Paper deep dive
When Stress Becomes Signal: Detecting Antifragility-Compatible Regimes in Multi-Agent LLM Systems
Jose Manuel de la Chica, Juan Manuel Vera, Jairo Rodríguez
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
Last extracted: 7/8/2026, 9:14:27 AM
Summary
This paper introduces CAFE (Cognitive Antifragility Framework for Evaluation), a statistical framework designed to detect antifragility-compatible regimes in multi-agent LLM systems. Unlike traditional robustness evaluations that focus on performance preservation under stress, CAFE measures whether semantic stress (conflict, load, ambiguity, temporal drift) induces a structured, convex-expansive deformation in the system's response. Using a multi-output polynomial response model and a distributional Jensen Gap, CAFE compares expected versus observed stress distributions. Evaluated on a banking-risk analysis benchmark across five architectures (flat, hierarchical, debate, meta-adaptive, ensemble), the framework reveals that while all systems experience quality degradation under stress, they all exhibit positive Jensen Gaps. This indicates that immediate performance drops can coexist with statistically detectable stress geometry suitable for future antifragile learning. CAFE serves as a measurement layer to identify optimal conditions for applying adaptive learning mechanisms.
Entities (11)
Relation Signals (11)
Positive Distributional Jensen Gap → indicates → Antifragility-compatible regime
confidence 96% · A positive gap indicates a convex-expansive deformation, which we interpret as an antifragility-compatible opportunity...
CAFE → utilizes → Distributional Jensen Gap
confidence 96% · Finally, CAFE compares the expected and observed stress distributions through a distributional Jensen Gap.
CAFE → detects → Antifragility-compatible regime
confidence 95% · CAFE is a statistical framework for detecting whether a multi-agent architecture is operating in an antifragility-compatible regime.
Multi-agent LLM systems → evaluatedon → Banking-risk analysis benchmark
confidence 95% · We evaluate CAFE on a controlled banking-risk analysis benchmark with five multi-agent architectures...
CAFE → servesas → measurement layer
confidence 95% · CAFE is therefore not an antifragile learner itself, but a measurement layer for identifying when and where antifragility learning may be worth applying.
Banking-risk analysis benchmark → incorporates → Semantic stress
confidence 94% · The stress vector contains four semantic stress dimensions: conflict, load, ambiguity, and temporal drift.
Hierarchical → isa → Multi-agent LLM systems
confidence 93% · A1 decomposes the problem into credit, market, liquidity, and operational-risk specialists before synthesis.
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:Multi-agent LLM systems are increasingly used to solve complex tasks through decomposition, debate, specialization, and ensemble reasoning. However, these systems are usually evaluated in terms of robustness: whether performance is preserved under perturbation. This paper studies a different question: whether semantic stress exposes structured variation that could support future antifragile learning. We introduce CAFE (Cognitive Antifragility Framework for Evaluation), a statistical framework for detecting antifragility-compatible regimes in multi-agent architectures. CAFE models a controlled expected distribution of semantic stressors, reconstructs an architecture-specific observed effective stress distribution from multi-dimensional judge signals, and compares both distributions using a distributional Jensen Gap under a convex stress potential. A positive gap does not imply immediate performance improvement; instead, it indicates a convex-expansive deformation of the observed stress distribution, suggesting that the architecture exposes learnable stress structure. We evaluate CAFE on a banking-risk analysis benchmark with five multi-agent architectures: flat, hierarchical, debate, meta-adaptive, and ensemble. Across all architectures, semantic stress reduces average judged quality by roughly one third. Yet all architectures exhibit positive distributional Jensen Gaps with bootstrap confidence intervals above zero. These results show that immediate quality degradation can coexist with statistically detectable antifragility-compatible stress geometry. CAFE is therefore not an antifragile learner itself, but a measurement layer for identifying when and where antifragility learning may be worth applying.
Tags
Links
- Source: https://arxiv.org/abs/2605.02463v2
- Canonical: https://arxiv.org/abs/2605.02463v2
Trouble viewing inline? Open PDF directly →
Full Text
62,627 characters extracted from source content.
Expand or collapse full text
3 .chica@gruposantander.com When Stress Becomes Signal: Detecting Antifragility-Compatible Regimes in Multi-Agent LLM Systems Jose Manuel de la Chica1, † Juan Manuel Vera1 Jairo Rodíguez1 1Santander AI Lab Abstract Multi-agent LLM systems are increasingly used to solve complex tasks through decomposition, debate, specialization, and ensemble reasoning. However, these systems are usually evaluated in terms of robustness: whether performance is preserved under perturbation. This paper studies a different question: whether semantic stress exposes structured variation that could support future antifragile learning. We introduce CAFE (Cognitive Antifragility Framework for Evaluation), a statistical framework for detecting antifragility-compatible regimes in multi-agent architectures. CAFE models a controlled expected distribution of semantic stressors, reconstructs an architecture-specific observed effective stress distribution from multi-dimensional judge signals, and compares both distributions using a distributional Jensen Gap under a convex stress potential. A positive gap does not imply immediate performance improvement; instead, it indicates a convex-expansive deformation of the observed stress distribution, suggesting that the architecture exposes learnable stress structure. We evaluate CAFE on a banking-risk analysis benchmark with five multi-agent architectures: flat, hierarchical, debate, meta-adaptive, and ensemble. Across all architectures, semantic stress reduces average judged quality by roughly one third. Yet all architectures exhibit positive distributional Jensen Gaps with bootstrap confidence intervals above zero. These results show that immediate quality degradation can coexist with statistically detectable antifragility-compatible stress geometry. CAFE is therefore not an antifragile learner itself, but a measurement layer for identifying when and where antifragility learning may be worth applying. 1 Introduction Large language models are increasingly deployed as multi-agent systems: flat pipelines, specialist hierarchies, adversarial debates, ensembles, and meta-controlled workflows. These architectures are attractive because complex tasks often require decomposition, disagreement, synthesis, and adaptation. However, real inputs are rarely clean. In high-stakes analytical domains, such as financial risk assessment, prompts may contain contradictory evidence, overloaded context, ambiguous references, and temporally stale information. These conditions are not peripheral noise; they are part of the operating environment. Most evaluation protocols ask whether a model or agentic architecture remains robust under such perturbations. Robustness is important, but it is not the same as antifragility. A robust system preserves performance under stress. A fragile system degrades. An antifragile system, in the stronger sense, should eventually benefit from adversity. For current LLM-based multi-agent systems, claiming immediate improvement under harder inputs is usually too strong: semantic stress often lowers answer quality. The more useful question is whether stress exposes structured variation that a future adaptive mechanism could exploit. This paper studies that intermediate regime. We ask whether a multi-agent architecture, when exposed