §A.3.1 · p. 72, §A.3.2 · p. 72

A.3.1. Inference

• Inference optimizes the current state belief while holding observations and parameters fixed; iterative gradient flow is one implementation, not part of Bayesian inference itself.In a small categorical model, the posterior can instead be evaluated directly in a single normalized update.Source: §A.3.1 · p. 72

A.3.2. Learning

• Learning changes model mappings and regularities, including likelihoods, state priors, or temporal transition probabilities.State inference and parameter learning may be implemented as alternating or simultaneous updates; their distinction is the variable updated, not a strict timescale boundary.Source: §A.3.2 · p. 72, Appendix Equations (A24) and (A27) can… · p. 73

Appendix Equations (A24) and (A27) can be implemented as alternating or simultaneous updates.

• Inference is often faster than learning, but timescale is a common pattern rather than the fundamental distinction between them.The formal updates do not require biological or artificial systems to complete one process before beginning the other.Source: Appendix Equations (A24) and (A27) can… · p. 73

A.3.3. Action

• Action changes the observations available through the agent’s relation to the environment, while discrete policies are prospectively evaluated using expected free energy.Planning compares expected observations under different possible action sequences before future observations are available.Source: §A.3.3 · p. 73

A.4. A discrete POMDP generative model

• The discrete POMDP model represents hidden states, probabilistic observation generation, and action-dependent state transitions.Its generative model represents an agent’s beliefs and may be inaccurate relative to the external generative process.Source: §A.4 · p. 74
• For each candidate policy, the model predicts future states and outcomes, then considers possible observations and the counterfactual posteriors they would produce.These are predictions before future events occur; when exact counterfactual inference is intractable, an optimized variational posterior approximates it.Source: §A.4 · pp. 74–75

A.5.1. Expected information gain

• Expected free energy evaluates whether policies are expected to reduce uncertainty and realize preferred outcomes, using future rather than already available observations.Expected information gain is high when outcomes are expected to discriminate among plausible states, not merely when observations vary.Source: §A.5 · p. 75, §A.5.1 · p. 76

A.5.2. Pragmatic value

• Pragmatic value evaluates predicted outcomes under prior preferences and is not synonymous with linguistic pragmatics or communicative inference.With uniform prior preferences, pragmatic value is identical across policies and does not affect their relative ranking.Source: §A.5.2 · pp. 76–77

A.5.3. The epistemic-preference decomposition

• Expected free energy favors policies that are informative and consistent with preferred outcomes, with information gain and preference-based value as complementary decompositions.In the risk-ambiguity form, risk measures mismatch between predicted and preferred outcomes, while ambiguity concerns uncertainty in the state-to-outcome mapping.Source: §A.5.3 · p. 77

Appendix Equation (A44) makes this distinction explicit:

• Unpredictable observations are not necessarily informative: information gain requires expected observations to discriminate among state hypotheses.Variation generated by observation noise does not provide the diagnostic evidence needed for information gain.Source: Appendix Equation (A44) makes this… · p. 79

A.5.4 Why complexity in VFE and information gain in EFE have opposite signs

• VFE evaluates how economically current evidence is explained, whereas EFE evaluates the expected usefulness of future evidence.This difference explains why belief revision for an observed outcome contributes differently from the prospect of a future belief-changing observation.Source: §A.5.4 · p. 79

A.5.5 Policy priors and policy posteriors

• Policy priors encode bias distinct from current expected free energy, while policy posteriors can also reflect evidence from observations already available.A frequently selected policy can have strong prior support without minimal current EFE, and a weakly supported policy can become probable when its EFE is sufficiently low.Source: §A.5.5 · pp. 79–80
• The framework’s explanatory content depends on specifying its states, observations, likelihoods, transitions, preferences, and admissible policies.EFE minimization alone does not determine these variables.Source: §A.5.5 · p. 80