# GVSS-06 — Diagnostic Visual Control and Minimal Intervention Policies ## 診斷式視覺控制與最小介入策略：失敗信念、資訊價值、澄清行動與分層控制成本 **Series:** Global Visual Space & Generative Navigation — Paper 06 **Bridge:** GVSS × frozen Reflexive Representation Theory (RRT) **Author:** Neo.K / EveMissLab **Version:** v0.1 **Date:** 2026-08-17 **Status:** Formal diagnostic-control paper. Controlled belief-state recursion, finite-horizon Bellman control, budget monotonicity, one-step value-of-diagnosis, perfect-information thresholds, human-clarification thresholds, repeated-cheap-versus-decisive diagnostic dominance, stopping optimality, posterior robustness under learned diagnostic likelihood error, finite-horizon policy-regret bounds, and myopic-action counterexamples are proved under the stated hypotheses. POMDP belief control, Bayesian value of information, Blackwell experiment comparison, sequential Bayesian experimental design, active visual reasoning, clarification policies, and state-aware agentic image generation are established neighboring work and are not claimed as GVSS inventions. No strong novelty claim is made. **Keywords:** diagnostic visual control, value of information, POMDP, visual generation agent, failure belief, human clarification, evaluator calibration, minimal intervention, text-to-image control, GVSS, reflexive visual navigation --- # Abstract GVSS-05 introduced a latent visual failure state $$ \boxed{ F_t \in \mathcal F = \{ F_{\mathrm{sample}}, F_{\mathrm{constraint}}, F_{\mathrm{compile}}, F_{\mathrm{search}}, F_{\mathrm{reach}}, F_{\mathrm{eval}}, F_{\mathrm{intent}} \} } $$ and a posterior failure belief $$ \boxed{ b_t(k) = P(F_t=F_k\mid H_t). } $$ It also defined one-step posterior action risk $$ \boxed{ \rho_t(a) = c(a) + \sum_k b_t(k)L(a,k), } $$ together with a **least-cost justified intervention** heuristic. GVSS-06 replaces that myopic heuristic with sequential belief-space control. The controller must choose among actions with different roles: $$ \boxed{ \mathcal A = \mathcal A_{\mathrm{diag}} \cup \mathcal A_{\mathrm{correct}} \cup \mathcal A_{\mathrm{clarify}} \cup \{\mathrm{STOP}\}. } $$ Examples include: - independent reroll; - evaluator calibration; - alternate evaluator; - alternate search policy; - RECOMPILE; - REPAIR; - REBIND; - SWITCH_BACKEND; - HUMAN_REVIEW; - human clarification question; - STOP. An action can change the hidden failure state. Let $$ \boxed{ T_a(k'\mid k) = P( F_{t+1}=F_{k'} \mid F_t=F_k, a_t=a ) } $$ be the failure-transition kernel. After taking action $a$, the predicted failure belief is $$ \boxed{ \bar b^a(k') = \sum_k T_a(k'\mid k)b(k). } $$ The action can then produce diagnostic report $$ Y\sim Q_a(\cdot\mid F_{t+1}). $$ Bayesian correction gives $$ \boxed{ b^{a,y}(k') = \frac{ Q_a(y\mid k')\bar b^a(k') }{ \sum_j Q_a(y\mid j)\bar b^a(j) }. } $$ This is the controlled failure-belief recursion. Let $$ B $$ be remaining visual-control budget. For finite horizon, define Bellman value $$ \boxed{ V_t(b,B) = \min_{ a: c(a)\le B } \left\{ c(a) + \ell(b,a) + \mathbb E_{ Y\mid b,a } V_{t+1} ( b^{a,Y}, B-c(a) ) \right\}. } $$ A STOP action terminates with current terminal correction/acceptance risk $$ \boxed{ R(b) = \min_u \sum_k b(k)L(u,k). } $$ This gives the central GVSS-06 decision rule: $$ \boxed{ \text{diagnose} \vee \text{correct} \vee \text{clarify} \vee \text{stop} } $$ as a function of belief, future value, and budget. The first major theorem isolates the one-step value of diagnosis. Suppose diagnostic action $d$: - does not itself change the failure state; - produces report $Y$ ; - is followed immediately by the best terminal correction. Then its total risk is $$ \boxed{ J_d(b) = c(d) + \mathbb E_Y R(b^Y). } $$ Its **value of diagnosis** is $$ \boxed{ \operatorname{VoD}(d\mid b) = R(b) - \mathbb E_YR(b^Y) - c(d). } $$ Therefore: $$ \boxed{ d \text{ is better than immediate terminal correction} \iff \operatorname{VoD}(d\mid b)>0. } $$ More information is useful only through the downstream decision it improves. For a perfect diagnostic that reveals the exact failure state, define the expected value of perfect failure information $$ \boxed{ \operatorname{EVPI}(b) = R(b) - \sum_k b(k) \min_u L(u,k). } $$ A perfect diagnostic of cost $c_*$ is worth taking before terminal correction exactly when $$ \boxed{ c_* < \operatorname{EVPI}(b). } $$ This yields a clean human-clarification threshold. Consider two unresolved intents $$ \theta_1,\theta_2 $$ with posterior $$ p, \quad 1-p. $$ Suppose each intent has its own zero-loss correction, while applying the wrong correction incurs loss $L>0$. Without clarification, optimal expected correction loss is $$ \boxed{ L\min(p,1-p). } $$ If a human clarification query perfectly reveals the