to a known distribution of semantic stressors, produces an observed stress-response geometry that is statistically compatible with future antifragile learning. We call such a regime antifragility-compatible: the system is not necessarily improving yet, but its response to stress contains structured, convex-expansive variation rather than mere collapse or noise. We propose CAFE, a statistical framework for detecting this regime. CAFE starts from a controlled expected stress distribution over four semantic stress dimensions: conflict, load, ambiguity, and temporal drift. Each architecture is then evaluated with a multi-dimensional judge that measures coherence, grounded novel inference, contradiction resolution, and structural preservation. A multi-output polynomial response model maps designed stress intensities to judge response signals. We then solve an inverse reconstruction problem to estimate the architecture-specific observed effective stress distribution. Finally, CAFE compares the expected and observed stress distributions through a distributional Jensen Gap under a convex stress potential. The resulting statistic is not a Jensen Gap over task quality. Instead, it measures whether the observed effective stress distribution expands or compresses relative to the expected stress distribution. A positive gap indicates a convex-expansive deformation, which we interpret as an antifragility-compatible opportunity: the architecture exposes learnable stress structure. A near-zero gap indicates resilience, and a negative gap indicates fragile compression. We evaluate CAFE on a controlled banking-risk analysis benchmark with five multi-agent architectures: a flat baseline, a hierarchical specialist system, an adversarial debate system, a meta-adaptive controller, and an ensemble. The main empirical finding is intentionally two-sided. All architectures lose average judged quality under stress, with relative quality drops of roughly one third. Nevertheless, all architectures exhibit positive distributional Jensen Gaps with bootstrap confidence intervals above zero. This shows that immediate quality degradation can coexist with statistically detectable antifragility-compatible stress geometry. Our contributions are: • We formalize antifragility-compatible evaluation for multi-agent LLM architectures as a distributional deformation problem rather than as immediate performance improvement. • We introduce a multi-output polynomial response model for reconstructing observed effective stress from judge response signals. • We define a distributional Jensen Gap that compares expected and observed stress distributions under a convex stress potential. • We evaluate five multi-agent architectures under controlled semantic stress and show that quality degradation can coexist with positive antifragility-compatible stress geometry. CAFE is therefore not itself an antifragile learner. It is a measurement layer: it identifies when and where antifragility learning may be worth applying. This distinction matters because adaptive systems need reliable signals before they can learn from adversity rather than merely endure it. 2 Related Work Antifragility and convex response. Antifragility distinguishes systems that merely tolerate stress from systems that can extract useful structure from volatility, uncertainty, or perturbation. Taleb and Douady formalize antifragility through nonlinear exposure to dispersion and model error, connecting beneficial stress response to convexity [undef]. Related work further develops the link between convex response, fragility, and beneficial variation [undefa, undefb]. Systems and software research has adapted this idea to systems-of-systems, software architectures, and cloud settings [undefc, undefd, undefe]. These works typically study operational stress such as failures, latency, recovery, or chaos-engineering perturbations. CAFE instead studies semantic and epistemic stress in language-agent architectures. Its goal is not to claim that an architecture immediately improves under adversity, but to detect whether the observed stress-response geometry is statistically compatible with future antifragile adaptation. Response surfaces and distributional comparison. CAFE uses response-surface modeling to estimate how judge signals vary as a function of controlled stress intensities. This connects to classical computer-experiment methodology, where expensive systems are probed at controlled input settings and approximated by interpretable surrogate models [undeff]. Our use of a polynomial model is not the final antifragility test; it is an instrument for reconstructing an architecture-specific observed stress distribution. The final statistic compares the designed and observed stress distributions through a distributional Jensen Gap. This places CAFE near distributional comparison methods such as Jensen-Shannon divergence [undefg], maximum mean discrepancy [undefh], and energy-distance statistics [undefi]. Unlike these generic distances, CAFE asks whether the observed distribution expands under a convex stress potential, revealing a regime that could be exploited by antifragile learning. LLM agents and coordination. Recent LLM systems increasingly use multiple agents with specialized roles, communication protocols, and coordination mechanisms. AutoGen provides a general framework for multi-agent LLM conversations [undefj]; CAMEL studies role-playing agents as a substrate for cooperative behavior [undefk]; and MetaGPT encodes structured workflows into multi-agent collaboration [undefl]. Surveys of LLM-based multi-agent systems organize this space around profiling, communication, planning, cooperation, and evaluation [undefm]. Our experimental architectures instantiate common coordination patterns: a flat baseline, hierarchical decomposition, debate, meta-adaptive control, and independent ensemble synthesis. Prior work shows that multi-agent debate can improve reasoning and factuality [undefn] and that sampling multiple reasoning paths can improve answers through self-consistency [undefo]. CAFE complements these results by asking a different question: which coordination patterns expose structured stress variation that an adaptive system could later learn from? Reflection, adaptation, and learning from adversity. Several agentic methods improve outputs through feedback, reflection, search, or memory. Self-Refine iteratively revises outputs using self-feedback [undefp]; Reflexion stores verbal feedback to improve future trials [undefq]; Tree of Thoughts searches over intermediate reasoning states [undefr]; and ReAct interleaves reasoning with action [undefs]. These methods demonstrate that LLM systems can use additional signals to adapt at inference time or across trials. However, they usually measure adaptation by final task success or preference. CAFE targets the condition that precedes such adaptation: whether stress produces structured, convex-expansive variation in the observed stress space. In this sense, CAFE is a detector of when antifragile learning may be worth applying. Stress testing and holistic evaluation. Average benchmark accuracy is insufficient for evaluating language systems under distribution shift. CheckList introduced behavioral tests for targeted NLP capabilities [undeft]; Robustness Gym unified subpopulation, transformation, and adversarial evaluations [undefu]; Dynabench proposed dynamic model-in-the-loop benchmarking [undefv]; and HELM argues for multi-metric evaluation across scenarios and desiderata [undefw]. Our stress dimensions connect to benchmarks for truthfulness and verification [undefx, undefy], ambiguity [undefz], long-context stress [undefaa], and automated red-teaming [undefab]. CAFE differs by treating stress as a continuous random variable and by measuring the distributional deformation from expected to observed stress, rather than only reporting accuracy on a fixed challenge set. LLM-as-judge evaluation. Open-ended multi-agent responses require structured evaluation beyond exact-match