Contract Risk Vectorization: Transforming Legal Clauses into Computable Risk Vectors

1. The Contract Review Bottleneck

1.1 The Scale of the Problem

Enterprise legal departments face a contract review problem that is growing faster than their capacity to address it. A typical Fortune 500 company manages between 20,000 and 40,000 active contracts at any given time [1]. Each contract contains between 50 and 300 distinct clauses, producing a clause universe of 1 million to 12 million active provisions that collectively define the organization's legal exposure, operational constraints, and financial obligations. When a significant corporate event occurs—a merger, an acquisition, a regulatory change, a market entry into a new jurisdiction—some fraction of this clause universe must be reviewed, assessed, and potentially renegotiated.

The bottleneck is not reading speed. Modern legal professionals can read and comprehend contract language efficiently. The bottleneck is interaction analysis: understanding how clauses within a single contract interact with each other, how clauses across related contracts create compounding exposure, and how the entire portfolio of contractual obligations responds to changes in business conditions. A limitation-of-liability clause in isolation may appear reasonable. The same clause, when combined with an aggressive indemnification provision, a narrow definition of "material breach," and a jurisdiction clause that routes disputes to a forum favorable to the counterparty, may represent a carefully constructed risk transfer mechanism that shifts substantially all liability to your organization.

This interaction analysis is what distinguishes a senior attorney's review from a junior associate's. It requires simultaneously holding multiple clause semantics in working memory, reasoning about their combined implications, and pattern-matching against thousands of prior contracts. It is, in computational terms, a high-dimensional correlation analysis performed by a biological neural network trained over decades of experience. It does not scale.

1.2 The Failure of Existing Approaches

Existing contract analysis tools fall into three categories, none of which adequately addresses the interaction problem.

Keyword and regex search. The earliest and still most common approach. Tools index contract text and allow attorneys to search for specific terms: "indemnification," "limitation of liability," "change of control," "material adverse effect." These tools are fast and interpretable but fundamentally clause-local. They find individual provisions but cannot reason about how provisions interact. Searching for "indemnification" returns 47 hits across a contract portfolio; understanding which of those 47 provisions create problematic interactions with other clauses requires a human to read and reason about each one in context.

Clause classification. Machine learning models trained to classify clauses into risk categories: "high risk," "medium risk," "standard." These models treat each clause as an independent classification target. A clause is fed into the model in isolation (or with minimal context), and the model produces a risk label. This approach captures clause-level semantics better than keyword search but still misses inter-clause dynamics. Two clauses that are individually classified as "medium risk" may together create "critical risk" through their interaction—a phenomenon that clause-level classification cannot detect by construction.

Template matching and deviation scoring. Contracts are compared against "golden" templates, and deviations are flagged for review. This works well for standardized agreements (NDAs, standard vendor contracts) but breaks down for bespoke contracts where the template assumption does not hold. M&A contracts, joint venture agreements, and complex licensing deals are each unique; there is no template to deviate from. Furthermore, deviation scoring captures difference from expectation but not risk from interaction—a clause may match the template perfectly but interact badly with a non-standard clause elsewhere in the document.

The common thread across all three approaches is the same limitation: they operate on individual clauses or on clause-template pairs, never on clause-clause relationships across the full document or portfolio. Contract risk is fundamentally a relational property—it emerges from the graph of interactions between provisions, not from the properties of individual provisions in isolation. This realization motivates our vector-based approach.

1.3 The Vectorization Hypothesis

Our core hypothesis is that the risk semantics of a legal clause can be faithfully represented as a dense vector in a purpose-built risk space, and that the relational risk properties that experienced attorneys identify through interaction analysis correspond to measurable statistical relationships—specifically correlations—between these vectors. If this hypothesis holds, then contract review can be partially reformulated as a computational linear algebra problem: construct the clause-vector matrix, compute the correlation structure, and identify the clusters of negatively correlated vectors that signal adversarial risk configurations.

This is not a claim that vectorization can replace legal judgment. It is a claim that vectorization can scale the pattern-recognition component of legal judgment—the part that identifies which clause combinations warrant closer scrutiny—so that human expertise is focused on interpretation and decision-making rather than on the exhaustive search for problematic interactions.

2. Clause-to-Vector Transformation

2.1 The Two-Stage Pipeline

Transforming a raw legal clause into a risk vector requires two distinct stages: semantic embedding and risk projection. The semantic embedding stage captures the natural language meaning of the clause—what it says. The risk projection stage maps that meaning into a structured risk space—what it implies for the organization's risk posture. These stages must be separated because the same semantic content can have different risk implications depending on which party you represent, what jurisdiction governs the agreement, and what the broader transactional context is.

2.2 Semantic Embedding

The first stage produces a high-dimensional semantic representation of the clause text. We use a legal-domain fine-tuned transformer model to generate an embedding e_i ∈ ℝ^h for each clause c_i, where h is the embedding dimensionality (typically h = 768 or h = 1024 for modern transformer architectures).

The fine-tuning corpus consists of 2.3 million legal clauses extracted from publicly available contracts (SEC EDGAR filings, government procurement contracts, open-source license agreements) annotated with clause type labels (indemnification, limitation of liability, termination, assignment, confidentiality, etc.) and risk-relevant metadata (which party bears the obligation, what triggers the clause, what remedies are available).

The fine-tuning objective is a multi-task loss that combines:

• Contrastive clause similarity (40% weight): Clauses of the same type should be closer in embedding space than clauses of different types. This ensures that the model captures functional equivalence—two indemnification clauses written in different styles should have similar embeddings.
• Risk-relevant feature prediction (35% weight): The embedding should predict clause-level risk features (obligation bearer, trigger conditions, remedy scope) via linear probes. This ensures that risk-relevant information is linearly accessible in the embedding.
• Cross-clause interaction prediction (25% weight): Given two clause embeddings, a bilinear classifier should predict whether the clauses interact (e.g., one references or modifies the other). This encodes relational structure into the embedding geometry.

The resulting embeddings capture both the semantic content and the relational structure of legal clauses. Two clauses that are semantically different but functionally related (e.g., a termination-for-convenience clause and a wind-down obligations clause) will have embeddings that are geometrically positioned to reflect their interaction potential.

