1. TAMR+ Defined: Temporal-Adaptive Multi-hop Reasoning
TAMR+ is a knowledge graph reasoning methodology developed by Harish Kumar at Quantamix Solutions B.V. and published in SSRN working paper 6359818. It was designed specifically to address the failure modes of standard large language model retrieval architectures when applied to structured regulatory domains.
The name encodes the three core innovations that differentiate TAMR+ from prior graph reasoning approaches:
Every regulatory node in the knowledge graph carries temporal validity metadata: date entered into force, date applicable, and date superseded. TAMR+ filters nodes by temporal validity at query time — it cannot retrieve a regulatory requirement that is not yet applicable or has been superseded. Standard graph RAG approaches lack this temporal layer and hallucinate superseded article versions.
TAMR+ dynamically adjusts its reasoning strategy based on query classification. Obligation queries (what must we do?) use a depth-first traversal that prioritizes direct obligation nodes. Penalty queries use a breadth-first approach that collects all applicable penalty provisions. Classification queries use a decision-tree traversal through risk classification nodes. This adaptive routing eliminates the noise inherent in uniform retrieval strategies.
EU AI Act obligations are rarely self-contained in a single article. Article 9 (risk management) is prerequisite for Article 43 (conformity assessment). Article 13 (transparency) generates obligations for both Article 28 (deployer) and Article 53 (GPAI provider). TAMR+ follows these dependency edges across multiple hops — up to seven in the most complex obligation chains — producing answers that reflect the full legal context.
2. Why Vector Search Fails for Regulatory Compliance: 38.5% Accuracy and Hallucinated Citations
Vector search — the retrieval backbone of most commercial RAG systems — converts text into high-dimensional embeddings and finds chunks with the highest cosine similarity to the query embedding. For many knowledge domains, this works adequately. For regulatory compliance, it fails systematically, and EU-RegQA data quantifies exactly where.
The Five Failure Modes
Article fragmentation
EU AI Act articles are split into recitals, paragraphs, and sub-paragraphs when chunked for embedding. Obligation chains that span multiple paragraphs (e.g., Article 9(1) through 9(8)) are retrieved as disconnected fragments. The assembling LLM then synthesizes an answer from incomplete context, producing plausible but legally inaccurate responses.
Cross-reference blindness
EU regulatory texts use extensive cross-referencing. 'As referred to in Article 6(2)' and 'in accordance with Annex III' are precise legal pointers. Vector search cannot follow these references — it retrieves the chunk containing the reference but not the target. Multi-hop reasoning resolves this by traversing reference edges in the graph.
Temporal staleness
EU AI Act has a staggered applicability timeline: August 2024 (prohibitions), August 2025 (GPAI), August 2026 (high-risk AI). Vector embeddings do not encode this temporal structure. Asking 'what are my obligations today?' to a vector system returns all articles regardless of whether they are yet applicable.
Exception logic failures
Regulatory exceptions modify or override general obligations. Article 53(2) creates an open-source GPAI exemption that modifies the general Article 53 obligations. Vector search retrieves both the general obligation and the exception as separate chunks; the LLM frequently fails to correctly apply the exception to the general rule when synthesizing its answer.
Citation hallucination
When retrieved chunks do not contain a sufficient answer, LLMs fill the gap by generating plausible-sounding article numbers. In EU-RegQA testing, vector-based systems produced hallucinated citations (article numbers that do not exist or do not say what the model claims) in 23% of responses. TAMR+ produces zero hallucinated citations — it can only cite nodes that exist in the verified knowledge graph.
3. Graph Representation: EU AI Act as a Knowledge Graph with 31 OWL Entity Types and Temporal Edges
TAMR+ represents the EU AI Act (and the five regulations in the EU-RegQA benchmark) as an OWL (Web Ontology Language) knowledge graph. This representation captures the legal structure of the regulation, not merely its text.
The graph contains over 4,200 obligation nodes across 31 entity types. Key entity types include AISystem, HighRiskAISystem, GPAIModel, SystemicRiskGPAI, Provider, Deployer, Obligation, ProhibitedPractice, Exception, Threshold, ConformityAssessmentProcedure, Annex, ImplementingAct, DelegatedAct, and HarmonisedStandard. Each entity type has defined properties and relationship types with formal OWL semantics — enabling logical inference rather than just graph traversal.
Temporal Edges
Every obligation node carries four temporal edge types: IN_FORCE_FROM (regulatory entry into force date), APPLICABLE_FROM (date organizations must comply), SUPERSEDED_BY (if replaced by a later provision), and MODIFIED_BY (if an implementing act changes the obligation). At query time, TAMR+ accepts a reference date and filters the graph to return only nodes whose APPLICABLE_FROM is before the reference date and whose SUPERSEDED_BY edge either does not exist or points to a node with a future APPLICABLE_FROM.