metrics. LLM-as-judge methods such as G-Eval use explicit rubrics to align automatic evaluation with human judgment [undefac], while MT-Bench and Chatbot Arena study the scalability and biases of judge-based evaluation [undefad, undefae]. CAFE uses an explicit judge as a measurement component that returns multiple response signals: coherence, grounded inference, contradiction resolution, and structural preservation. These scores are not treated as a final scalar performance measure. Instead, they constrain the reconstruction of an observed effective stress distribution, which is then compared to the expected stress distribution through the CAFE Jensen Gap. 3 Method CAFE is a statistical framework for detecting whether a multi-agent architecture is operating in an antifragility-compatible regime. The framework does not define antifragility as immediate improvement in average output quality. Instead, it asks whether stress induces a structured, convex-expansive deformation between the expected stress distribution and the observed effective stress distribution. Such a regime is valuable because it exposes variation that future antifragile learning, routing, memory, or architecture-selection mechanisms could exploit. 3.1 Problem Formulation Let A be a set of candidate agentic architectures. For an architecture a∈a , a clean prompt u, and a stress vector =(ψ1,ψ2,ψ3,ψ4)∈[0,1]4, ψ=( _1, _2, _3, _4)∈[0,1]^4, (1) a perturbation operator τ generates a stressed prompt u~=τ(u,). u=τ(u, ψ). (2) The architecture produces an output ya=a(u~).y_a=a( u). (3) An evaluator J maps the prompt-output pair into a vector of response signals a=J(u~,ya)∈[0,1]K.s_a=J( u,y_a)∈[0,1]^K. (4) In our experiments K=4K=4, corresponding to coherence, grounded novel inference, contradiction resolution, and structural preservation. We keep these signals as a vector rather than collapsing them into a single quality score, because the inverse reconstruction of observed stress is better constrained by multiple response measurements. The empirical dataset for architecture a is a=(n,a,n)n=1Na.D_a=\( ψ_n,s_a,n)\_n=1^N_a. (5) 3.2 Stress Space The stress vector contains four semantic stress dimensions: =(ψconflict,ψload,ψambiguity,ψdrift). ψ=( _conflict, _load, _ambiguity, _drift). (6) These dimensions encode contradictory evidence, semantic overload, structural or referential ambiguity, and temporal inconsistency. We center stress coordinates as xi=ψi−12,xi∈[−1/2,1/2],x_i= _i- 12, x_i∈[-1/2,1/2], (7) and write x for the centered stress vector. 3.3 Multi-Output Response Model For each architecture a, we assume a latent response-signal surface a:[−1/2,1/2]4→[0,1]K,S_a:[-1/2,1/2]^4→[0,1]^K, (8) with observations a,n=a(n)+a,n,[a,n∣n]=.s_a,n=S_a(x_n)+ _a,n, [ _a,n _n]=0. (9) Each response dimension is approximated with the same interpretable polynomial basis. For judge dimension k, we fit ^a,k()= S_a,k(x)= θ0,a,k+∑i=14θi,a,kxi+∑i=14αi,a,kxi2+∑1≤i<j≤4γij,a,kxixj \; _0,a,k+ _i=1^4 _i,a,kx_i+ _i=1^4 _i,a,kx_i^2+ _1≤ i<j≤ 4 _ij,a,kx_ix_j +δ12,a,kx1x22+δ34,a,kx3x42. \;+ _12,a,kx_1x_2^2+ _34,a,kx_3x_4^2. (10) The linear terms estimate direct stress sensitivity, the quadratic terms estimate marginal curvature, the bilinear terms capture cross-stressor interference, and the two selected cubic terms allow conflict to modulate the effect of load and ambiguity to modulate the effect of drift. The full multi-output predictor is ^a()=(^a,1(),…,^a,K()). S_a(x)=( S_a,1(x),…, S_a,K(x)). (11) Coefficients are estimated with ridge-regularized least squares: ^a,k=argmin∑n=1Na(sa,n,k−(n))2+ρ∥−0∥22, β_a,k= _ β _n=1^N_a (s_a,n,k-S_ β(x_n) )^2+ρ β_-0 _2^2, (12) where the intercept is excluded from the penalty. This model is not itself the antifragility criterion. It is an instrument for reconstructing the effective stress profile that best explains the observed response signals. 3.4 Observed Effective Stress Reconstruction All architectures are exposed to the same designed stress distribution PΨP_ , or PXP_X in centered coordinates. However, different architectures can transform the same designed stress into different observed effective stress distributions. Given the observed judge vector a,ns_a,n, we reconstruct the effective observed stress by solving ^a,nobs=argmin∈[−1/2,1/2]4‖a,n−^a()‖W2+λR(), x^obs_a,n= _x∈[-1/2,1/2]^4 \|s_a,n- S_a(x) \|_W^2+λ R(x), (13) where ∥W2=⊤W _W^2=z Wz. The regularizer resolves local non-identifiability and stabilizes the inverse. We use either a distributional prior, R()=(−X)⊤ΣX−1(−X),R(x)=(x- μ_X) _X^-1(x- μ_X), (14) or an anchored prior, R()=∥−n∥22.R(x)= -x_n _2^2. (15) The reconstructed stress vector in the original scale is ^a,nobs=^a,nobs+12. ψ^obs_a,n= x^obs_a,n+ 121. (16) The resulting empirical observed stress distribution is P^Ψ,aobs=1Na∑n=1Naδ^a,nobs. P^obs_ ,a= 1N_a _n=1^N_a _ ψ^obs_a,n. (17) 3.5 Distributional Deformation CAFE studies the deformation from expected to observed stress. For each architecture, define a map Ta:[−1/2,1/2]4→[−1/2,1/2]4,^a,nobs≈Ta(n).T_a:[-1/2,1/2]^4→[-1/2,1/2]^4, x^obs_a,n≈ T_a(x_n). (18) The push-forward Ta#PXT_a\#P_X is the architecture-specific observed stress law. To evaluate whether this deformation is expansive under a convex notion of stress magnitude, we introduce a convex potential ϕ:[−1/2,1/2]4→ℝ+.φ:[-1/2,1/2]^4 _+. (19) In the experiments we use ϕ()=∥22φ(x)= _2^2, so the statistic measures total dispersion around the mean stress vector. Other convex potentials can emphasize specific stress dimensions. 3.6 Distributional Jensen Gap The expected Jensen dispersion is exp=X∼PX[ϕ(X)]−ϕ(X∼PX[X]).V^exp=E_X P_X[φ(X)]-φ(E_X P_X[X]). (20) The observed Jensen dispersion for architecture a is aobs=X∼PX[ϕ(Ta(X))]−ϕ(X∼PX[Ta(X)]).V^obs_a=E_X P_X[φ(T_a(X))]-φ(E_X P_X[T_a(X)]). (21) The CAFE distributional Jensen Gap is a=aobs−exp.G_a=V^obs_a-V^exp. (22) A positive aG_a indicates a convex-expansive deformation of the observed stress distribution. We call this an antifragility-compatible regime: the system is not necessarily improving yet, but the stress response exposes structured variation that can be used by later adaptation. A gap near zero indicates resilience, and a negative gap indicates compression of observed stress variability. 4 Experimental Setup We evaluate CAFE on a controlled banking-risk analysis task. The experiment is designed to answer a specific question: when multi-agent architectures are exposed to semantic stress, do their responses reveal an antifragility-compatible stress geometry that could later be exploited by adaptive learning? 4.1 Synthetic Stress Dataset The task domain is banking-risk assessment. Each clean prompt asks an architecture to assess systemic risk for a financial institution using indicators such as CET1 ratio, liquidity coverage ratio, non-performing loans, trading VaR, operational losses, wholesale funding gap, interest-rate conditions, and mitigation recommendations. The domain is useful because it naturally combines multiple interacting risk channels and requires explicit handling of conflicting, stale, overloaded, or ambiguous information. We generate 5050 clean prompts and 1010 perturbed variants per clean prompt, for 500500 stressed prompts. Stress intensities are sampled independently from Gaussian distributions and clipped to [0,1][0,1]: ψi∼clip[0,1]((μi,τi2)). _i _[0,1](N( _i, _i^2)). (23) Stress dimension Mean Std. Perturbation operator ψconflict _conflict 0.40 0.18 Contradictory banking-risk claims. ψload _load 0.58 0.20 Extra caveats, ratios, dependencies, and supervisory notes. ψambiguity _ambiguity 0.32 0.16 Ambiguous entities, metrics, and references. ψdrift _drift 0.46 0.18 Stale or temporally inconsistent reporting windows. The generation seed is 2026042820260428. Clean prompts are retained as the reference condition, while perturbed prompts define the expected stress distribution. 