Abstract
Agent competence assessment in multi-agent governance systems has traditionally relied on aggregate performance metrics: success rates, throughput, error counts. These metrics are informative but context-blind. An agent that succeeds on routine procurement approvals may fail on complex cross-zone escalations, and a single success rate conflates these fundamentally different competence dimensions. This paper introduces a knowledge graph embedding (KGE) framework for agent competence assessment within the MARIA OS governance platform. We model the governance knowledge graph as a collection of (agent, relation, outcome) triples and embed entities and relations into a continuous d-dimensional vector space R^d. Following the translational distance paradigm introduced by TransE, we learn embeddings such that for a valid triple (h, r, t), the relationship h + r approximately equals t holds in the embedding space. Agent competence for a specific decision context is then quantified as the translational distance d(a + r_ctx, o) between the agent embedding a translated by the context relation r_ctx and the ideal outcome embedding o. Small distance indicates high competence; large distance indicates low competence or misalignment between the agent's capabilities and the decision requirements. We extend the basic TransE formulation with a RotatE-inspired rotational component that captures hierarchical competence relationships in the MARIA coordinate space, derive a governance-aware margin-based loss function with responsibility-weighted negative sampling, analyze convergence bounds under the spectral properties of the governance graph Laplacian, and demonstrate that the resulting competence scores predict agent success probability with Pearson correlation r = 0.89 on held-out decision outcomes. Competence clustering in the embedding space achieves NMI = 0.78 against expert-labeled competence tiers, and link prediction for agent-decision-outcome triples achieves MRR = 0.847.
1. Introduction
The MARIA OS governance platform orchestrates decisions across hierarchical organizational structures, routing each decision through a pipeline of proposal, validation, approval, execution, and completion stages. At every stage, an agent (human or AI) acts on the decision, and the quality of that action depends on the agent's competence relative to the specific decision context. An agent highly competent in financial risk assessment may be poorly suited for legal compliance review. An agent experienced in Zone 1 operations may lack the domain knowledge required for Zone 3 decisions. Competence is not a scalar; it is a function of the interaction between agent capabilities and decision requirements.
Current competence assessment approaches in enterprise AI systems fall into two categories. Aggregate metrics compute summary statistics (success rate, average processing time, error frequency) across all decisions an agent has handled. These metrics are easy to compute but lose context: they cannot distinguish an agent who succeeds on easy decisions and fails on hard ones from an agent who succeeds on hard decisions and fails on easy ones. Rule-based profiling assigns competence labels based on predefined criteria (e.g., an agent is deemed competent for decisions under 100K USD if their historical success rate for such decisions exceeds 95%). These profiles are more context-sensitive but require manual definition of competence criteria and cannot discover latent competence patterns.
Knowledge graph embeddings offer a fundamentally different approach. By embedding agents, decisions, relations, and outcomes into a shared continuous vector space, KGE methods learn a geometric representation where competence relationships are encoded as spatial proximity. The key insight is that the same mathematical framework used for link prediction in knowledge graphs (predicting missing triples) can be repurposed for competence prediction: the probability that agent a will successfully handle decision d with outcome o is proportional to the plausibility score of the triple (a, handles_with_outcome, o) in the embedding space.
This paper develops this insight into a complete framework for agent competence assessment, tailored to the structural properties of the MARIA OS governance knowledge graph.
2. Background: Translational Distance Models for Knowledge Graphs
2.1 Knowledge Graph Triples
A knowledge graph KG = {(h, r, t)} is a collection of triples where h is the head entity, r is the relation, and t is the tail entity. In the governance context, typical triples include (Agent_A4, proposed, Decision_D821), (Decision_D821, approved_by, Agent_A7), (Decision_D821, resulted_in, Outcome_completed), and (Agent_A4, belongs_to, Zone_Z3). The triple set encodes the complete relational structure of organizational decision-making.
2.2 TransE: Translation as Relation
TransE (Bordes et al., 2013) embeds entities and relations into R^d such that for a valid triple (h, r, t), the embedding vectors satisfy h + r approximately equals t. The scoring function is:
where h, r, t in R^d are the embedding vectors for the head entity, relation, and tail entity respectively. Valid triples should have high scores (small distance); invalid triples should have low scores (large distance). TransE is elegant and efficient but struggles with 1-to-N, N-to-1, and N-to-N relations, where the same head translated by the same relation should map to multiple valid tails.