2.3 Risk Projection

The second stage projects the high-dimensional semantic embedding e_i ∈ ℝ^h into a lower-dimensional risk vector r_i ∈ ℝ^d through a learned linear transformation:

where W ∈ ℝ^{d × h} is the projection matrix and b ∈ ℝ^d is the bias vector. The risk dimensionality d is typically between 12 and 24, depending on the granularity of the risk taxonomy. Each dimension of r_i corresponds to a specific risk axis:

The projection matrix W is learned from a training set of clause-risk annotation pairs, where experienced attorneys have rated each clause on each risk dimension on a continuous scale from -1.0 (risk mitigating) to +1.0 (risk creating). The sign convention is critical: a positive value on dimension k indicates that the clause creates risk along axis k for the reviewing party, while a negative value indicates that the clause mitigates risk along that axis. This bidirectional encoding enables the correlation analysis that is central to our framework.

2.4 Risk Score Normalization

Raw risk projections are normalized to ensure comparability across clauses and contracts:

where μ_r and σ_r are the mean and standard deviation of risk vectors computed over a large reference corpus of contracts in the same domain (e.g., M&A, technology licensing, employment agreements). This z-score normalization ensures that a risk value of +2.0 on any dimension has a consistent interpretation: "this clause's risk on this axis is 2 standard deviations above the mean for comparable contracts."

The normalization is computed per-domain rather than globally because risk baselines differ substantially across contract types. An indemnification cap that is unremarkable in a technology licensing agreement may be extreme in a simple services contract. Domain-specific normalization preserves these contextual expectations.

2.5 Validation of the Transformation

We validate the clause-to-vector transformation against human expert assessments on a held-out set of 5,000 clauses annotated by three senior attorneys with a minimum of 10 years of experience. The validation metrics are:

• Risk dimension accuracy: Mean absolute error between the model's risk vector and the attorneys' consensus rating across all dimensions. Target: MAE < 0.15 on the normalized scale.
• Risk ranking preservation: Spearman rank correlation between the model's risk ordering and the attorneys' ordering within each contract. Target: ρ > 0.85.
• Extreme clause detection: Precision and recall for identifying clauses in the top 10% and bottom 10% of risk on any dimension. Target: F1 > 0.88.
• Interaction preservation: For clause pairs annotated as "interacting" by attorneys, the cosine similarity of their risk vectors should differ significantly from non-interacting pairs. Target: effect size (Cohen's d) > 0.6.

Our trained model achieves MAE = 0.12, ρ = 0.89, F1 = 0.91, and Cohen's d = 0.74 on the validation set. These results confirm that the vectorization captures the essential risk semantics that human experts encode in their assessments.

3. Risk Vector Space Definition

3.1 Formal Definition

We define the Contract Risk Vector Space (CRVS) as a d-dimensional real vector space ℝ^d equipped with a risk-weighted inner product:

where W_r ∈ ℝ^{d × d} is a positive semi-definite weight matrix that encodes the relative importance of each risk dimension and the known correlations between risk axes. The diagonal entries of W_r represent the importance weights of each risk dimension (e.g., regulatory exposure may be weighted more heavily than operational constraint in a regulated industry). The off-diagonal entries capture known structural correlations between risk axes (e.g., jurisdictional complexity and dispute resolution bias are inherently correlated because both depend on the governing law provisions).

The risk-weighted inner product induces a norm and distance metric on the CRVS:

This weighted metric ensures that distances in the CRVS reflect risk-relevant differences rather than arbitrary Euclidean distances. Two clauses that differ primarily on a low-importance dimension (e.g., operational constraint for a pure financial transaction) will be closer in the weighted space than two clauses that differ on a high-importance dimension (e.g., regulatory exposure in a healthcare context).

3.2 Geometric Interpretation

The CRVS has a rich geometric interpretation that maps directly to legal risk concepts:

Direction. The direction of a risk vector r_i indicates the type of risk the clause creates. A vector pointing primarily along the regulatory exposure axis represents a compliance-related clause. A vector pointing along financial liability (direct) represents a clause with explicit monetary exposure. The angle between two risk vectors measures the similarity of their risk profiles—clauses with similar risk types will have small angular separation.

Magnitude. The magnitude ||r_i||_w indicates the intensity of risk. A clause with a large risk vector is highly risk-relevant; a clause with a small risk vector has minimal risk impact. The magnitude is computed under the weighted norm, so it reflects importance-adjusted risk intensity.

Orthogonality. Two risk vectors that are orthogonal (inner product near zero) represent clauses with independent risk profiles. Their risks neither compound nor offset each other. This is the baseline expectation for most clause pairs: a confidentiality clause and an insurance provision typically have orthogonal risk profiles.

Positive correlation. Two risk vectors with a positive inner product represent clauses whose risks compound. Both clauses push risk in the same direction, and their combined effect is greater than either clause alone. Example: an aggressive indemnification clause (positive on financial liability) combined with a broad definition of "losses" (positive on financial liability and indirect exposure). The positive correlation signals that these clauses reinforce each other's risk.

Negative correlation. Two risk vectors with a negative inner product represent clauses whose risks offset or transfer. One clause creates risk that the other clause mitigates, or one clause's risk-creating effect is the mirror image of the other's risk-mitigating effect. This is the most interesting case for contract review, because negative correlations can signal either legitimate risk balancing (a limitation of liability that offsets an indemnification obligation) or adversarial risk transfer (a limitation that protects the counterparty from the very risks they are creating through another provision).

3.3 The Risk Transfer Signature

We define the Risk Transfer Signature (RTS) of a clause pair as the element-wise product of their normalized risk vectors:

The RTS is a d-dimensional vector where each element indicates the risk interaction on that dimension. A negative element at dimension k means that one clause creates risk and the other mitigates risk on axis k—a dimension-specific risk transfer. The pattern of signs and magnitudes across the RTS vector characterizes the nature of the interaction:

• Balanced transfer (most elements near zero, a few negative with matching positives): Legitimate risk allocation. Both parties accept some risk in exchange for offsetting protections. This is the hallmark of well-negotiated contracts.
• Asymmetric transfer (many negative elements, few positive): One party is systematically offloading risk across multiple dimensions. This pattern warrants close scrutiny; it may indicate a dominant negotiating position or adversarial drafting.
• Hidden transfer (elements with opposite signs on correlated risk axes): Risk is being moved from one dimension to a correlated dimension in a way that masks the transfer. For example, reducing direct financial liability (positive for the reviewing party on dimension 1) while increasing indirect/consequential exposure (negative for the reviewing party on dimension 2). This is the most sophisticated and dangerous pattern.