4.2 Architectures We evaluate five architectures with different coordination mechanisms. All architectures receive the same prompts and are instructed to preserve banking-risk terminology, reason over the stressed input as given, explicitly handle contradiction, overload, ambiguity, and drift, and produce concrete risk recommendations. ID Architecture Coordination Expected calls A0 Flat Pipeline none 1 A1 Hierarchical top-down delegation 5 A2 Adversarial Debate thesis–antithesis–synthesis 3 A3 Meta-Adaptive feedback-driven switching 4+4+ A4 Simple Ensemble independent diversity and consensus 4 A0: Flat Pipeline A1: Hierarchical A2: Debate A3: Meta-Adaptive A4: Ensemble Figure 1: Agentic architectures evaluated in CAFE. Figure 1 shows implemented architectures where A0 is a single-agent baseline. A1 decomposes the problem into credit, market, liquidity, and operational-risk specialists before synthesis. A2 uses a risk optimist (bull), a risk pessimist (bear), and an arbitrator. A3 begins with debate and adds a meta-controller that can request stricter synthesis when coherence or drift degrades. A4 runs three independent analysts and aggregates them through a consensus builder. 4.3 Judge and Response Signals Each response is scored by a deterministic judge using four dimensions: a,n=(sa,ncoh,sa,ninf,sa,ncontr,sa,nstruct)∈[0,1]4.s_a,n=(s^coh_a,n,s^inf_a,n,s^contr_a,n,s^struct_a,n)∈[0,1]^4. (24) The dimensions are coherence, novel inference rate, contradiction resolution, and structural drift inverse. The judge uses only the input prompt and the system output. It penalizes unsupported claims, ignored contradiction, ignored temporal drift, ignored overload, and overconfident handling of ambiguity. The four scores are used as response signals for reconstructing observed effective stress; they are not treated as a single final performance metric in the CAFE criterion. 4.4 Modeling and Reconstruction For each architecture, clean and perturbed samples are merged into a modeling table. A fully evaluated architecture contributes 550550 rows: 5050 clean and 500500 perturbed samples. We center stress intensities as xi=ψi−1/2x_i= _i-1/2 and fit the multi-output polynomial model from Section 3 with ridge regularization ρ=10−3ρ=10^-3. We report R2R^2, RMSE, and MAE for the fitted response-signal surfaces. Observed effective stress is reconstructed with the inverse problem in Equation (13). We use an anchored regularizer, inverse weight λ=0.05λ=0.05, L-BFGS-B optimization, bounds [−1/2,1/2]4[-1/2,1/2]^4, and at most 100100 iterations. We then fit an architecture-specific deformation map TaT_a from designed to reconstructed stress using the same polynomial basis. 4.5 Distributional Jensen Evaluation We compute the expected Jensen dispersion from the designed stress vectors and the observed Jensen dispersion from the reconstructed observed stress vectors. The convex potential is ϕ()=∥22φ(x)= _2^2, so the gap measures expansion or compression of total stress dispersion around the mean. We classify gaps using a resilience tolerance of 0.010.01: values above 0.010.01 are antifragility-compatible, values below −0.01-0.01 are fragile, and intermediate values are resilient. Uncertainty is estimated with 500500 bootstrap resamples using seed 77, and 2.5%2.5\% and 97.5%97.5\% quantiles are reported as confidence intervals. 5 Results We report results for A0 Flat, A1 Hierarchical, A2 Debate, A3 Meta-Adaptive, and A4 Ensemble. The main empirical finding is deliberately two-sided: average judge quality decreases under stress for every architecture, yet every architecture exhibits a positive distributional Jensen Gap. CAFE therefore detects antifragility-compatible regimes, not automatic improvement under adversity. 5.1 Quality Drops Under Perturbation Table 1 reports mean judge quality on clean and perturbed prompts, computed as the average of the four judge dimensions. All architectures degrade under perturbation. The largest relative drop is observed for A4 Ensemble, despite A4 later showing the strongest CAFE gap. Table 1: Mean judge quality on clean and perturbed prompts. CAFE separates this immediate quality drop from the distributional opportunity for antifragile adaptation. Architecture Clean quality Perturbed quality Drop Relative drop A0 Flat 0.8309 0.5663 -0.2646 31.8% A1 Hierarchical 0.8139 0.5473 -0.2665 32.8% A2 Debate 0.8339 0.5527 -0.2812 33.7% A3 Meta-Adaptive 0.8206 0.5532 -0.2674 32.6% A4 Ensemble 0.8400 0.5426 -0.2974 35.4% This result rules out a naive interpretation of antifragility as immediate performance improvement. The architectures do not become better simply because the prompts are stressed. The relevant question is whether stress reveals structured variation that an adaptive mechanism could learn from. 5.2 Positive Jensen Gaps Reveal Antifragility-Compatible Regimes Table 2 shows the CAFE distributional Jensen Gap. All gaps are positive and all 95%95\% bootstrap confidence intervals lie strictly above zero. Under the CAFE criterion, all architectures therefore expose antifragility-compatible stress geometry. Table 2: Distributional Jensen Gap by architecture. Positive gaps indicate convex-expansive observed stress deformation relative to the expected stress distribution. Architecture Expected disp. Observed disp. Jensen Gap 95% CI A0 Flat 0.1861 0.2648 0.0787 [0.0661, 0.0935] A1 Hierarchical 0.1861 0.2728 0.0867 [0.0719, 0.1014] A2 Debate 0.1861 0.2641 0.0780 [0.0647, 0.0927] A3 Meta-Adaptive 0.1866 0.2675 0.0809 [0.0667, 0.0956] A4 Ensemble 0.1861 0.2836 0.0975 [0.0822, 0.1146] Figure 2 visualizes the same result. The dashed lines mark the resilience band. Every confidence interval lies above the upper resilience threshold, so the conclusion does not depend on small numerical fluctuations around zero. Figure 2: Distributional Jensen Gap by architecture. Error bars denote bootstrap 95%95\% confidence intervals, and dashed lines mark the resilience tolerance. The ranking by antifragility-compatible opportunity is A4>A1>A3>A0>A2.A4>A1>A3>A0>A2. This ranking should not be read as a ranking of immediate output quality. A4 has the largest gap and the largest quality drop. The correct interpretation is that A4 exposes the largest amount of structured stress variation, and thus the largest opportunity for antifragile adaptation. 5.3 Stress-Deformation Patterns Table 3 reports the increase in observed standard deviation relative to the designed stress distribution. These values explain where the positive Jensen Gap comes from. Table 3: Increase in observed stress standard deviation relative to the designed stress distribution. Architecture Conflict Load Ambiguity Drift A0 Flat 0.0474 0.0178 0.0602 0.0457 A1 Hierarchical 0.0568 0.0169 0.0614 0.0513 A2 Debate 0.0597 0.0238 0.0279 0.0538 A3 Meta-Adaptive 0.0372 0.0284 0.0497 0.0576 A4 Ensemble 0.0563 0.0372 0.0607 0.0517 The dominant expansion aligns with architectural structure. A2 Debate expands most strongly along conflict, consistent with adversarial disagreement. A3 Meta-Adaptive expands most strongly along drift, consistent with its coherence-and-drift monitoring role. A0, A1, and A4 expand most strongly along ambiguity, with A4 also showing broad expansion across conflict, ambiguity, and drift. These patterns suggest that different coordination strategies expose different learnable stress modes. Figure 3 shows representative marginal deformation plots. We keep the full set of marginal diagnostics in Appendix A; the main text reports only the examples that best explain the architecture-specific patterns in Table 3. A2 conflict A3 drift A4 load Figure 3: Representative expected-to-observed marginal deformations. These examples show how different coordination mechanisms expose different stress modes: adversarial debate expands conflict, meta-adaptive control expands drift, and ensemble consensus expands load. 5.4 Response-Surface Fit Diagnostics Table 4 summarizes response-surface fit quality averaged over the four judge dimensions. The fits are moderate but nontrivial, supporting the use of the response model for inverse stress reconstruction while motivating bootstrap uncertainty estimates. Table 4: Mean response-surface fit diagnostics across judge dimensions. Architecture Mean R2R^2 Mean RMSE Mean MAE A0 Flat 0.4888 0.1044 0.0783 A1 Hierarchical 0.4549 0.1164 0.0886 A2 Debate 0.4794 0.1126 0.0847 A3 Meta-Adaptive 0.4672 0.1149 0.0876 A4 Ensemble 0.4488 0.1293 0.0940 Structural drift inverse is the most predictable judge dimension, with R2R^2 values between 0.6690.669 and 0.7170.717. Novel inference rate is also moderately explained, with R2R^2 between 0.4490.449 and 0.5740.574. Contradiction resolution is noisier, with R2R^2 between 0.2410.241 and 0.3460.346, reflecting the difficulty of modeling fine-grained semantic reconciliation. 