Coherence-Driven Inference (CDI)

• Coherence-driven inference (CDI) is a reasoning paradigm that maximizes coherence in weighted proposition graphs by evaluating pairwise consistency and conflict relations.
• It uses a MAX-CUT optimization framework to partition propositions into accepted and rejected sets, accommodating ambiguity and uncertainty.
• CDI integrates LLM-based relation extraction with symbolic solvers to support robust decision-making in cybersecurity and broader applications.

Searching arXiv for the named CDI papers and closely related work to ground the article in current literature. arxiv_search(query="(Huntsman, 23 Sep 2025)", max_results=5) Coherence-driven inference (CDI) is a formal reasoning paradigm in which inference is performed by maximizing the coherence of a set of propositions, claims, hypotheses, or observations represented as a weighted graph. In the cybersecurity formulation, each datum is a vertex, edges encode relevance relations, and weights in the interval $[-1,1]$ encode pairwise consistency, so that reasoning reduces to finding a bipartition of propositions into accepted and rejected sets that maximizes coherence. In this form, CDI is presented as an early application of automatic reasoning relevant to red and blue team operations, with near- to medium-term promise for decision-making in cybersecurity and eventual relevance to autonomous blue team operations (Huntsman, 23 Sep 2025).

1. Conceptual basis

CDI is defined as a reasoning paradigm based on the maximization of coherence among a set of propositions, claims, or pieces of data. Its intellectual background is explicitly linked to cognitive science, philosophy, and law, particularly the coherence-based work associated with Thagard. In this tradition, reasoning is treated as a process of finding the most coherent partitioning of information, rather than deducing conclusions from fixed logical rules or relying only on statistical dependency (Huntsman et al., 19 Feb 2025).

A coherence graph models this process. Each proposition is a vertex, and each edge represents a substantive relation between two propositions. In the signed-graph formulation, a coherence graph is written as $G_\sigma=(V,E,\sigma)$, where $V$ is the set of propositions, $E$ is the set of dependent pairs, and $\sigma:E\rightarrow\{\pm1\}$ marks pairs as consistent or inconsistent. The weighted formulation generalizes this by assigning edge weights in $[-1,1]$, with $+1$ denoting high consistency, $-1$ denoting high inconsistency, and $0$ denoting no substantive relation. This makes CDI a global constraint-satisfaction approach that can accommodate ambiguity, uncertainty, and conflicting evidence rather than excluding them from the outset (Huntsman et al., 19 Feb 2025).

The distinctive claim of CDI is therefore methodological rather than merely representational. Classical logic and probabilistic reasoning follow fixed rules or statistical dependency structures; CDI instead evaluates all pairwise support and conflict relations together and searches for the globally most coherent assignment of acceptance and rejection. This suggests a form of inference designed for settings in which evidence is incomplete, heterogeneous, or internally inconsistent.

2. Mathematical formulation and optimization

The core CDI objective is defined on a weighted adjacency matrix $A$, where $G_\sigma=(V,E,\sigma)$0 is the weight associated with the edge between propositions $G_\sigma=(V,E,\sigma)$1 and $G_\sigma=(V,E,\sigma)$2. Given a subset $G_\sigma=(V,E,\sigma)$3 of propositions interpreted as accepted, coherence is quantified as

$G_\sigma=(V,E,\sigma)$4

CDI seeks the partition $G_\sigma=(V,E,\sigma)$5 that maximizes this quantity:

$G_\sigma=(V,E,\sigma)$6

Under this objective, positive edges should remain within a part, because cutting them loses coherence, whereas negative edges should cross from accepted to rejected, because cutting them increases coherence (Huntsman, 23 Sep 2025).

The optimization is equivalent to a weighted MAX-CUT problem up to sign. In the cybersecurity paper, the negative sign is emphasized because the algorithm is described as minimizing total inconsistency across the acceptance boundary. In the neurosymbolic formulation, the same structure is described as cutting the most negative weights with a bipartition into accepted, understood as estimated true, and rejected, understood as estimated false, propositions (Huntsman et al., 19 Feb 2025).

This formalism gives CDI a precise inferential semantics. The output is not a proof in the classical-logical sense and not a posterior distribution in the standard probabilistic sense. It is a maximally coherent partition of a proposition set, conditioned on pairwise relevance and consistency judgments. A simple three-proposition example in the cybersecurity presentation compares alternative cuts and shows that the preferred solution is the one that cuts both negative edges, thereby maximizing coherence (Huntsman, 23 Sep 2025).