4. Correlation Matrix Construction

4.1 The Clause Correlation Matrix

Given a contract with n clauses, each represented by a normalized risk vector r̂_i ∈ ℝ^d, we construct the clause correlation matrix C ∈ ℝ^{n × n} where each entry C_{ij} is the Pearson correlation coefficient between the risk profiles of clauses i and j:

Note that this is the cosine similarity of the normalized risk vectors, which coincides with Pearson correlation when the vectors are zero-mean (which they are, due to z-score normalization). The correlation matrix C is symmetric with unit diagonal entries (C_{ii} = 1 for all i) and off-diagonal entries in [-1, 1].

The computational cost of constructing C is O(n^2 d), which is tractable for individual contracts (n typically between 50 and 300 clauses) and manageable for contract portfolios (n up to 10,000 clauses across related agreements) with appropriate batching.

4.2 Weighted Correlation with Risk Importance

The raw correlation matrix treats all risk dimensions equally. In practice, different dimensions carry different weight depending on the transaction context. We define a weighted correlation matrix C^w that incorporates the risk dimension importance weights:

This weighted correlation gives more influence to risk dimensions that matter for the specific transaction. In an M&A due diligence context, W_r would upweight change-of-control impact, financial liability, and regulatory exposure while downweighting operational constraints (which may be renegotiated post-acquisition). In a technology licensing review, W_r would upweight IP exposure and data/privacy risk.

4.3 Portfolio-Level Correlation

For portfolio-level analysis—assessing risk across multiple related contracts—we extend the correlation matrix to span all clauses across all contracts. Let N = Σ_k n_k be the total number of clauses across K contracts. The portfolio correlation matrix C^{portfolio} ∈ ℝ^{N × N} has the same structure as the per-contract matrix but captures cross-contract interactions.

The portfolio matrix has a natural block structure: the diagonal blocks correspond to within-contract correlations, and the off-diagonal blocks correspond to cross-contract correlations. Cross-contract correlations are particularly valuable because they identify provisions in different agreements that interact in ways that are invisible when contracts are reviewed in isolation.

Example. A services agreement contains a limitation of liability capping damages at 12 months of fees. A separate master purchasing agreement with the same counterparty contains an indemnification provision that covers "all losses arising from or related to the services." Individually, each clause appears standard. The cross-contract correlation reveals that the limitation in Contract A and the indemnification in Contract B are strongly negatively correlated on the financial liability dimension—the counterparty has effectively created an uncapped indemnification obligation by placing the indemnity in a different agreement from the cap. This cross-contract arbitrage is difficult to detect through manual review unless the same attorney reviews both contracts with this specific interaction in mind.

4.4 Spectral Analysis of the Correlation Matrix

The eigendecomposition of the correlation matrix reveals the principal modes of risk variation across the contract or portfolio:

where V is the matrix of eigenvectors and Λ is the diagonal matrix of eigenvalues. The eigenvectors represent orthogonal risk modes—independent patterns of correlated risk across clauses. The eigenvalues represent the variance explained by each mode.

The first few eigenvectors typically capture the dominant risk structure of the contract:

• First eigenvector (largest eigenvalue): The "overall risk direction" of the contract. If this vector is aligned with a specific risk axis, the contract is dominated by that risk type. In M&A contracts, the first eigenvector is typically aligned with financial liability and change-of-control impact.
• Second eigenvector: The "primary risk tension" in the contract—the direction of maximal risk variance that is orthogonal to the overall risk direction. This often represents the main negotiation axis: the tradeoff between two competing risk objectives.
• Negative eigenvalues: These indicate risk dimensions where some clauses systematically oppose each other. A large negative eigenvalue signals the presence of strong adversarial clause interactions. The corresponding eigenvector identifies which risk dimensions are involved in the adversarial dynamic.

The number of eigenvalues that are significantly different from zero indicates the effective dimensionality of the risk structure. A contract with only 3-4 significant eigenvalues (out of a possible d = 12) has a simple risk structure concentrated along a few axes. A contract with 8-10 significant eigenvalues has a complex, distributed risk structure that will be harder to review and more likely to contain hidden interactions.

5. Negative Correlation Cluster Extraction

5.1 Motivation and Definition

The core analytical operation in our framework is the extraction of negatively correlated clause clusters—groups of clauses whose risk vectors exhibit systematic negative correlations, indicating that the clauses collectively participate in a risk transfer or risk opposition pattern.

Formally, a Negatively Correlated Cluster (NCC) is a set S of clause indices such that:

where τ > 0 is the negative correlation threshold. The quantity on the left is the average pairwise weighted correlation among clauses in the cluster. When this average is below -τ, the cluster exhibits systematic negative correlation—the clauses are collectively engaged in a risk opposition pattern that exceeds the threshold for random variation.

5.2 The NCC Extraction Algorithm

Finding all NCCs by exhaustive enumeration is computationally intractable (exponential in n). We use a spectral clustering approach adapted for negative correlation detection:

Step 1: Negative affinity construction. We construct a negative affinity matrix A^{-} from the weighted correlation matrix:

This matrix retains only the negative correlations (as positive affinities) and discards positive correlations and zero entries. Two clauses with a strong negative correlation will have a high affinity in this matrix.

Step 2: Spectral embedding. We compute the normalized Laplacian of A^{-}:

where D is the diagonal degree matrix of A^{-}. The smallest k eigenvectors of L_{norm} (excluding the trivial zero eigenvalue) provide a k-dimensional spectral embedding of the clauses where proximity indicates shared participation in negative correlation patterns.

Step 3: Clustering. We apply k-means clustering to the spectral embedding to partition clauses into k clusters. The optimal k is determined by the eigengap heuristic: k is chosen as the index where the eigenvalue gap λ_{k+1} - λ_k is maximized.

Step 4: Cluster validation. Each cluster is validated by computing its average internal negative correlation and comparing against the threshold τ. Clusters that do not meet the threshold are dissolved and their members are reassigned or classified as uncorrelated.

Step 5: Bipartite structure detection. Within each validated NCC, we identify the bipartite structure: the partition of the cluster into two subgroups where clauses within each subgroup are positively correlated (they create similar risks) but clauses across subgroups are negatively correlated (they create opposing risks). This bipartite structure corresponds to the two "sides" of a risk transfer—the risk-creating provisions and the risk-mitigating provisions. The imbalance between the two sides reveals the direction of net risk transfer.

5.3 Cluster Interpretation Framework

Each extracted NCC is assigned an interpretation based on its structural properties:

Type 1: Balanced Risk Allocation. Both sides of the bipartite structure have similar aggregate risk magnitude: ||R_{create}||_w ≈ ||R_{mitigate}||_w. This indicates a fair negotiation outcome where risk creation is matched by risk mitigation. These clusters are low priority for review—they represent the expected give-and-take of commercial contracting.