5.5 Summary The results support the intended interpretation of CAFE. The framework does not certify that a multi-agent architecture is already antifragile in the sense of improving output quality under stress. Instead, it detects whether the architecture enters a statistically antifragility-compatible regime. In all five architectures, stress lowers average quality but expands the observed stress distribution. This means the systems expose structured variation under adversity. Such variation is the raw material for future antifragile learning: adaptive routing, memory updates, architecture selection, or feedback-driven coordination could use this signal to improve from adversity rather than merely endure it. 6 Discussion The results support a deliberately narrow interpretation of CAFE. The evaluated architectures do not improve their average judged quality under semantic stress. In fact, all architectures exhibit substantial quality degradation under perturbation. However, this degradation is accompanied by a positive distributional Jensen Gap in every case. The key implication is therefore not that the current architectures are already antifragile in an operational sense, but that they enter regimes in which stress produces structured, convex-expansive variation in the observed effective stress distribution. CAFE is a detector of this opportunity. 6.1 Quality Degradation and Antifragility Opportunity A central risk in studying antifragility is to conflate two different claims. The first claim is immediate performance improvement: a system receives a harder input and produces a better output. Our experiments do not support that claim. Mean judge quality decreases by roughly one third across all architectures. The second claim is statistical opportunity: a system’s response to stress becomes more informative, more differentiated, or more structured in a way that a future adaptive mechanism could exploit. The positive Jensen Gaps support this second claim. This distinction is important for the interpretation of CAFE. A positive gap is not a certificate of final task success. It indicates that the observed stress distribution has expanded relative to the expected stress distribution under a convex potential. In practical terms, the architecture exposes more variation about how it experiences contradiction, overload, ambiguity, and drift. Such variation is useful only if there is a mechanism that can learn from it: adaptive routing, memory updates, stress-aware model selection, prompt repair, or architecture reconfiguration. Without such a mechanism, the system may remain brittle despite having an antifragility-compatible signal. 6.2 Architectural Effects The architecture ranking induced by CAFE differs from a ranking based on immediate quality. A4 Ensemble has the largest quality drop and also the largest Jensen Gap. This makes A4 a useful example of the intended reading of the metric: the ensemble does not solve the stressed prompts better in the short term, but it exposes the richest observed stress geometry. The diversity of independent analysts appears to create broader variation across stress dimensions, especially load, ambiguity, and drift. A1 Hierarchical has the second-largest gap, suggesting that decomposition into risk-specific specialists also increases stress differentiation. This is consistent with a division-of-labor interpretation: different specialists may react differently to semantic overload, ambiguous references, or temporal inconsistency, even if the final synthesized answer still loses quality under stress. A2 Debate expands most strongly along conflict, which matches its adversarial structure. The debate architecture is designed to surface disagreement, so it is expected to be sensitive to contradictory evidence. However, A2 has the smallest global Jensen Gap among the five architectures. This suggests that adversarial debate may expose one stress mode sharply without producing the broadest distributional expansion across the full stress space. A3 Meta-Adaptive expands most strongly along drift. This is consistent with a meta-controller that reacts to coherence and temporal inconsistency. The result is promising but not conclusive: the current meta-adaptive architecture exposes drift-related variation, but the experiment does not yet close the loop by allowing the controller to learn from repeated exposure. 6.3 What the Jensen Gap Measures The distributional Jensen Gap should be read as a geometric statistic, not as a generic distance between distributions. A generic divergence can say that the expected and observed distributions differ, but it does not specify whether the difference corresponds to expansion or compression under a convex stress potential. CAFE focuses on this directionality. Positive values indicate that the observed effective stress distribution is more dispersed than the designed stress distribution; negative values would indicate compression; values close to zero indicate resilience or preservation of the designed stress geometry. This makes the choice of potential ϕφ conceptually important. In this paper we use ϕ()=∥22φ(x)= _2^2, which treats all stress dimensions symmetrically and measures total dispersion. This is a conservative first choice because it avoids hand-tuning the metric to favor one architecture. In future work, domain-specific potentials could assign greater weight to particular stresses, such as contradiction in factual verification tasks or temporal drift in longitudinal decision support. 6.4 Limitations The first limitation is that observed stress is reconstructed rather than directly measured. The inverse problem is constrained by four judge signals, regularization, and the fitted polynomial response model. This makes the observed distribution an effective latent quantity, not a ground-truth physical measurement. The fit diagnostics show moderate explanatory power, which is enough for a first controlled study but not enough to treat individual reconstructed stress vectors as exact. For this reason, CAFE should be used as a distributional diagnostic rather than as a per-sample stress oracle. The second limitation is that the current experiment is single-domain. Banking risk is a useful stress-test domain because it naturally combines conflicting evidence, temporal drift, overloaded context, and ambiguity. Nevertheless, the stress geometry may differ in medical reasoning, legal analysis, software engineering, scientific question answering, or open-ended planning. A stronger claim would require repeating the analysis across domains with different stress semantics. The third limitation is that CAFE identifies opportunity but does not implement the adaptation loop. The present study stops after detecting convex-expansive stress deformation. It does not update memories, retrain routers, change architecture selection policies, or optimize prompts based on the detected stress modes. Therefore, the paper should not claim that the evaluated architectures already improve from adversity. It should claim that CAFE identifies when such improvement may be learnable. The fourth limitation concerns the judge. The response signals are produced by an automatic evaluator, and the reconstruction depends on their stability. Although the judge is deterministic and multi-dimensional, it may still encode rubric biases. Human calibration, judge ensembles, or cross-judge sensitivity analysis would strengthen the empirical claim. 