intended interpretation and costs $c_H$, then asking the human is optimal before correction exactly when $$ \boxed{ c_H < L\min(p,1-p). } $$ Thus human clarification is not a last-resort social feature. It is a value-of-information action whose worth depends on ambiguity, consequence, and cost. This is closely aligned with current interactive multimodal work that explicitly learns when to clarify ambiguous visual questions and with progressive image-generation systems that use co-adaptive dialogue to reduce prompt ambiguity. GVSS-06 also proves when one expensive decisive diagnostic dominates repeated cheap tests. Let $D_c^{\otimes n}$ denote $n$ fixed cheap diagnostic tests, each costing $c_c$. Let $D_*$ be a decisive diagnostic experiment such that $$ \boxed{ D_* \succeq_B D_c^{\otimes n} } $$ in Blackwell order. If $$ \boxed{ c_* \le n c_c, } $$ then for every bounded terminal decision problem: $$ \boxed{ \text{decisive-test total Bayes risk} \le \text{fixed-}n\text{ cheap-test total Bayes risk}. } $$ This theorem does not cover a sequential cheap-test policy that can stop early. The correct comparison must include the whole adaptive policy. The paper also provides a stopping theorem. Let: $$ R(b) $$ be the cost of stopping now. For every feasible continuation action $a$, let: $$ Q_t(b,B,a) $$ be its Bellman action value. Then: $$ \boxed{ \mathrm{STOP} \text{ is optimal} \iff R(b) \le Q_t(b,B,a) \quad \forall a\neq\mathrm{STOP}. } $$ A controller should stop when no available diagnostic/corrective action has positive net future value. This prevents infinite diagnostic loops just as GVSS-05 prevented infinite reroll loops. GVSS-06 also corrects a limitation of the GVSS-05 **least-cost justified intervention**. Suppose: $$ P(F_1)=P(F_2)=1/2. $$ There are two zero-cost correction actions $u_1,u_2$. Each has zero loss on its matching failure and loss $100$ on the other. With justification threshold $\eta=1/2$, both corrections are immediately justified and have zero action cost. A myopic least-cost rule may choose one and incur expected loss: $$ 50. $$ But a perfect diagnostic costing $1$ reveals which correction is appropriate, giving total expected loss: $$ 1. $$ Therefore: $$ \boxed{ \text{least-cost currently justified correction} \not\Rightarrow \text{optimal sequential control}. } $$ Information acquisition can dominate immediate intervention. Online diagnostic learning introduces another RRT-style conditioning issue. Let true diagnostic likelihood for observed report $y$ be $$ q_k = Q(y\mid F_k), $$ and learned approximation $$ \widehat q_k. $$ For prior $b$, assume weighted likelihood error $$ \boxed{ \sum_k b(k) | q_k-\widehat q_k | \le \varepsilon. } $$ Let true evidence probability be $$ \boxed{ Z = \sum_k b(k)q_k \ge \zeta>0. } $$ If $\varepsilon<\zeta$, then the true and approximate posteriors satisfy $$ \boxed{ \operatorname{TV} ( b^y, \widehat b^y ) \le \frac{ \varepsilon }{ \zeta }. } $$ Thus diagnostic-likelihood error is amplified by inverse evidence probability. Rare reports can produce unstable posterior updates even when average likelihood error is small. This is the diagnostic-control analogue of RRT conditioning debt. Finally, GVSS-06 gives a finite-horizon diagnostic-regret theorem. Let: $$ V_t $$ be optimal Bellman value. Suppose implemented policy $\pi$ chooses an action whose optimal Bellman $Q$ -value satisfies $$ \boxed{ Q_t( b,\pi_t(b) ) \le V_t(b) + \epsilon_t } $$ for every reachable belief. Then its finite-horizon excess expected cost satisfies $$ \boxed{ V_t^\pi(b) - V_t(b) \le \sum_{s=t}^{T-1} \epsilon_s. } $$ Therefore locally approximate diagnostic decisions accumulate at most additively under the stated finite-horizon model. The central GVSS-06 principle is: $$ \boxed{ \textbf{ Visual control should spend information only when the expected reduction in future correction risk exceeds the cost of acquiring that information. } } $$ --- # 1. From diagnosis to control GVSS-05 answers: > Which failure layer is plausible? GVSS-06 answers: > Given uncertainty over failure layers, what should the controller do next? The difference is fundamental. A posterior belief is not yet a policy. --- # 2. Current neighboring research Modern agentic image generation already treats multi-turn generation as a state-dependent action problem. Generation Navigator explicitly reformulates image generation as state-conditioned action making and trains a controller to adapt actions to an evolving generation trajectory. GenAgent uses multimodal reasoning, tool invocation, judgment, reflection, and multi-turn refinement. Twin-Co uses co-adaptive dialogue with the user to reduce ambiguity in image-generation prompts. These systems demonstrate that dynamic action