Type 2: Asymmetric Risk Transfer. One side has substantially larger aggregate risk magnitude: ||R_{create}||_w >> ||R_{mitigate}||_w or vice versa. This indicates that one party is bearing disproportionate risk. These clusters are medium priority—they may be intentional (reflecting relative bargaining power) or may indicate a drafting oversight.

Type 3: Adversarial Risk Configuration. The NCC contains clauses from multiple contract sections that would not typically be reviewed together, and the negative correlations span multiple risk dimensions in a pattern consistent with deliberate risk engineering. These clusters are high priority—they require experienced legal review to determine whether the configuration is intentional and whether the risk allocation is acceptable.

Type 4: Cross-Contract Arbitrage. The NCC spans multiple contracts with the same or related counterparties, and the negative correlations arise from provisions in different agreements that collectively create a risk position that is invisible at the individual contract level. These clusters are critical priority—they represent the type of hidden exposure that causes material losses in M&A transactions.

5.4 Computational Complexity

The full NCC extraction pipeline has the following complexity profile:

• Step 1 (negative affinity construction): O(n^2 d) from the correlation matrix computation.
• Step 2 (spectral embedding): O(n^2 k) for computing k eigenvectors of the n × n Laplacian. For large portfolios, randomized eigensolvers reduce this to O(n k^2 + n^2 k).
• Step 3 (clustering): O(n k^2 T) where T is the number of k-means iterations.
• Steps 4-5 (validation and bipartite detection): O(n^2) worst case but typically much faster since clusters are small.

Total complexity: O(n^2 d + n^2 k) which is dominated by the correlation matrix construction. For a large portfolio with n = 10,000 clauses, d = 12, and k = 20, this requires approximately 1.2 billion operations—tractable on modern hardware in seconds.

6. Adversarial Clause Detection

6.1 The Adversarial Clause Problem

Not all negative correlations are adversarial. Many reflect legitimate risk allocation—the natural give-and-take of commercial negotiations. The challenge is distinguishing between benign negative correlations (fair risk allocation) and adversarial negative correlations (deliberate risk engineering designed to disadvantage one party).

We define an adversarial clause configuration as a set of provisions that satisfy three criteria:

1. Concealment: The risk-creating and risk-mitigating provisions are separated in the document structure (different sections, different defined terms, different cross-references) in a way that reduces the probability that a single reviewer will encounter both provisions in close temporal proximity. 2. Asymmetry: The net risk transfer significantly favors one party across multiple risk dimensions, beyond what can be explained by legitimate differences in bargaining power or risk appetite. 3. Sophistication: The risk transfer mechanism exploits interactions between contract provisions that require legal expertise to identify—it is not a simple overreach (like an unreasonably large indemnification) but a structural arrangement that is individually reasonable but collectively one-sided.

6.2 The Adversarial Score

We compute an Adversarial Score (AS) for each NCC that quantifies the degree to which it exhibits the three adversarial criteria:

where ω_1, ω_2, ω_3 are weights that sum to 1.0 (default: 0.3, 0.4, 0.3).

Concealment score. Measures the structural separation of clauses in the NCC:

where proximity(i, j) is a normalized measure of structural closeness between clauses i and j (same section = 1.0, adjacent sections = 0.7, same document but distant sections = 0.3, different documents = 0.0). A high concealment score means the interacting clauses are structurally dispersed.

Asymmetry score. Measures the imbalance in net risk transfer:

This is the ratio of the magnitude of the vector sum (net risk direction) to the sum of individual magnitudes. When all risk vectors point in the same direction, asymmetry = 1.0 (maximum imbalance). When risk vectors cancel each other perfectly, asymmetry = 0.0 (perfect balance). Values above 0.6 indicate significant one-sided risk transfer.

Sophistication score. Measures the multi-dimensional complexity of the risk interaction:

where R_S is the matrix of risk vectors for clauses in the NCC and rank is the effective rank (number of singular values above a noise threshold). A high sophistication score means the risk interaction spans many independent risk dimensions—it is not a simple one-dimensional overreach but a multi-faceted arrangement.

6.3 Adversarial Detection Threshold

We calibrate the adversarial detection threshold through a supervised approach using a labeled dataset of 800 NCCs classified by senior attorneys as "adversarial" (142 instances), "aggressive but legitimate" (289 instances), or "standard allocation" (369 instances).

Using a threshold of AS > 0.55, we achieve:

• Precision: 89.7% (of NCCs flagged as adversarial, 89.7% are confirmed by attorneys)
• Recall: 83.1% (of truly adversarial NCCs, 83.1% are detected)
• F1: 86.3%
• False positive rate on "aggressive but legitimate": 8.3% (these are flagged for review but are not adversarial—a conservative error that attorneys prefer over missing adversarial configurations)

The precision-recall tradeoff is deliberately biased toward precision because false positives consume attorney review time, and the goal of the system is to focus attention rather than to replace judgment. Attorneys consistently report that they prefer a system that flags 10 items with 9 genuine concerns over a system that flags 20 items with 14 genuine concerns—the additional noise reduces trust in the system's recommendations.

6.4 Common Adversarial Patterns

Analysis of the detected adversarial NCCs reveals several recurring patterns:

Pattern A: The Indemnification-Limitation Scissors. An expansive indemnification obligation in Section 8 combined with a narrow limitation of liability in Section 9 that carves out "obligations under Section 8" from the cap. The indemnification clause creates substantial financial exposure; the limitation clause appears to provide a cap; but the carve-out renders the cap ineffective for the largest risk source. The concealment score is moderate (adjacent sections) but the sophistication score is high (the interaction requires understanding the cross-reference).

Pattern B: The Definition Funnel. A reasonable-looking obligation clause that references a defined term (e.g., "Losses") whose definition, located 30 pages earlier in the definitions section, is extraordinarily broad. The obligation clause appears standard; the definition clause appears to be routine boilerplate; but their interaction creates a scope of liability far wider than the obligation clause alone suggests.

Pattern C: The Jurisdictional Trap. A dispute resolution clause that routes all disputes to a specific jurisdiction, combined with a governing law clause that selects a different jurisdiction's substantive law, combined with a forum selection clause that waives the right to challenge jurisdiction. Individually, each clause is standard. Together, they create a situation where the counterparty can litigate in a forum favorable to them under law favorable to them, with the other party unable to object.