6.5 Implications The main implication is that robustness and antifragility should be separated in the evaluation of multi-agent LLM systems. Robustness asks whether quality is preserved under perturbation. CAFE asks whether stress produces a structured signal that could support future improvement. These are related but distinct properties. A system can be non-robust in immediate quality while still exposing an antifragility-compatible stress geometry. This perspective suggests a concrete research program. First, use CAFE to detect which architectures and stress dimensions produce positive distributional expansion. Second, attach adaptive mechanisms to those stress modes: route high-conflict cases to debate, route high-drift cases to temporal verification, or update memory when repeated overload patterns appear. Third, measure whether repeated use of these mechanisms turns antifragility-compatible opportunity into actual performance gains over time. Under this view, CAFE is not the final antifragile system. It is the measurement layer needed to decide where antifragile learning should be applied. 7 Conclusions and Future Work We introduced CAFE, a statistical framework for identifying antifragility-compatible regimes in multi-agent LLM architectures. CAFE separates immediate performance from antifragility opportunity. In our experiments, semantic stress reduces average judge quality across all architectures, so the systems should not be described as already antifragile in the strong operational sense. At the same time, every architecture exhibits a positive distributional Jensen Gap: the observed effective stress distribution expands relative to the expected stress distribution under a convex potential. This suggests that the stressed systems expose structured variation that could be exploited by future adaptation. The contribution of CAFE is therefore methodological. It provides a way to ask whether a given stress scenario is statistically antifragility-compatible before building the adaptive mechanism that would learn from it. This is a useful separation: without a measurement layer, antifragility learning risks optimizing against noisy degradation rather than against structured stress signals. 7.1 Antifragility Learning The first future direction is to design explicit antifragility learning methods. In the current paper, CAFE detects where useful stress variation appears; it does not yet convert that variation into improved behavior. A next step is to use the recovered stress modes as training or control signals. For example, high-conflict observations could trigger debate-based routing, high-drift observations could trigger temporal verification, and high-load observations could trigger decomposition or summarization before final synthesis. More generally, antifragility learning should optimize architectures to benefit from repeated exposure to stress. This could be implemented through stress-aware routers, memory systems that store failure modes, curriculum policies that sample perturbations with positive CAFE gaps, or meta-controllers that select coordination strategies based on the inferred stress profile. The key open question is whether positive distributional Jensen Gaps can be turned into later gains in quality, calibration, factuality, or robustness. 7.2 Evolution of Adapted Multi-Agent Systems The second direction is to study how the antifragile capacity of a multi-agent system changes after it has been adapted with antifragility learning. The present experiments evaluate each architecture at a single point: prompts are generated, responses are judged, observed stress is reconstructed, and the Jensen Gap is estimated. In an adaptive MAS, this measurement should become a trajectory. After each adaptation step, CAFE can estimate a,tG_a,t across time windows and quantify whether the system’s antifragility-compatible regime strengthens, weakens, shifts across stress dimensions, or disappears. This joint temporal and architectural view is important because adaptation can change both performance and stress geometry. A system may initially show a positive gap because stress exposes many unresolved failure modes. After adaptation, the same gap could decrease because the system has learned to absorb the stress more smoothly. Alternatively, the gap could remain positive while quality improves, indicating that the system continues to extract useful variation from new stressors. The relevant question is therefore not only whether the MAS improves, but how its antifragile capacity changes: by how much the gap changes, which stress dimensions drive the change, and whether the change is stable over repeated stress exposure. Current multi-agent architectures are usually specified manually: flat pipelines, hierarchies, debates, meta-controllers, or ensembles. A CAFE-driven system could instead adapt its topology as its stress geometry evolves. It could add specialists when a stress dimension repeatedly expands, prune agents that do not contribute useful stress information, or switch between debate, hierarchy, and ensemble modes depending on the inferred stress regime. This opens a broader question: what kinds of multi-agent organization emerge when the optimization target is not only immediate answer quality, but also the ability to learn from adversity? Studying this question requires logging architecture changes, stress distributions, response quality, and CAFE gaps over long horizons. The resulting systems may not converge to a single fixed architecture; they may become adaptive populations of agents whose structure changes with the stress landscape. 7.3 Forecasting Antifragile Regimes The third direction is forecasting. If CAFE can estimate whether a scenario is currently antifragility-compatible, a natural next question is whether such regimes can be predicted before full evaluation. Forecasting could use early judge signals, partial responses, prompt-level stress descriptors, historical CAFE trajectories, or architecture metadata to predict the future Jensen Gap and its uncertainty. Such forecasting would support proactive control. A system could allocate more compute to prompts likely to produce useful stress variation, preselect architectures that historically benefit from a given stress profile, or avoid adaptation when the forecast suggests concave compression and likely fragility. In deployment, this would turn CAFE from an offline diagnostic into an online decision layer for stress-aware multi-agent systems. 7.4 Closing Remarks CAFE reframes antifragility evaluation as a distributional measurement problem. Rather than asking only whether performance survives perturbation, it asks whether stress creates a structured signal that future systems can learn from. The present results show that this signal can be detected even when immediate quality decreases. The next step is to close the loop: build multi-agent systems that use CAFE signals to adapt, track whether their antifragility evolves over time, and forecast when adversity is likely to become useful rather than merely damaging. References [undef] Nassim Nicholas Taleb and Raphael Douady “Mathematical definition, mapping, and detection of (anti) fragility” In Quantitative Finance 13.11 Taylor & Francis, 2013, p. 1677–1689 [undefa] Nassim N Taleb “’Antifragility’as a mathematical idea” In Nature 494.7438 Nature Publishing Group UK London, 2013, p. 430–430 [undefb] Nassim Nicholas Taleb and Jeffrey West “Working with convex responses: Antifragility from finance to oncology” In Entropy 25.2 MDPI, 2023, p. 343 [undefc] John Johnson and Adrian V Gheorghe “Antifragility analysis and measurement framework for systems of systems” In International journal of disaster risk science 4.4 Springer, 2013, p. 159–168 [undefd] Daniel Russo and Paolo Ciancarini “Towards antifragile software architectures” In Procedia Computer Science 109 Elsevier, 2017, p. 929–934 [undefe] Joseph S Botros, Lamis F Al-Qora’n and Amro Al-Said Ahmad “Towards antifragility of cloud