selection and human interaction are already active research directions. GVSS-06 does not claim state-aware agentic image control as new. --- # 3. Sequential information acquisition precedent Active visual reasoning work in 2026 formulates visual information acquisition as sequential Bayesian optimal experimental design. The agent decides which evidence is worth acquiring before committing to an answer. This is mathematically close to GVSS-06's diagnostic-control layer. GVSS specializes the hidden state to **visual generation failure causes** and the downstream decision to **visual corrective actions**. --- # 4. Clarification precedent Current multimodal-agent research explicitly studies whether an agent should clarify an ambiguous request rather than answer immediately. Clarify-or-Answer introduces a dataset and policy-learning setup for choosing clarification questions when visual context is ambiguous. Twin-Co applies iterative user dialogue directly to progressive image generation. Therefore GVSS-06's clarification action is not claimed as a new interaction paradigm. --- # 5. Evaluator uncertainty precedent VLM Judges Can Rank but Cannot Score studies conformal uncertainty for multimodal judges and finds strongly task-dependent uncertainty. Calibrating MLLM-as-a-judge via Multimodal Bayesian Prompt Ensembles studies calibration specifically for TTI evaluation. GVSS-06 uses these as evidence that evaluator state should include uncertainty/calibration rather than treating judge scores as exact. --- # 6. Controlled failure state ## Definition GVSS06-D1 Let: $$ F_t \in \mathcal F. $$ An action: $$ a_t $$ can change the failure state through: $$ \boxed{ T_a(k'\mid k). } $$ Examples: ### RESAMPLE May preserve the dominant structural failure state but refresh stochastic sample state. ### RECOMPILE May convert: $$ F_{\mathrm{compile}} $$ into: $$ F_{\mathrm{sample}} $$ if the new compiler succeeds but a new stochastic draw is still needed. ### REPAIR May remove a local artifact while leaving style or intent ambiguity. ### REBIND May remove provider reachability failure while injecting switching/style-consistency risk. ### HUMAN_CLARIFY May remove intent ambiguity without changing generator capability. --- # 7. Predictive belief after action ## Definition GVSS06-D2 Before observing the action result: $$ \boxed{ \bar b^a(k') = \sum_k T_a(k'\mid k)b(k). } $$ This is the action-predicted failure belief. --- # 8. Diagnostic report model Let: $$ Q_a(y\mid k') $$ be the report likelihood after action $a$ if the post-action failure state is $F_{k'}$. --- # 9. GVSS06-T1 — Controlled belief update ## Theorem GVSS06-T1 Given prior belief $b$, action transition $T_a$, and observation likelihood $Q_a$, the posterior after action $a$ and report $y$ is: $$ \boxed{ b^{a,y}(k') = \frac{ Q_a(y\mid k') \sum_kT_a(k'\mid k)b(k) }{ \sum_j Q_a(y\mid j) \sum_kT_a(j\mid k)b(k) }. } $$ whenever the denominator is positive. ### Proof Predict with the transition kernel, then condition by Bayes' rule. $\square$ This is the standard controlled hidden-state belief update. --- # 10. Belief-state sufficiency Under the Markov failure model and known kernels, the full diagnostic history can be compressed into: $$ \boxed{ (b_t,B_t,r_t) } $$ for optimal control, provided the visual regime coordinates needed to determine future kernels are included in $r_t$. This is the standard POMDP sufficient-statistic principle. --- # 11. GVSS06-T2 — Belief-state dynamic programming ## Theorem GVSS06-T2 Under finite hidden state/action/observation spaces, known controlled kernels, additive stage costs, and finite horizon, an optimal history-dependent policy can be represented as a policy on current belief and remaining budget: $$ \boxed{ a_t = \pi_t^*(b_t,B_t,r_t). } $$ ### Reason The conditional law of future hidden states and reports depends on past history only through the current controlled belief and regime state. This is classical POMDP theory. GVSS does not claim the theorem as new. --- # 12. Budget state Let: $$ \boxed{ B_t\ge0 } $$ be remaining diagnostic/control budget. Action $a$ is feasible when: $$ \boxed{ c(a)\le B_t. } $$ Update: $$ \boxed{ B_{t+1} = B_t-c(a_t). } $$ --- # 13. Terminal decision Let: $$ u \in \mathcal U $$ be a terminal corrective decision. Examples: - ACCEPT; - RESAMPLE; - final RECOMPILE; - final REPAIR; - final REBIND; - human handoff. Let: $$ \boxed{ L(u,k) } $$ be terminal loss if failure is $F_k$. --- # 14. Terminal Bayes risk ## Definition GVSS06-D3 $$ \boxed{ R(b) = \min_{ u\in\mathcal U } \sum_k b(k)L(u,k). } $$ This is the risk of stopping information acquisition and making the best current terminal decision. --- # 15. Finite-horizon Bellman equation ## Definition GVSS06-D4 For $t