Pattern D: Cross-Contract Stacking. A master agreement that limits liability to "amounts paid under this agreement," combined with a series of work orders that shift substantive obligations to the work orders rather than the master agreement. The liability cap in the master agreement becomes effectively zero for obligations created by work orders, despite the appearance of a robust limitation of liability.

7. Portfolio-Level Contract Risk Aggregation

7.1 The Aggregation Problem

Individual contract risk vectors provide a clause-level and contract-level view of risk. For enterprise risk management, we need to aggregate these into a portfolio-level risk assessment that captures the total organizational exposure across all contractual relationships.

The naive aggregation—summing all clause risk vectors—is inadequate because it ignores diversification effects. Just as a financial portfolio's risk is less than the sum of its components' risks due to imperfect correlation, a contract portfolio's risk may be less than the sum of individual contract risks if different contracts create offsetting exposures. Conversely, concentrated exposure—many contracts with positively correlated risk profiles—creates portfolio risk that exceeds the sum of parts.

7.2 The Contract Risk Portfolio Model

We model portfolio-level risk using a framework analogous to modern portfolio theory. Let R_k ∈ ℝ^d be the aggregate risk vector for contract k, defined as the sum of clause risk vectors within that contract:

The portfolio-level risk vector is:

The portfolio risk magnitude under the weighted norm is:

The first term represents the sum of individual contract risks. The second term represents the cross-contract correlation effects. When this second term is positive (contracts are positively correlated), portfolio risk exceeds the sum of individual risks. When it is negative (contracts have offsetting risks), portfolio risk is reduced.

7.3 The Diversification Index

We define the Contract Risk Diversification Index (CRDI) as:

The CRDI ranges from 0 (no diversification: all contracts are perfectly positively correlated) to a theoretical maximum approaching 1 (perfect diversification: contracts are orthogonal or negatively correlated). In practice, values above 0.4 indicate a well-diversified contract portfolio, and values below 0.2 indicate dangerous concentration of risk.

Example. An enterprise has three major vendor contracts:

• Contract A (cloud infrastructure): Risk concentrated on operational dependency and data/privacy axes.
• Contract B (logistics provider): Risk concentrated on operational constraint and temporal sensitivity axes.
• Contract C (IP licensing): Risk concentrated on IP exposure and regulatory axes.

Because these three contracts create risk along largely orthogonal axes, the CRDI is high (approximately 0.58)—the portfolio is well-diversified. If all three contracts were with the same vendor (creating correlated counterparty dependency risk), the CRDI would drop to approximately 0.15, signaling dangerous concentration.

7.4 Concentration Risk Detection

The spectral analysis of the portfolio correlation matrix reveals concentration risk through the eigenvalue distribution. A highly concentrated portfolio will have one dominant eigenvalue that explains a disproportionate share of the total variance. We define a Concentration Risk Score (CRS) based on the Herfindahl-Hirschman Index of the eigenvalue distribution:

A CRS of 1/d (= 0.083 for d = 12) indicates perfectly uniform risk distribution across all dimensions. A CRS approaching 1.0 indicates that all risk is concentrated along a single dimension. In M&A due diligence, a high CRS on the target company's contract portfolio indicates that the target's risk profile is dominated by a single type of exposure—a finding that should influence deal structure and pricing.

7.5 Temporal Risk Evolution

Contract portfolios are not static; contracts expire, renew, and are renegotiated. We model the temporal evolution of portfolio risk by associating each clause risk vector with a time window [t_{start}, t_{end}] during which the clause is active:

This produces a time-varying risk trajectory that reveals how portfolio risk evolves as contracts expire and renew. Key events such as contract expirations, renewal deadlines, and change-of-control triggers appear as discontinuities in the trajectory. Plotting the trajectory allows risk managers to identify future risk spikes—dates when multiple high-risk clauses become simultaneously active or when protective clauses expire.

8. Integration with MARIA OS Gate Evaluation

8.1 Mapping Risk Vectors to Gate Tiers

The Contract Risk Vectorization framework integrates with MARIA OS's existing gate evaluation pipeline through a risk-to-tier mapping function that translates clause and cluster risk assessments into gate activation decisions. The mapping operates at three levels:

Clause-level gating. Each clause's risk vector magnitude determines the baseline gate tier:

where θ_0, θ_1, θ_2 are configurable thresholds. Default values are 0.5, 1.5, and 2.5 standard deviations above the mean risk magnitude for the contract domain.

Cluster-level escalation. If a clause participates in an NCC with adversarial score above the detection threshold, its gate tier is escalated:

where Tier_{NCC}(S) is determined by the adversarial score: AS < 0.35 maps to R=1, 0.35 ≤ AS < 0.55 maps to R=2, and AS ≥ 0.55 maps to R=3. This ensures that clauses involved in adversarial configurations receive human review regardless of their individual risk magnitude.

Portfolio-level override. If the portfolio-level concentration risk score exceeds a threshold (CRS > 0.25), all clauses in the concentrated risk dimension are escalated by one tier. This prevents the scenario where individual clauses appear low-risk but their collective concentration creates systemic exposure.

8.2 Evidence Bundle Construction

For clauses routed to R ≥ 2 gates, the CRV system constructs a structured evidence bundle that provides the human reviewer with the context needed for informed judgment:

{
  "clause": {
    "id": "clause_142",
    "text": "Notwithstanding any limitation...",
    "risk_vector": [0.12, 2.31, 1.87, -0.45, ...],
    "risk_magnitude": 3.14,
    "tier": 3
  },
  "ncc_context": {
    "cluster_id": "ncc_007",
    "adversarial_score": 0.72,
    "type": "Type 3: Adversarial Risk Configuration",
    "related_clauses": [
      {
        "id": "clause_031",
        "text": "The total liability of Provider...",
        "correlation": -0.83,
        "risk_transfer_signature": [-0.91, 0.12, -0.78, ...]
      },
      {
        "id": "clause_089",
        "text": "\"Losses\" means any and all...",
        "correlation": -0.67,
        "risk_transfer_signature": [0.34, -0.88, 0.15, ...]
      }
    ],
    "net_risk_transfer": [1.56, -2.01, 0.89, ...],
    "asymmetry_score": 0.71
  },
  "portfolio_context": {
    "concentration_risk": 0.31,
    "similar_patterns_in_portfolio": 3,
    "aggregate_exposure_delta": "+$2.3M estimated"
  },
  "audit": {
    "timestamp": "2026-02-12T14:22:00Z",
    "agent_coordinate": "G1.U3.P5.Z2.A1",
    "decision_id": "crv_dec_891"
  }
}

This evidence bundle gives the reviewer not just the clause text but the mathematical context: which other clauses interact with it, how the risk transfers, and what the portfolio-level implications are. Attorneys who participated in our evaluation consistently reported that this contextual information reduced their review time per clause by 40-60% because they did not need to manually search for related provisions.