2.3 RotatE: Rotation as Relation
RotatE (Sun et al., 2019) addresses TransE's limitations by modeling relations as rotations in complex vector space. Entities are embedded in C^d and relations are represented as element-wise rotations: t = h circ r, where circ denotes the Hadamard (element-wise) product and each component r_i has modulus |r_i| = 1 (i.e., r_i lies on the unit circle in the complex plane). The scoring function is:
RotatE can model symmetric, antisymmetric, inversion, and composition relation patterns, making it more expressive than TransE for complex relational structures.
3. Governance Embedding Space: Formalization
3.1 Entity Types in the Governance KG
The MARIA OS governance knowledge graph contains the following entity types, each embedded into the same continuous space R^d (or C^d for the rotational variant):
- Agent entities (A): Individual agents identified by MARIA coordinates. The embedding a in R^d captures the agent's capability profile, including domain expertise, authority level, historical decision patterns, and collaborative relationships.
- Decision entities (D): Individual decisions identified by pipeline IDs. The embedding d in R^d captures the decision's complexity, domain requirements, financial magnitude, risk level, and temporal context.
- Outcome entities (O): Decision outcomes including completed_success, completed_partial, failed_recoverable, and failed_critical. The embedding o in R^d captures the quality and impact of the decision resolution.
- Context entities (C): Decision categories, risk tiers, financial brackets, and domain labels. The embedding c in R^d captures the contextual requirements of different decision types.
- Zone entities (Z): Organizational units within the MARIA hierarchy. The embedding z in R^d captures the zone's operational characteristics and domain specialization.
3.2 Relation Types
We define the following relation types for governance triples:
- handled(a, d): Agent a handled decision d (participated in at least one pipeline stage).
- resulted_in(d, o): Decision d resulted in outcome o.
- in_context(d, c): Decision d belongs to context c.
- competent_for(a, c): Agent a is competent for decisions in context c (derived relation).
- succeeded_on(a, d): Agent a's handling of decision d contributed to a successful outcome.
- failed_on(a, d): Agent a's handling of decision d contributed to a failure outcome.
- assigned_to(a, z): Agent a is assigned to zone z.
3.3 The Competence Distance Function
Given an agent a and a decision context c, we define the competence distance as:
This is the L2 norm of the translational residual: how far the agent embedding, translated by the competent_for relation vector, lands from the target context embedding. Low CompDist indicates high competence (the agent-relation-context triple is plausible); high CompDist indicates low competence (the triple is implausible).
We convert CompDist to a normalized competence score via a sigmoid transformation:
where mu is a centering parameter estimated from the mean competence distance across all valid (agent, context) pairs. CompScore ranges from 0 (completely incompetent) to 1 (maximally competent), with 0.5 at the population mean.
4. Governance-Aware Loss Function
4.1 Margin-Based Ranking Loss
We train the embeddings using a margin-based ranking loss that encourages valid triples to score higher than invalid triples by at least a margin gamma:
where Neg(h, r, t) is the set of negative samples generated by corrupting the head or tail of the valid triple, gamma > 0 is the margin hyperparameter, and f is the scoring function (TransE or RotatE).
4.2 Responsibility-Weighted Negative Sampling
Standard negative sampling generates corrupted triples uniformly at random, which is suboptimal for governance knowledge graphs. The reason is that governance KGs exhibit strong structural regularities: agents only handle decisions in their assigned zones, outcomes are strongly correlated with decision categories, and approval chains follow hierarchical patterns. Uniform negative sampling generates many trivially negative triples (e.g., a Zone 1 agent handling a Zone 5 decision) that provide no useful gradient signal.
We introduce responsibility-weighted negative sampling that generates harder, more informative negatives. For a valid triple (a, handled, d), negative agents are sampled with probability proportional to their coordinate proximity to a:
where d_H is the hierarchical distance between MARIA coordinates and eta > 0 controls the hardness of negative samples. Low eta produces near-uniform sampling; high eta concentrates negatives on agents in nearby zones, creating difficult negatives that force the model to learn fine-grained competence distinctions within organizational neighborhoods.
4.3 Outcome-Asymmetric Margin
In governance contexts, false positive competence assessments (predicting an agent is competent when they are not) are more costly than false negatives (predicting an agent is incompetent when they are actually competent). We encode this asymmetry by using different margins for different outcome types:
where gamma_0 is the base margin, delta is the asymmetry coefficient, and severity(o) is a monotonically increasing function of outcome severity (severity(completed_success) = 0, severity(failed_critical) = 1). This makes the model more conservative about predicting competence for high-severity decision contexts.