Practical impact: On August 1, 2026 — one day before the high-risk AI provisions became applicable — a TAMR+ query about high-risk AI obligations correctly returns zero applicable high-risk obligations. On August 2, 2026, the same query returns all Article 9–17 obligations. Vector-based systems cannot make this distinction and generate incorrect answers in both cases.
4. Multi-Hop Reasoning: How the Algorithm Traverses Regulatory Article Dependencies
The most legally sophisticated questions in EU-RegQA require the system to traverse four or more dependency edges to produce a correct answer. An example: “Does a European SME providing a high-risk AI system for medical diagnosis need to undergo a third-party conformity assessment?”
Answering this correctly requires the system to: (1) classify the system as high-risk under Annex III (medical diagnosis); (2) determine whether Article 43 requires third-party assessment for this category (yes, for medical devices); (3) check whether the SME exception in Article 55 applies (it does not for third-party assessment requirements in medical); (4) identify which conformity assessment procedure is applicable; and (5) note that Article 10 data quality obligations must be met before conformity assessment can begin.
TAMR+ handles this through a directed graph traversal that follows REQUIRES, QUALIFIES, OVERRIDES, and REFERENCES edge types. The traversal algorithm maintains a reasoning trace that records every node visited and every edge followed — producing not just the answer but the full reasoning path with article citations, which is essential for regulatory audit documentation.
5. Adaptive Weighting: Temporal Relevance Scoring for Recently Amended Articles
The EU AI Act is a living document. The EU AI Office has issued implementing acts, the GPAI Code of Practice has been finalized, and harmonised standards under Article 40 are progressively being published. TAMR+'s adaptive weighting system assigns a temporal relevance score to each knowledge graph node, which modulates retrieval priority.
| Signal | Weight Modifier | Rationale |
|---|---|---|
| Published < 90 days ago | +0.3 | Recently amended provisions have highest compliance relevance |
| Supersedes earlier provision | +0.2 | Superseding node is the current authoritative text |
| Referenced by harmonised standard | +0.15 | Presumption of conformity elevates operational relevance |
| Under consultation / pending | -0.2 | Reduce retrieval priority for non-final provisions |
| Not yet applicable | -0.4 | Pre-applicability nodes are lower priority but visible for planning |
6. EU-RegQA Benchmark: Methodology, 500 Questions, Evaluation Criteria
EU-RegQA was developed as a rigorous evaluation dataset for EU regulatory reasoning systems, published alongside the TAMR+ methodology in SSRN 6359818. It is the first benchmark purpose-built for European AI regulation compliance tasks.
Dataset Construction
500 questions were generated through a three-stage process: (1) expert legal review of each regulation to identify the 100 highest-frequency compliance decision points; (2) question authoring by regulatory compliance specialists with 10+ years of EU regulatory practice; (3) independent answer verification against the official EUR-Lex consolidated regulatory texts. No LLM was used in question authoring or answer verification — the benchmark is fully human-constructed.
Risk classification, obligations, GPAI
Data subject rights, processing basis
ICT risk, third-party, incident reporting
Security measures, reporting obligations
Data sharing, portability, switching
Evaluation Criteria
Answers are evaluated on three criteria: correctness (binary: does the answer correctly resolve the legal question?), citation accuracy (do cited article numbers and provisions match the ground truth?), and completeness (does the answer include all relevant obligations, not just the primary one?). The headline accuracy figure (74% TAMR+ vs 38.5% vector) is based on correctness. Citation accuracy shows an even larger gap: 98% for TAMR+ (graph nodes can only cite verified entities) vs 61% for vector systems (hallucinated citations account for the 39% failure rate).
7. 74% vs 38.5%: Accuracy Breakdown by Question Type
| Question Type | TAMR+ Accuracy | Best Vector Accuracy | Gap | Primary Failure Mode (Vector) |
|---|---|---|---|---|
| Classification | 81% | 52% | +29pp | Exception logic failures |
| Obligation | 76% | 41% | +35pp | Article fragmentation |
| Penalty | 79% | 33% | +46pp | Cross-reference blindness |
| Timeline / applicability | 68% | 28% | +40pp | Temporal staleness |
| Overall | 74% | 38.5% | +35.5pp | Mixed |
The largest accuracy gap (46 percentage points) is on penalty questions. This is because EU AI Act penalty provisions require the system to: identify the applicable article tier (prohibited, high-risk, or informational); determine whether the organization is a provider, deployer, or operator; apply the correct fine calculation (absolute amount vs percentage of turnover, whichever is higher); and note whether mitigating circumstances under Article 99(6) might apply. Each step requires a separate graph traversal — exactly the multi-hop capability that vector search lacks.