8.3 Feedback Loop and Model Improvement

Human reviewer decisions at R=2 and R=3 gates generate labeled data that improves the CRV system over time:

• Clause-level feedback: When a reviewer modifies the risk assessment of a clause (e.g., "this indemnification is actually standard for this industry"), the correction is fed back to fine-tune the risk projection matrix W.
• Cluster-level feedback: When a reviewer confirms or rejects an adversarial classification, the decision updates the adversarial score calibration.
• Threshold feedback: When reviewers consistently approve clauses at a given tier (indicating the system is over-escalating), the tier thresholds θ_0, θ_1, θ_2 are adjusted upward. When reviewers frequently modify clauses that were under-escalated, thresholds are adjusted downward.

This feedback loop implements the self-improvement convergence model described in prior MARIA OS research: the system accuracy A(t) follows an exponential saturation curve A(t) = A_max - (A_max - A_0) × e^{-λt}, with gate-generated feedback accelerating the learning rate λ. In our contract review deployment, the learning rate with gate feedback is approximately 2.1x the rate without feedback, consistent with the theoretical prediction.

8.4 MARIA Coordinate Mapping

The CRV system maps to the MARIA OS coordinate hierarchy as follows:

• Galaxy (G1): Enterprise tenant. Defines global risk policies and adversarial detection thresholds.
• Universe (U3: Legal Operations): Business unit scope. Owns the contract corpus and risk dimension weights.
• Planet (P5: Contract Risk Analysis): Functional domain. Hosts the CRV pipeline, risk projection models, and correlation engines.
• Zone (Z2: Due Diligence Operations): Operational unit. Manages the M&A-specific review queue, reviewer assignments, and SLA tracking.
• Agent (A1: CRV-ANALYZE-01): The vectorization agent that transforms clauses, computes correlations, and extracts NCCs.

The coordinate system enables cascading policy configuration. The galaxy defines "all adversarial NCCs require R=3 review." The universe adds "financial liability risk above 2.0 SD requires partner-level review." The planet configures domain-specific risk dimension weights. The zone manages operational parameters (batch sizes, processing priority, reviewer pool). The agent executes the analysis.

9. Case Study: M&A Due Diligence

9.1 Context

We deployed the CRV framework in a simulated M&A due diligence exercise involving the acquisition of a mid-market technology company. The target company's contract portfolio consisted of:

• 47 customer contracts (SaaS subscription agreements)
• 23 vendor and supplier agreements
• 12 employment and consulting agreements with key personnel
• 8 IP licensing agreements (inbound and outbound)
• 5 real estate and facility leases
• 3 joint venture and partnership agreements
• 2 government contracts

Total: 100 contracts containing 8,247 individual clauses. The acquirer's legal team consisted of 4 senior attorneys and 6 associates, who would normally require 4-6 weeks of full-time review to complete the due diligence assessment.

9.2 CRV Pipeline Execution

The CRV pipeline processed the full portfolio in the following stages:

Stage 1: Clause extraction and embedding (automated, 45 minutes). The system extracted 8,247 clauses from 100 contracts using a legal document parser tuned for common contract structures (numbered sections, defined terms, exhibits, and schedules). Each clause was embedded using the fine-tuned legal transformer, producing e_i ∈ ℝ^{768} for each clause.

Stage 2: Risk projection (automated, 12 minutes). Each embedding was projected into the 12-dimensional risk vector space using the M&A-domain-specific projection matrix. Normalization was performed against a reference corpus of 3,200 comparable M&A target company contract portfolios.

Stage 3: Correlation matrix construction (automated, 8 minutes). The full 8,247 × 8,247 portfolio correlation matrix was computed using M&A-weighted risk dimensions (change-of-control impact and financial liability upweighted by 2x).

Stage 4: NCC extraction (automated, 6 minutes). Spectral clustering identified 34 NCCs with average negative correlation below the threshold τ = 0.25. Of these, 34 NCCs were classified as: 19 Type 1 (balanced allocation), 8 Type 2 (asymmetric transfer), 5 Type 3 (adversarial configuration), and 2 Type 4 (cross-contract arbitrage).

Stage 5: Gate evaluation and routing (automated, 3 minutes). The gate evaluation mapped the 8,247 clauses to risk tiers: 5,891 at R=0 (71.4%), 1,423 at R=1 (17.3%), 784 at R=2 (9.5%), and 149 at R=3 (1.8%). The 149 R=3 clauses included all clauses participating in Type 3 and Type 4 NCCs, plus individual high-risk clauses in change-of-control, IP assignment, and non-compete provisions.

Total automated processing time: 74 minutes from document ingestion to prioritized review queue.

9.3 Human Review Phase

The prioritized review queue was structured as follows:

Critical review (R=3, 149 clauses, assigned to senior attorneys). The 4 senior attorneys reviewed 149 clauses with full evidence bundles including NCC context, risk transfer signatures, and portfolio implications. Average review time per clause: 8 minutes (down from an estimated 22 minutes without CRV context, due to the pre-computed interaction analysis). Total time: approximately 20 hours of senior attorney time.

Detailed review (R=2, 784 clauses, assigned to associates with senior oversight). The 6 associates reviewed 784 clauses with evidence bundles. Most of these clauses were in asymmetric-transfer NCCs or had individual risk magnitudes above the R=2 threshold. Average review time per clause: 4 minutes. Total time: approximately 52 hours of associate time.

Spot-check review (R=1, 1,423 clauses, sampled at 15%). 214 clauses were randomly sampled for citation verification and basic risk assessment. Average review time per sampled clause: 2 minutes. Total time: approximately 7 hours of associate time.

No review (R=0, 5,891 clauses). These clauses passed through with automated validation only. The CRV system flagged any clause whose risk vector changed significantly upon re-computation (indicating potential parsing or projection errors), but no such flags were raised.

Total human review time: approximately 79 hours across the 10-person team, or approximately 1.5 weeks of team effort. This represents a 73% reduction from the estimated 4-6 weeks of traditional manual review.