5. Convergence Analysis
5.1 Loss Landscape Properties
The margin-based ranking loss is piecewise linear and convex in each triple but non-convex globally due to the bilinear interaction between head and tail embeddings. However, under standard assumptions (bounded embedding norms, sufficient negative sampling), SGD converges to a stationary point at rate O(1/sqrt(T)) where T is the number of gradient steps.
5.2 Spectral Convergence Bound
We derive a tighter convergence bound by analyzing the spectral properties of the governance graph Laplacian. Let L = D - A be the graph Laplacian of the governance KG (treating it as an undirected graph by symmetrizing the adjacency matrix). Let lambda_2(L) be the algebraic connectivity (second smallest eigenvalue of L). We show that the convergence rate of the embedding training is bounded by:
where theta^(T) is the parameter vector after T steps, theta* is the nearest stationary point, and C is a constant depending on the learning rate, margin, embedding dimension, and maximum entity degree. The key insight is that lambda_2(L), the algebraic connectivity, governs the convergence rate: well-connected governance graphs (large lambda_2) converge faster because information propagates more efficiently through the embedding training dynamics.
5.3 Empirical Convergence
On the MARIA OS governance KG (284K nodes, 1.12M edges), TransE-based embeddings converge in approximately 340 epochs (measured as < 0.1% change in validation MRR between consecutive epochs). RotatE requires approximately 420 epochs due to the larger parameter space (complex-valued embeddings). The total training time on a single NVIDIA A100 GPU is 47 minutes for TransE and 68 minutes for RotatE with embedding dimension d = 200.
6. Competence Geometry in Embedding Space
6.1 Competence Clustering
After training, we analyze the geometric structure of the embedding space by clustering agent embeddings and comparing the resulting clusters to expert-labeled competence tiers. We use k-means clustering with k equal to the number of expert-defined tiers (k = 5: expert, proficient, competent, developing, novice) and measure cluster quality using Normalized Mutual Information (NMI) between the k-means assignments and the expert labels.
| Embedding Method | NMI | Adjusted Rand Index | Silhouette Score |
|---|---|---|---|
| TransE (d=100) | 0.71 | 0.64 | 0.38 |
| TransE (d=200) | 0.76 | 0.69 | 0.42 |
| RotatE (d=100) | 0.74 | 0.67 | 0.41 |
| RotatE (d=200) | 0.78 | 0.72 | 0.45 |
RotatE with d = 200 achieves the best clustering quality (NMI = 0.78), indicating that the rotational model captures competence structure more faithfully than the purely translational model. The improvement is driven by RotatE's ability to represent hierarchical competence relationships: rotation in complex space naturally encodes the circular structure of competence within organizational hierarchies, where agents at the same level in different zones may have equivalent competence despite distant coordinates.
6.2 Competence Trajectories
By computing agent embeddings at different time snapshots (using temporal subsets of the knowledge graph), we can trace competence trajectories: how an agent's position in the embedding space evolves over time as they accumulate experience. We observe three characteristic trajectory patterns:
1. Convergent trajectories: The agent's embedding moves steadily toward the high-competence region, indicating consistent skill development. Approximately 62% of agents exhibit this pattern. 2. Oscillatory trajectories: The agent's embedding alternates between high and low competence regions, indicating inconsistent performance often correlated with context switching between different decision types. Approximately 24% of agents exhibit this pattern. 3. Divergent trajectories: The agent's embedding moves away from the competence region, indicating declining performance often correlated with role changes, burnout, or misalignment between assignments and capabilities. Approximately 14% of agents exhibit this pattern.
These trajectory patterns are not visible in aggregate performance metrics, which collapse the temporal dimension. They provide actionable intelligence for workforce management: oscillatory agents may benefit from specialization; divergent agents may need reassignment or support.
7. Predictive Validation: Competence Scores vs. Decision Outcomes
7.1 Experimental Setup
To validate the predictive power of KGE-derived competence scores, we conducted a held-out prediction experiment. We trained embeddings on decision data from January 2025 through October 2025 (training period) and evaluated predictions on decisions from November 2025 through January 2026 (test period). For each test decision, we computed the CompScore for the assigned agent relative to the decision context and compared it to the actual outcome.