3. LLM-mediated graph construction

A central operational question for CDI is how to obtain the coherence graph from natural-language material. The recent literature answers this by using LLMs as local semantic evaluators and CDI as the global symbolic reasoner. The cybersecurity paper explicitly frames this as “LLMs as System 1” and “CDI as System 2”: LLMs perform fast, surface-level extraction of relations between claims, while CDI performs slow, rigorous symbolic reasoning over the resulting graph (Huntsman, 23 Sep 2025).

The pipeline begins by extracting propositions relevant to a decision problem. These may include facts, beliefs, hypotheses, logs, operator knowledge, or hypothetical outcomes. An LLM is then prompted to examine proposition pairs, rate their substantive relation and consistency on a $G_\sigma=(V,E,\sigma)$7 to $G_\sigma=(V,E,\sigma)$8 scale, and compile an edge list in which only substantively related pairs receive edges. The scores are mapped to edge weights in $G_\sigma=(V,E,\sigma)$9, producing a weighted coherence graph. To improve robustness, the construction is repeated multiple times, for example $V$0 or $V$1 times, and the median edge weight is taken for each proposition pair. The resulting median graph is then passed to a symbolic solver that computes the coherence-maximizing partition (Huntsman, 23 Sep 2025).

This architecture is presented as auditable. Because the LLM emits explicit edge lists, the intermediate representation is transparent and can be checked for hallucinations. In the broader automatic-CDI literature on arguments, the same separation of concerns is emphasized: the LLM extracts propositions and estimates pairwise relevance and consistency, while combinatorial optimization computes the globally most coherent accepted/rejected partition. That literature also notes the use of median aggregation, cut sparsifiers, and Gibbs distributions over near-optimal solutions (Huntsman, 23 Sep 2025).

The neurosymbolic AI paper extends the same idea in a different direction by constructing natural-language proposition sets that objectively instantiate a target coherence graph. It then benchmarks whether LLMs can reconstruct the underlying graph from the propositions. In that setting, micro $V$2-score and the $V$3 adjacency-matrix norm are used to evaluate reconstruction fidelity, and the best models are reported to achieve close to perfect fidelity on synthetic graphs up to $V$4 propositions, with uncertainty not degrading performance (Huntsman et al., 19 Feb 2025).

4. Cybersecurity deployment

In cybersecurity, CDI is proposed as a way to aggregate heterogeneous operational evidence into an explainable and reproducible decision procedure. The paper focuses on both red team and blue team use cases, with the coherence graph serving as a common representation for facts, observations, priors, and candidate explanations (Huntsman, 23 Sep 2025).

In the red team example, a penetration tester or agent gathers observations such as a host with port $V$5 open, information that some hosts are Linux and some are Windows, and SSH brute-force logs. The proposition set includes both low-level observations and higher-level hypotheses, such as the generalization that port $V$6 is often open on Windows hosts and the specific hypothesis that a target host is Windows. CDI then aggregates all evidence and prior patterns and supports reasoning about which operating-system hypothesis is most coherent with the available information.

In the blue team example, the task is live-attack detection, including cases such as LDAP brute forcing described as “living off the land.” The propositions include observations about commands used, logs showing authentication attempts and failures, RDP connections, and competing hypotheses such as whether a living-off-the-land LDAP attack occurred. CDI provides a formal and reproducible way to decide which hypotheses are most coherent with the evidence, thereby aiding incident response and triage (Huntsman, 23 Sep 2025).

The practical workflow is described as a five-stage sequence: gather relevant evidence and hypotheses; have an LLM evaluate relationships and consistencies and form a weighted coherence graph; aggregate multiple graph realizations by median; solve the MAX-CUT problem to obtain the globally most coherent belief state; and integrate the result into decision systems as an interpretable recommendation. The paper further states that such recommendations can evolve as new evidence arrives. This suggests CDI is intended not only as a one-shot classifier of hypotheses but as a reasoning layer for evolving cyber situations.

5. Robustness, uncertainty, and neurosymbolic extensions

The recent CDI literature places strong emphasis on robustness and uncertainty handling. In the cybersecurity setting, repeated graph construction followed by median aggregation is intended to smooth out LLM randomness and hallucination, and convergence is diagnosed via $V$7 distance plots. When multiple partitions have near-identical coherence, the “Rashomon set” of near-optimal solutions can be used to induce probability distributions over hypotheses, for example via Gibbs measures. The same paper also states that CDI is domain-agnostic and can support hierarchical or sequential reasoning for scalability (Huntsman, 23 Sep 2025).