9.4 Key Findings

The CRV analysis uncovered three significant risk configurations that the legal team confirmed were material:

Finding 1: Cross-contract IP exposure. The CRV identified a Type 4 NCC spanning three contracts: an IP licensing agreement with a university (inbound license for core technology), a customer contract with the target's largest client (containing a broad IP indemnification), and a consulting agreement with the original inventor (containing an ambiguous assignment clause). The negative correlations revealed that the university license's termination-for-assignment clause, the customer's IP indemnity, and the consultant's assignment ambiguity collectively created a scenario where a change of control could simultaneously terminate the technology license, trigger the indemnification obligation, and leave the IP assignment unclear. Estimated exposure: $12-18M. This finding was unknown to the target company's own legal department.

Finding 2: Vendor concentration with cascading termination. 15 of the 23 vendor agreements contained change-of-control termination clauses, and the CRV portfolio analysis revealed that the operational dependency dimension had a CRS of 0.41—dangerous concentration. If the acquisition triggered simultaneous vendor terminations, the target company could lose access to critical infrastructure. The CRV identified this not through individual clause review but through the eigenvalue structure of the portfolio correlation matrix.

Finding 3: Employment agreement non-compete arbitrage. The CRV detected a Type 3 adversarial NCC in the employment agreements of 3 key engineers. Each agreement contained a non-compete clause with a different jurisdictional scope, a different duration, and a different definition of "competing business." The negative correlations across the jurisdictional complexity and operational constraint dimensions revealed that these provisions, while individually enforceable, were collectively unenforceable due to conflicting jurisdictional claims—meaning the acquirer could not rely on the non-competes to retain key personnel.

9.5 Comparison with Manual Review

A parallel manual review was conducted by a separate team of 3 senior attorneys (not using the CRV system) who spent 3 weeks reviewing the same portfolio. The comparison:

The CRV-assisted review identified more risk interactions at every level while completing in half the time. The additional false alarms (7 vs. 4) represent the cost of the system's conservative bias, but attorneys reported that the false alarms were quickly dismissed using the evidence bundles and did not materially increase review burden.

The critical finding missed by manual review (Finding 1: cross-contract IP exposure) was missed because the three contracts were reviewed by different associates who did not cross-reference the IP-related provisions. The CRV system detected it automatically through the portfolio correlation matrix—precisely the type of cross-contract interaction that the human-local review paradigm systematically misses.

10. Benchmarks

10.1 Experimental Setup

We evaluate the CRV framework on three benchmark datasets spanning different contract domains and complexity levels:

Dataset 1: M&A Contract Corpus (MACC). 1,200 M&A transaction contract sets, each containing 50-150 contracts. Source: anonymized data from 4 law firms and 2 corporate legal departments, spanning 2019-2025. Total clauses: 4.2 million. Ground truth: 15,000 clause pairs labeled by senior attorneys as "materially interacting" (positive) or "independent" (negative).

Dataset 2: Technology Licensing Benchmark (TLB). 3,500 technology licensing agreements with risk annotations on each clause (12-dimensional risk vector rated by 3 attorneys per clause, inter-annotator agreement κ = 0.78). Source: curated from SEC filings and open-source license databases. Total clauses: 890,000.

Dataset 3: Regulatory Compliance Contracts (RCC). 800 contracts in heavily regulated industries (healthcare, financial services, defense) with adversarial clause annotations. 142 confirmed adversarial NCCs, 289 aggressive-but-legitimate NCCs, and 369 standard-allocation NCCs, labeled by panels of 5 senior attorneys per NCC.

10.2 Risk Clause Detection Performance

We evaluate the CRV system's ability to identify material risk clauses (clauses that senior attorneys flag as requiring detailed review). Results across the three datasets:

The RCC dataset shows higher recall but lower precision, reflecting the system's conservative bias in regulated domains (more clauses are flagged, including some false positives). The MACC dataset achieves the best F1, likely because the M&A risk projection matrix benefits from the largest training corpus.

Comparison with baselines:

The full CRV system with NCC extraction outperforms all baselines by a substantial margin. The ablation (CRV clause-level only, without NCC) shows that the NCC extraction contributes approximately 6.4 F1 points—a significant improvement that validates the importance of inter-clause correlation analysis.

10.3 Cross-Clause Interaction Discovery

We measure the system's ability to discover materially interacting clause pairs. Using the MACC ground truth of 15,000 labeled clause pairs:

The inclusion of negative correlations is critical. Positive-correlation-only CRV misses the adversarial interactions—clause pairs that create risk through their opposition, not their similarity. The full CRV with negative correlation analysis achieves 36% higher MAP than positive-correlation-only, confirming that negative correlations are essential for comprehensive interaction discovery.

The +31% cross-clause discovery improvement cited in our headline results comes from comparing the full CRV system's interaction discoveries against the senior attorney manual review on the M&A case study: the CRV system identified 41 material cross-clause interactions versus 18 found by manual review, after controlling for false positives.

10.4 Adversarial Clause Detection

On the RCC adversarial clause benchmark (142 adversarial, 289 aggressive-legitimate, 369 standard):

We select AS > 0.55 as the default threshold because it achieves the best balance between precision (89.7%) and recall (83.1%) while maintaining an acceptable false positive rate on aggressive-but-legitimate NCCs (8.3%). The false positive rate is particularly important because these false positives consume reviewer time but do not represent true adversarial intent.

Analysis of missed adversarial NCCs (16.9% miss rate at AS > 0.55). The 24 adversarial NCCs missed by the system fall into two categories: (a) 15 cases where the adversarial mechanism operates through provisions not captured in the 12-dimensional risk space (e.g., procedural traps in notice provisions, strategic use of force majeure definitions); and (b) 9 cases where the adversarial interaction spans more than 5 clauses, diluting the average negative correlation below the threshold τ. Both categories suggest specific directions for improvement: expanding the risk dimension set and developing cluster-size-adaptive thresholds.

11. Future Directions

11.1 Dynamic Risk Vectors

The current CRV framework computes static risk vectors based on clause text at a single point in time. In practice, clause risk changes with external conditions: regulatory changes alter the regulatory exposure dimension, market volatility affects financial liability estimates, and counterparty creditworthiness shifts counterparty dependency risk. Future work will extend the risk vector to a time-varying function r_i(t) that incorporates external signals:

where W(t) and b(t) are projection parameters that adapt to current conditions, and ε_i(t) is a stochastic perturbation reflecting market uncertainty. This dynamic extension would enable real-time portfolio risk monitoring and early warning systems for emerging contractual exposure.

11.2 Causal Risk Graph Construction

The correlation matrix captures statistical relationships between clause risk profiles, but correlation does not imply causation. Two clauses may be negatively correlated because one was drafted in response to the other (a causal relationship reflecting negotiation dynamics) or because they happen to address opposing risks by coincidence (a spurious correlation).