systems: An adaptive chaos driven framework” In Information and Software Technology 174 Elsevier, 2024, p. 107519 [undeff] Jerome Sacks, William J Welch, Toby J Mitchell and Henry P Wynn “Design and analysis of computer experiments” In Statistical science 4.4 Institute of Mathematical Statistics, 1989, p. 409–423 [undefg] Jianhua Lin “Divergence measures based on the Shannon entropy” In IEEE Transactions on Information theory 37.1 IEEE, 2002, p. 145–151 [undefh] Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf and Alexander Smola “A kernel two-sample test” In The journal of machine learning research 13.1 JMLR. org, 2012, p. 723–773 [undefi] Gábor J Székely and Maria L Rizzo “Energy statistics: A class of statistics based on distances” In Journal of statistical planning and inference 143.8 Elsevier, 2013, p. 1249–1272 [undefj] Qingyun Wu, Gagan Bansal, Jieyu Zhang, Yiran Wu, Beibin Li, Erkang Zhu, Li Jiang, Xiaoyun Zhang, Shaokun Zhang and Jiale Liu “Autogen: Enabling next-gen LLM applications via multi-agent conversations” In First conference on language modeling, 2024 [undefk] Guohao Li, Hasan Hammoud, Hani Itani, Dmitrii Khizbullin and Bernard Ghanem “Camel: Communicative agents for" mind" exploration of large language model society” In Advances in neural information processing systems 36, 2023, p. 51991–52008 [undefl] Sirui Hong, Mingchen Zhuge, Jonathan Chen, Xiawu Zheng, Yuheng Cheng, Jinlin Wang, Ceyao Zhang, Zili Wang, Steven Ka Shing Yau and Zijuan Lin “MetaGPT: Meta programming for a multi-agent collaborative framework” In The twelfth international conference on learning representations, 2023 [undefm] Taicheng Guo, Xiuying Chen, Yaqi Wang, Ruidi Chang, Shichao Pei, Nitesh V Chawla, Olaf Wiest and Xiangliang Zhang “Large language model based multi-agents: A survey of progress and challenges” In arXiv preprint arXiv:2402.01680, 2024 [undefn] Yilun Du, Shuang Li, Antonio Torralba, Joshua B Tenenbaum and Igor Mordatch “Improving factuality and reasoning in language models through multiagent debate” In Forty-first international conference on machine learning, 2024 [undefo] Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery and Denny Zhou “Self-consistency improves chain of thought reasoning in language models” In arXiv preprint arXiv:2203.11171, 2022 [undefp] Aman Madaan, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon, Nouha Dziri, Shrimai Prabhumoye and Yiming Yang “Self-refine: Iterative refinement with self-feedback, 2023” In URL https://arxiv. org/abs/2303.17651 2303, 2023 [undefq] Noah Shinn, Federico Cassano, Ashwin Gopinath, Karthik Narasimhan and Shunyu Yao “Reflexion: Language agents with verbal reinforcement learning” In Advances in neural information processing systems 36, 2023, p. 8634–8652 [undefr] Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao and Karthik Narasimhan “Tree of thoughts: Deliberate problem solving with large language models” In Advances in neural information processing systems 36, 2023, p. 11809–11822 [undefs] Shunyu Yao, Jeffrey Zhao, Dian Yu, Nan Du, Izhak Shafran, Karthik Narasimhan and Yuan Cao “React: Synergizing reasoning and acting in language models” In arXiv preprint arXiv:2210.03629, 2022 [undeft] Marco Tulio Ribeiro, Tongshuang Wu, Carlos Guestrin and Sameer Singh “Beyond accuracy: Behavioral testing of NLP models with CheckList” In Proceedings of the 58th annual meeting of the association for computational linguistics, 2020, p. 4902–4912 [undefu] Karan Goel, Nazneen Fatema Rajani, Jesse Vig, Zachary Taschdjian, Mohit Bansal and Christopher Ré “Robustness gym: Unifying the NLP evaluation landscape” In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies: Demonstrations, 2021, p. 42–55 [undefv] Douwe Kiela, Max Bartolo, Yixin Nie, Divyansh Kaushik, Atticus Geiger, Zhengxuan Wu, Bertie Vidgen, Grusha Prasad, Amanpreet Singh and Pratik Ringshia “Dynabench: Rethinking benchmarking in NLP” In Proceedings of the 2021 conference of the North American chapter of the Association for Computational Linguistics: human language technologies, 2021, p. 4110–4124 [undefw] Percy Liang, Rishi Bommasani, Tony Lee, Dimitris Tsipras, Dilara Soylu, Michihiro Yasunaga, Yian Zhang, Deepak Narayanan, Yuhuai Wu and Ananya Kumar “Holistic evaluation of language models” In arXiv preprint arXiv:2211.09110, 2022 [undefx] James Thorne, Andreas Vlachos, Christos Christodoulopoulos and Arpit Mittal “FEVER: a large-scale dataset for fact extraction and VERification” In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), 2018, p. 809–819 [undefy] Stephanie Lin, Jacob Hilton and Owain Evans “Truthfulqa: Measuring how models mimic human falsehoods” In Proceedings of the 60th annual meeting of the association for computational linguistics (volume 1: long papers), 2022, p. 3214–3252 [undefz] Sewon Min, Julian Michael, Hannaneh Hajishirzi and Luke Zettlemoyer “AmbigQA: Answering ambiguous open-domain questions” In Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP), 2020, p. 5783–5797 [undefaa] Yushi Bai, Xin Lv, Jiajie Zhang, Hongchang Lyu, Jiankai Tang, Zhidian Huang, Zhengxiao Du, Xiao Liu, Aohan Zeng, Lei Hou, Yuxiao Dong, Jie Tang and Juanzi Li “LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding” In arXiv preprint arXiv:2308.14508, 2023 [undefab] Ethan Perez, Saffron Huang, Francis Song, Trevor Cai, Roman Ring, John Aslanides, Amelia Glaese, Nat McAleese and Geoffrey Irving “Red Teaming Language Models with Language Models” In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, 2022, p. 3419–3448 DOI: 10.18653/v1/2022.emnlp-main.225 [undefac] Yang Liu, Dan Iter, Yichong Xu, Shuohang Wang, Ruochen Xu and Chenguang Zhu “G-eval: NLG evaluation using gpt-4 with better human alignment” In Proceedings of the 2023 conference on empirical methods in natural language processing, 2023, p. 2511–2522 [undefad] Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li and Eric Xing “Judging llm-as-a-judge with mt-bench and chatbot arena” In Advances in neural information processing systems 36, 2023, p. 46595–46623 [undefae] Wei-Lin Chiang, Lianmin Zheng, Ying Sheng, Anastasios Nikolas Angelopoulos, Tianle Li, Dacheng Li, Hao Zhang, Banghua Zhu, Michael Jordan and Joseph E Gonzalez “Chatbot arena: An open platform for evaluating llms by human preference” In arXiv preprint arXiv:2403.04132, 2024 Appendix A Marginal Stress Deformation Diagnostics This appendix reports the complete set of marginal expected-to-observed stress deformation plots. The main results use the aggregate distributional Jensen Gap and a small number of representative marginals. The figures below are included to make the architecture-specific deformation patterns auditable. In each panel, the horizontal axis corresponds to the designed stress intensity ψi _i, the vertical axis corresponds to the reconstructed observed effective stress intensity, and the diagonal line denotes no marginal deformation. Figures 4–8 report the complete marginal diagnostics for A0 through A4. A0 conflict A0 load A0 ambiguity A0 drift Figure 4: Marginal stress deformation diagnostics for A0 Flat. A1 conflict A1 load A1 ambiguity A1 drift Figure 5: Marginal stress deformation diagnostics for A1 Hierarchical. A2 conflict A2 load A2 ambiguity A2 drift Figure 6: Marginal stress deformation diagnostics for A2 Adversarial Debate. A3 conflict A3 load A3 ambiguity A3 drift Figure 7: Marginal stress deformation diagnostics for A3 Meta-Adaptive. A4 conflict A4 load A4 ambiguity A4 drift Figure 8: Marginal stress deformation diagnostics for A4 Ensemble. Appendix B Additional Statistical Diagnostics This appendix reports response-surface diagnostics at the level of individual judge signals. The main text reports averages across the four judge dimensions; Table 5 shows the full breakdown used to assess whether the polynomial response model provides enough structure for inverse stress reconstruction. Table 6 summarizes the number of rows used for each architecture after data consolidation. Table 5: Response-surface fit diagnostics by architecture and judge