The neurosymbolic AI paper broadens this picture by treating LLMs as “consistency oracles” that judge whether proposition pairs are consistent, inconsistent, or independent. It presents a constructive algorithm, ModelCoherenceGraph, that uses a clique edge cover and star forest decomposition to generate natural-language propositions realizing an arbitrarily specified coherence graph. This makes it possible to benchmark graph reconstruction independently of domain content. The paper reports that models including o1-mini, QwQ-32B, and Claude-3.5-sonnet reconstruct synthetic coherence graphs with close to perfect fidelity, and it further reports a case study in which ChatGPT-4 achieved superhuman accuracy in pairwise consistency judgments for the USS Vincennes incident (Huntsman et al., 19 Feb 2025).

Automatic CDI on arguments generalizes the same architecture to law, administration, and jurisprudence. There, LLMs extract propositions from arguments and assign pairwise consistency and relevance weights; the resulting weighted graph is then optimized by weighted MAX-CUT to assess argumentative coherence. The paper describes applications to legislative and policy analysis and legal reasoning, and emphasizes that the resulting cuts are explainable because they identify which propositions hang together coherently and which do not (Huntsman, 23 Sep 2025).

Several additional claims follow from this family of papers. First, CDI is not presented as replacing LLMs with a symbolic backend; rather, it is presented as separating their roles. Second, it is not limited to binary consistency judgments, because weighted graphs allow graded consistency. Third, the architecture can incorporate external constraints: the cybersecurity paper states that ethical or policy constraints can be encoded as “always accepted” nodes. At the same time, the arguments paper states that CDI will not immediately yield AGI and that scaling and hierarchical inference remain practical challenges (Huntsman, 23 Sep 2025).

6. Scope, neighboring frameworks, and acronym ambiguity

In current arXiv usage, the acronym “CDI” is polysemous. In the coherence-maximization literature, CDI denotes coherence-driven inference. In other literatures, the same acronym denotes unrelated methods.

Term	Domain	Core idea
Coherence-driven inference	Reasoning, cybersecurity, neurosymbolic AI	Maximize coherence on a weighted proposition graph
CDI-SAN	High-contrast imaging	Use DM modulation to separate coherent speckles from incoherent planet light
Chrono CDI	Coherent x-ray diffractive imaging	Use temporal coherence in time-series phase retrieval
Consistency with Degraded Image	Blind image restoration IQA	Evaluate fidelity by consistency with the degraded input

“Coherent differential imaging on speckle area nulling” uses the acronym CDI-SAN and refers to high-contrast exoplanet imaging. Its key distinction is physical rather than inferential: stellar speckles are coherent and planet light is incoherent, and the method exploits synchronized deformable-mirror modulations and five-image acquisition sets to separate the two contributions (Nishikawa, 2022). “Chrono CDI” likewise refers to coherent diffractive imaging of time-evolving samples, where temporal coherence across neighboring time points is used as a reconstruction constraint to improve temporal resolution by a factor of $V$8 to $V$9 (Ulvestad et al., 2016). “CDI: Blind Image Restoration Fidelity Evaluation based on Consistency with Degraded Image” uses CDI to mean consistency with degraded image, a wavelet-domain evaluation criterion for blind image restoration that judges a restoration by how well it reproduces the degraded observation under plausible degradation, rather than by direct similarity to a reference (Tang et al., 24 Jan 2025).

A broader, related statistical tradition concerns coherent modularized inference rather than proposition-graph CDI. “A conditional independence framework for coherent modularized inference” studies how disparate expert panels and probabilistic models can be networked so that inference remains coherent before and after evidence accommodation. Its key notions include soundness, distributivity, delegable, separately informed, cutting, commonly separated, and panel separability of the likelihood (Leonelli et al., 2018). This is a distinct framework, but it shares with coherence-driven inference the goal of preserving coherent global judgment under structured decomposition.

Taken together, these literatures show that coherence-driven inference in the strict contemporary sense is a proposition-graph method centered on coherence maximization and combinatorial optimization, typically coupled with LLM-based extraction or consistency evaluation. The neighboring uses of “CDI” are methodologically unrelated, and distinguishing them is necessary for accurate interpretation of the acronym in current research.