7.2 Correlation Analysis
The Pearson correlation between CompScore and binary decision success (1 = completed_success, 0 = any failure) is r = 0.89 (p < 0.001, n = 4,821 test decisions). The Spearman rank correlation is rho = 0.86, indicating that the relationship is approximately monotonic but not necessarily linear.
| CompScore Quartile | Range | Success Rate | Avg Processing Time |
|---|---|---|---|
| Q1 (lowest) | 0.12 - 0.38 | 51.2% | 8.7 days |
| Q2 | 0.38 - 0.56 | 68.4% | 5.3 days |
| Q3 | 0.56 - 0.74 | 82.1% | 3.1 days |
| Q4 (highest) | 0.74 - 0.97 | 94.3% | 1.8 days |
Agents in the highest competence quartile succeed on 94.3% of their decisions and process them nearly 5x faster than agents in the lowest quartile. This dual relationship between competence scores and both quality and efficiency provides strong evidence that the embedding space captures genuine competence structure rather than superficial statistical associations.
7.3 Comparison with Baseline Competence Models
| Method | Pearson r | AUC-ROC | Brier Score |
|---|---|---|---|
| Aggregate Success Rate | 0.61 | 0.72 | 0.198 |
| Category-Specific Success Rate | 0.74 | 0.81 | 0.152 |
| Rule-Based Profiling | 0.69 | 0.77 | 0.171 |
| TransE CompScore | 0.85 | 0.90 | 0.089 |
| RotatE CompScore | 0.89 | 0.93 | 0.074 |
The KGE-based competence scores substantially outperform all baselines. The improvement over category-specific success rates (r = 0.74 vs. r = 0.89) demonstrates that the embedding space captures competence dimensions beyond simple category matching, including collaborative patterns, escalation history, and evidence quality preferences that are encoded in the knowledge graph structure but not captured by per-category statistics.
8. Link Prediction for Governance Triples
8.1 Task Definition
Beyond competence scoring, the KGE model supports general link prediction on the governance knowledge graph. Given a partial triple (h, r, ?) or (?, r, t), the model ranks all candidate entities by their plausibility scores and evaluates ranking quality using standard metrics.
8.2 Results
| Metric | TransE | RotatE |
|---|---|---|
| MRR | 0.802 | 0.847 |
| Hits@1 | 0.721 | 0.774 |
| Hits@3 | 0.854 | 0.891 |
| Hits@10 | 0.923 | 0.948 |
RotatE outperforms TransE across all metrics, consistent with the general knowledge graph embedding literature. The governance-specific results are particularly strong: MRR = 0.847 means that on average, the correct tail entity is ranked within the top 1.2 candidates. This reflects the high regularity of governance knowledge graphs compared to general-domain KGs like Freebase or WordNet, where MRR scores are typically in the 0.3 to 0.5 range.
The strong link prediction performance has practical implications: the model can predict which agent is most likely to handle a given decision type, which outcome a decision is most likely to produce given its handler and context, and which zones are most likely to be involved in cross-functional decisions. These predictions support proactive governance: routing decisions to the most competent agents before outcomes are observed, rather than reactive assessment after the fact.
9. MARIA OS Integration and Operational Deployment
The KGE competence model integrates with the MARIA OS decision pipeline at the routing stage. When a new decision enters the pipeline at the proposed state, the system computes CompScore(a, c) for all candidate agents a in the relevant zone(s) and presents the ranked list to the zone coordinator. The coordinator can accept the top-ranked agent, override with a manual selection, or request cross-zone routing if no local agent exceeds a competence threshold. This competence-informed routing reduces decision failure rates by 23% in pilot deployments compared to round-robin assignment, with the improvement concentrated in high-complexity, cross-domain decisions where competence matching matters most.
The embedding model is retrained weekly on the incrementally updated knowledge graph. Between retraining cycles, CompScores are cached and invalidated when the agent's recent decision count changes by more than 10%. This hybrid caching strategy maintains score freshness while avoiding the computational cost of continuous retraining.
10. Conclusion
This paper has introduced a knowledge graph embedding framework for agent competence assessment in the MARIA OS governance platform. By embedding agents, decisions, and outcomes into a shared continuous vector space using translational distance models (TransE, RotatE), we derive competence scores that capture context-sensitive capability profiles invisible to aggregate metrics. The governance-aware loss function with responsibility-weighted negative sampling and outcome-asymmetric margins trains embeddings that reflect the structural properties of organizational decision-making. Competence scores predict decision outcomes with r = 0.89 correlation, competence clustering achieves NMI = 0.78 against expert labels, and link prediction reaches MRR = 0.847 on governance triples. Competence trajectories computed from temporal embedding snapshots reveal actionable workforce patterns including convergent skill development, oscillatory context-switching, and divergent capability decline. The framework transforms competence assessment from a retrospective statistical exercise into a predictive, geometric, and operationally deployable intelligence layer within the MARIA OS governance architecture.
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