signal. Architecture Judge signal R2R^2 RMSE MAE A0 Flat Coherence 0.403 0.100 0.079 A0 Flat Novel inference 0.574 0.077 0.053 A0 Flat Contradiction resolution 0.271 0.147 0.116 A0 Flat Structural preservation 0.708 0.094 0.066 A1 Hierarchical Coherence 0.371 0.105 0.084 A1 Hierarchical Novel inference 0.516 0.091 0.062 A1 Hierarchical Contradiction resolution 0.241 0.166 0.134 A1 Hierarchical Structural preservation 0.692 0.104 0.074 A2 Debate Coherence 0.386 0.108 0.087 A2 Debate Novel inference 0.502 0.092 0.062 A2 Debate Contradiction resolution 0.313 0.154 0.121 A2 Debate Structural preservation 0.717 0.097 0.068 A3 Meta-Adaptive Coherence 0.385 0.108 0.087 A3 Meta-Adaptive Novel inference 0.497 0.090 0.061 A3 Meta-Adaptive Contradiction resolution 0.285 0.160 0.129 A3 Meta-Adaptive Structural preservation 0.702 0.102 0.073 A4 Ensemble Coherence 0.331 0.128 0.096 A4 Ensemble Novel inference 0.449 0.114 0.074 A4 Ensemble Contradiction resolution 0.346 0.162 0.126 A4 Ensemble Structural preservation 0.669 0.113 0.080 Table 5 shows that the strongest fits occur for structural preservation, with R2R^2 between 0.669 and 0.717. Novel inference is moderately predictable, while contradiction resolution is the noisiest signal. This pattern is expected: temporal or structural drift leaves relatively stable traces in the response, whereas contradiction handling depends on fine-grained semantic reconciliation and therefore has higher residual variance. Table 6: Modeling rows by architecture after data consolidation. Architecture Clean rows Perturbed rows Modeling rows A0 Flat 50 500 550 A1 Hierarchical 50 500 550 A2 Debate 50 500 550 A3 Meta-Adaptive 50 498 548 A4 Ensemble 50 500 550 As shown in Table 6, the slightly smaller A3 sample is due to two missing perturbed evaluations after consolidation. The CAFE statistics are computed using the available rows for each architecture, and uncertainty is estimated with architecture-specific bootstrap resampling. Appendix C Prompt and Response Examples This appendix provides a concrete example of the synthetic stress generation and the corresponding multi-agent outputs. The examples are taken from prompt P001P001. Long responses are excerpted for readability, but the excerpts preserve the risk rating, the handling of stress, and the main supervisory recommendation pattern. Table 7 reports the perturbed prompt variants, Table 8 reports clean-prompt output excerpts, and Table 9 reports perturbed-prompt output excerpts. C.1 Clean Prompt You are preparing a quarterly supervisory review for Banco Norte, a retail banking institution in Spain. Use the following current-quarter indicators: CET1 ratio 10.8%, liquidity coverage ratio 104%, non-performing loan ratio 1.8%, one-day 99% VaR 4.5% of trading capital, operational loss events equal 0.4% of gross income, and a short-term wholesale funding gap of 1.2% of liabilities. Interest-rate conditions are volatile. Assess systemic risk across capital adequacy, liquidity, credit quality, market risk, operational resilience, and interconnectedness. Provide a clear risk rating and specific mitigation recommendations. C.2 Perturbed Prompt Variants Table 7 shows three perturbed versions of the same clean prompt. Each variant combines a different stress vector with semantic edits that inject contradiction, overload, ambiguity, and temporal drift. Table 7: Example perturbations for prompt P001P001. Variant Conflict Load Ambig. Drift Perturbation excerpt P001_V01P001\_V01 0.298 0.661 0.163 0.563 Adds an internal note stating that capital adequacy is both comfortably above target and below the recovery trigger; adds unaudited ratios, net-of-guarantee exposures, settlement-lag caveats, changed management overlays, excluded hedging desks, and stale Q4 2025/Q2 2024 reporting windows. P001_V02P001\_V02 0.159 0.617 0.412 0.442 Replaces concrete references with ambiguous phrases such as “that buffer” and “that exposure”; adds second-order effects from margin calls, drawdowns, payment-system contagion, deposit beta, collateral haircuts, sovereign spread widening, model-risk exceptions, and nine-month-old exposure data. P001_V03P001\_V03 0.152 0.494 0.500 0.580 Introduces ambiguous references such as “that position” and “this area”; adds a contradiction between contained volatility and severe mark-to-market losses; adds scenario-comparison requirements, unaudited ratios, settlement lags, and mismatched Q4 2025/Q2 2024 documents. C.3 Clean-Prompt Outputs Table 8 shows representative excerpts from the five architectures on the clean prompt. All architectures identify Banco Norte as solvent but exposed to thin liquidity, volatile rates, and limited capital headroom. Table 8: Representative clean-prompt output excerpts. Architecture Output excerpt A0 Flat “Overall risk rating: Moderate. Banco Norte appears broadly resilient but shows elevated sensitivity to market and funding shocks given volatile rates, a thin liquidity buffer, and reliance on wholesale funding.” A1 Hierarchical “Overall risk rating: Moderate-High. Banco Norte appears fundamentally solvent, but its risk profile is fragile because several buffers are thin rather than strong.” A2 Debate “Overall systemic risk rating: Moderate, with a negative outlook. Banco Norte appears currently stable but not unambiguously comfortable.” A3 Meta-Adaptive “Overall systemic risk rating: Moderate / Amber. Banco Norte does not appear immediately distressed, but several indicators are only modestly above or near supervisory comfort zones.” A4 Ensemble “Weighted consensus risk rating: Moderate-High / Elevated Watch. The bank is not in immediate distress, but its risk profile is fragile because liquidity is thin and wholesale funding reliance is non-trivial.” C.4 Perturbed-Prompt Outputs Table 9 shows excerpts for P001_V01P001\_V01. The perturbed prompt introduces contradiction, overload, ambiguity, and temporal drift. The outputs become more conservative and devote more space to resolving inconsistent or stale evidence. Table 9: Representative perturbed-prompt output excerpts for P001_V01P001\_V01. Architecture Output excerpt A0 Flat “Overall risk rating: Moderate-to-High / Watchlist. Banco Norte appears broadly solvent but increasingly vulnerable to a stress combination of capital pressure, funding fragility, and asset-quality deterioration.” A1 Hierarchical “Overall risk rating: High / Elevated systemic risk. Banco Norte is not an immediate capital failure case, but it shows a tight capital/liquidity position with elevated tail risk across credit, market, liquidity, and operational dimensions.” A2 Debate “Overall risk rating: Moderate-High. Banco Norte looks operationally viable today, but the combination of borderline liquidity, moderate credit stress, volatile interest rates, short-term wholesale funding dependence, and data-quality caveats supports elevated supervisory concern.” A3 Meta-Adaptive “Supervisory stance: Heightened monitoring / negative bias. Banco Norte is not in an immediate distress zone, but the combination of thin capital headroom, marginal liquidity coverage, short-term wholesale reliance, and data-quality/timeline inconsistencies makes the true risk profile uncertain.” A4 Ensemble “Overall risk rating: High / Elevated systemic vulnerability. Banco Norte does not appear to be in immediate collapse, but it shows multiple thin buffers, weak data reliability, and several reinforcing stress channels.” C.5 Interpretation The example illustrates the empirical pattern reported in the main text. Table 7 shows that the perturbed prompt does not make the task easier: it introduces conflicting capital information, additional caveats, ambiguous references, and stale reporting windows. Tables 8 and 9 show that the architectures respond by increasing caution and by surfacing different stress-handling strategies. This is the qualitative counterpart of the CAFE measurement: stress reduces immediate judged quality, but it also exposes architecture-specific variation that can be reconstructed as observed effective stress.