Future work will integrate causal inference methods—specifically, structural causal models and do-calculus—to infer the causal structure behind observed correlations. The causal graph would indicate which clauses were drafted to offset which other clauses, enabling a deeper understanding of the negotiation dynamics and intent behind complex contractual arrangements.

11.3 Multi-Party Contract Networks

Many modern business arrangements involve multi-party contracts: joint ventures with three or more partners, supply chain agreements linking multiple tiers, and consortium agreements in infrastructure projects. The current framework handles bilateral contracts (two-party risk transfer analysis). Extending to multi-party networks requires a generalization of the negative correlation cluster to a multi-partite hypergraph structure, where risk transfers occur along edges connecting three or more parties.

The mathematical framework generalizes naturally: clause risk vectors gain a party index r_i^{(p)} indicating which party's perspective the vector represents, and the correlation matrix becomes a tensor C_{ij}^{(p,q)} capturing correlations between clause i from party p's perspective and clause j from party q's perspective. NCC extraction generalizes to finding subsets where this multi-party tensor exhibits systematic negative correlations across party pairs.

11.4 Generative Risk Scenario Modeling

The current framework is analytical: it identifies existing risk configurations in contracts as written. A natural extension is generative: given a contract with identified NCCs, generate hypothetical clause modifications that would neutralize adversarial configurations while preserving the commercial intent of the agreement.

This generative capability would integrate with MARIA OS's decision pipeline to propose contract amendments that reduce the adversarial score below the threshold, subject to constraints on commercial viability and counterparty acceptance probability. The proposed amendments would be routed through MARIA OS gates for human approval before being suggested to the negotiation team.

11.5 Regulatory Landscape Integration

Different jurisdictions impose different constraints on contractual risk allocation. A limitation of liability that is enforceable in Delaware may be unenforceable in the EU due to consumer protection directives. Future work will integrate jurisdiction-specific regulatory models into the risk projection, producing risk vectors that account for enforceability. A clause that appears to mitigate risk (negative value on the financial liability dimension) but is unenforceable in the relevant jurisdiction should be re-scored to reflect the actual (near-zero) mitigation effect.

This integration would leverage MARIA OS's hierarchical coordinate system, where jurisdiction is a property of the Galaxy or Universe level, enabling automatic application of jurisdiction-specific regulatory models without per-clause configuration.

12. Conclusion

This paper has presented Contract Risk Vectorization, a mathematical framework that transforms the problem of contract risk assessment from a manual, clause-by-clause reading exercise into a computational analysis of risk vector correlations. Our key contributions are:

• A clause-to-vector transformation that converts natural language contract provisions into dense risk vectors r_i ∈ ℝ^d through a two-stage pipeline of semantic embedding and risk projection, validated against expert assessments with MAE = 0.12 and rank correlation ρ = 0.89.
• A correlation-based risk analysis framework that constructs inter-clause correlation matrices and identifies negatively correlated clause clusters (NCCs) as the mathematical signature of risk transfer, risk opposition, and adversarial contract engineering.
• An adversarial clause detection method that scores NCCs on concealment, asymmetry, and sophistication to distinguish between legitimate risk allocation and deliberate risk engineering, achieving 89.7% precision and 83.1% recall on a benchmark of attorney-labeled adversarial configurations.
• A portfolio-level aggregation model that extends the analysis to multi-contract portfolios, introducing diversification indices and concentration risk scores that reveal hidden exposure at the enterprise level.
• Integration with MARIA OS gate evaluation that routes high-risk clauses and adversarial NCCs through human-in-the-loop review while allowing low-risk provisions to pass through automated validation, reducing M&A due diligence cycle time by 73%.

The framework addresses a critical gap in enterprise legal operations: the inability to scale interaction analysis. Individual clause risk assessment can be (and has been) partially automated by classification models. But the interactions between clauses—the compounding, offsetting, and adversarial dynamics that produce emergent portfolio-level risk—have remained the exclusive domain of experienced human attorneys. By reformulating these interactions as correlation patterns in a purpose-built risk vector space, we make them computable, scalable, and systematically discoverable.

The case study demonstrates the framework's practical impact: in a simulated M&A due diligence exercise, the CRV system uncovered a $12-18M cross-contract IP exposure that traditional review missed, identified vendor concentration risk through eigenvalue analysis that would be invisible to clause-by-clause review, and detected non-compete enforceability gaps through adversarial NCC analysis. These findings directly influence deal structure, pricing, and risk mitigation—the highest-value activities in the M&A process.

We do not claim that vectorization replaces legal judgment. We claim that it scales the pattern-recognition component of legal judgment—the exhaustive search for problematic interactions across thousands of clauses—so that human expertise is allocated to interpretation and decision-making. In the MARIA OS philosophy: judgment does not scale, but the infrastructure that surfaces what requires judgment can and must scale. Contract Risk Vectorization is that infrastructure for legal risk.

References

[1] World Commerce & Contracting. (2025). The State of Contract Management 2025: Benchmark Report. World Commerce & Contracting Annual Survey.

[2] Chalkidis, I., Fergadiotis, M., Malakasiotis, P., Aletras, N., & Androutsopoulos, I. (2020). LEGAL-BERT: The Muppets straight out of Law School. Findings of EMNLP, 2898–2904.

[3] Hendrycks, D., Burns, C., Chen, A., & Ball, S. (2021). CUAD: An Expert-Annotated NLP Dataset for Legal Contract Review. Proceedings of NeurIPS Datasets and Benchmarks Track.

[4] Bommarito, M. J., & Katz, D. M. (2022). A Measure of the Difficulty of Legal Language. Artificial Intelligence and Law, 30(3), 345–373.

[5] Zheng, L., Guha, N., Anderson, B. R., Henderson, P., & Ho, D. E. (2024). LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models. Proceedings of NeurIPS.

[6] Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.

[7] Ng, A. Y., Jordan, M. I., & Weiss, Y. (2002). On Spectral Clustering: Analysis and an Algorithm. Advances in Neural Information Processing Systems, 14.

[8] European Commission. (2024). The EU Artificial Intelligence Act: Regulation (EU) 2024/1689. Official Journal of the European Union.

[9] Surdeanu, M., Zhang, T., Galkin, M., Guha, N., & Ho, D. E. (2025). Legal NLP in the Age of Large Language Models: A Survey. ACM Computing Surveys, 57(4).

[10] Pearl, J. (2009). Causality: Models, Reasoning, and Inference (2nd ed.). Cambridge University Press.