8. Cost Reduction: 50–800x Through Intelligent Subgraph Caching
The primary objection to graph-based reasoning for compliance workloads is computational cost. Multi-hop traversal across 4,200+ nodes is expensive if performed fresh for every query. TAMR+ addresses this through intelligent subgraph caching — the cost-reduction mechanism protected under Patent EP26162901.8.
The caching system operates on the observation that EU regulatory compliance questions have high query similarity within compliance domains. An organization performing a gap assessment asks approximately the same 50–200 questions repeatedly, with minor parameter variation (which AI system, which use case, which jurisdiction). TAMR+ pre-computes the reasoning paths for the most frequent query patterns in each compliance domain and caches the resulting subgraphs.
Cache integrity guarantee: The cache invalidation protocol ensures regulatory updates propagate within 2 minutes. When the EU AI Office publishes a new implementing act or the EUR-Lex consolidated text is updated, the graph update pipeline identifies affected nodes, marks their cached subgraphs as stale, and queues fresh traversal. No stale regulatory information is ever served from cache.
9. Patent EP26162901.8: What Is Protected and Why It Matters
Patent EP26162901.8, filed by Quantamix Solutions B.V. under the European Patent Convention, protects three core innovations:
OWL Regulatory Knowledge Graph with Temporal Validity Edges
The specific method of constructing legal knowledge graphs using OWL ontologies with temporal validity edge types (IN_FORCE_FROM, APPLICABLE_FROM, SUPERSEDED_BY, MODIFIED_BY) and the query-time temporal filtering algorithm that uses these edges to return only currently applicable provisions.
Adaptive Multi-hop Traversal with Query-Type Classification
The method of classifying incoming regulatory queries into obligation, penalty, classification, and timeline types, and dynamically selecting traversal strategies (depth-first, breadth-first, decision-tree) based on query type to optimize both accuracy and computational efficiency.
Temporal Relevance Subgraph Caching with Regulatory Update Invalidation
The caching architecture that pre-computes frequent regulatory reasoning paths as cached subgraphs, assigns temporal relevance scores to determine cache priority, and implements regulatory update detection with automatic cache invalidation for affected subgraphs within a defined propagation time.
The patent protection means that organizations seeking to build EU regulatory reasoning systems at the quality level demonstrated by TAMR+ must either license the methodology from Quantamix Solutions or develop alternative approaches that do not infringe the protected claims. GraQle, the commercial implementation, licenses TAMR+ under its enterprise tier.
10. FAQ
What does TAMR+ stand for?+
TAMR+ stands for Temporal-Adaptive Multi-hop Reasoning. Temporal reflects the algorithm's ability to weight regulatory articles by recency and applicability date. Adaptive means reasoning paths are dynamically adjusted based on query type. Multi-hop means the algorithm traverses multiple dependency edges. The '+' suffix denotes the enhanced version with subgraph caching and cross-framework reasoning, which are the basis of Patent EP26162901.8.
Why does vector search fail for regulatory compliance questions?+
Vector search fails because regulatory obligations are distributed across multiple cross-referenced articles (lost when chunked), temporal applicability cannot be represented in static embeddings, exception logic requires graph traversal to evaluate correctly, and LLMs hallucinate article citations when retrieved context is insufficient. EU-RegQA testing shows 38.5% accuracy for best vector implementations versus 74% for TAMR+.
How was the EU-RegQA benchmark designed?+
EU-RegQA contains 500 questions across five EU regulations (EU AI Act, GDPR, DORA, NIS2, Data Act), authored by regulatory compliance specialists and verified against EUR-Lex consolidated texts. No LLM was used in question authoring or answer verification. Questions span classification, obligation, penalty, and timeline categories, with binary correctness evaluation and citation accuracy scoring.
What does Patent EP26162901.8 protect?+
Patent EP26162901.8 protects the OWL regulatory knowledge graph construction method with temporal validity edges, the adaptive multi-hop traversal algorithm with query-type classification, and the temporal relevance subgraph caching system with regulatory update invalidation. These are the three core TAMR+ innovations that produce 74% EU-RegQA accuracy and 50–800x cost reduction.
How does TAMR+ handle regulatory amendments and updates?+
TAMR+ handles regulatory amendments through temporal edge management. Each node carries dateInForce, dateApplicable, and dateSuperseded properties. When regulatory updates are detected, affected nodes are updated, their temporal properties modified, and cached subgraphs invalidated within 2 minutes. Queries cannot retrieve nodes that the temporal filter marks as inactive for the query date.
Related Resources
Experience TAMR+ in GraQle
GraQle deploys TAMR+ for EU regulatory compliance reasoning. Ask any EU AI Act question and receive a multi-hop reasoning trace with cited article references — no hallucinations.
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