CortexDebate: Trust-Optimized MAD for LLMs

• CortexDebate is a multi-agent debate paradigm that employs a biologically-inspired, sparse debate graph to mitigate hallucinations, overconfidence, and context overload.
• By leveraging a McKinsey-based Debate Matter module, it dynamically computes trust scores to prune irrelevant agent interactions and focus on high-value information exchange.
• Empirical results show up to a 10% accuracy improvement and a 70% reduction in context length, demonstrating significant gains in efficiency and robustness.

CortexDebate denotes a novel multi-agent debate (MAD) paradigm for LLMs that addresses core limitations in reasoning, hallucination, context overload, and overconfidence by constructing a sparse, dynamically optimized debating graph among agents. Inspired by the brain’s cortical networks—where only select connections are engaged at each moment—CortexDebate leverages a directed, sparsified communication topology among LLM agents for more efficient and equitable debate. The McKinsey-based Debate Matter (MDM) module, built on quantitative trust metrics, governs the dynamic optimization of agent interactions. Empirical evaluation demonstrates substantial gains in both accuracy and input efficiency across a range of complex reasoning tasks and datasets, positioning CortexDebate as a significant advance in multi-agent LLM-based collaborative inference (Sun et al., 5 Jul 2025).

1. Motivation and Limitations of Traditional MAD Approaches

Conventional single-LLM deployments are highly susceptible to hallucinations and exhibit insufficient reasoning in complex tasks. Existing multi-agent debate frameworks, where all agents interact with every other agent in a fully connected communication graph, exacerbate two crucial bottlenecks:

• Context Explosion: With each additional agent and debate round, the input context for each agent grows combinatorially, overwhelming LLM context windows and introducing information irrelevant for each agent’s reasoning path. This leads to a measurable performance drop as agents “get lost” in extraneous debate information.
• Overconfidence Dilemma: Standard MAD protocols typically weight agent contributions based on internal (often overestimated) self-confidence scores. As a result, overconfident agents can dominate the debate, marginalizing diverse or dissenting viewpoints and hindering collaborative correction of errors.

CortexDebate is developed specifically to mitigate these limitations through architectural sparsity and trust-optimized agent selection.

2. Sparse Debating Graph Construction

Departing from the fully connected MAD paradigm, CortexDebate represents the ensemble of debating agents as a directed, weighted graph, with nodes as LLM agents and directed edges representing information flow from each agent to peers identified as “beneficial” for the recipient's performance. The edge weights are dynamically computed at each debate round, and only connections exceeding a round-specific average threshold are preserved:

• Dynamic Edge Pruning: After each round, only “above-average” beneficial connections (by computed trust) are retained, resulting in a graph that is sparse (i.e., the typical agent only attends to a small, pruned set of peers rather than all) and dynamically restructured per round. This ensures that each agent’s context is restricted to relevant, high-value information, sharply reducing the number of tokens processed and the associated cognitive load per agent.
• Balanced Influence: By construction, the architecture tempers the overconfidence dilemma; agents cannot dominate solely by internal certainty. Instead, collaborative potential and quality of information flow (as computed by trust metrics) regulate their influence.

3. Role of McKinsey-based Debate Matter (MDM) and Trust Computation

A central technical innovation in CortexDebate is the McKinsey-based Debate Matter (MDM), which operationalizes the construction and optimization of debate connections. MDM models an agent’s trustworthiness to another agent via the McKinsey Trust Formula from sociology:

$T = \frac{C \times R \times I}{S}$

where

• C (Credibility): Quantifies professional competence, parametrized via a scaling law of pre-training loss (e.g., $$L(N, M) = \frac{406.4}{N^{0.34}} + \frac{410.7}{M^{0.28}} + 1.69$$, then $C = 1/L(N, M)$ for model parameters $N, M$).
• R (Reliability): Encodes averaged historical confidence (recursive over rounds).
• I (Intimacy): Captures inter-agent diversity, computed via $$I_d = 1 - (\frac{1}{d} (\text{previous similarities} + \text{cosine}(O^{d-1}_i, O^{d-1}_j)))$$ for past outputs $O^{d-1}_i, O^{d-1}_j$.
• S (Self-orientation): Measures agent self-interest through frequency of participation.

For each directed edge $i \to j$ in debate round $d$:

$$W_{i \rightarrow j}^{(d)} = \frac{C_d \times R_d \times I_d}{S_d}$$

Only edges with $W_{i \rightarrow j}^{(d)}$ above the global average are maintained. This quantification not only evaluates individual competence but also intersectional collaborative value, penalizing dominant but less collaborative (“self-oriented”) participation.

4. Empirical Performance and Evaluation

CortexDebate has been validated across eight datasets spanning mathematical reasoning, world knowledge, multi-step reasoning, and long-context understanding. Key empirical findings:

• Accuracy Gains: On challenging math benchmarks (e.g., GSM-IC, MATH) and logical reasoning datasets (e.g., GPQA, ARC-C), CortexDebate achieves up to 9–10% accuracy improvement over both single-agent baselines and prior non-sparse MAD frameworks.
• Context Compression: Average context length per agent is reduced by up to approximately 70% relative to fully connected MAD, directly relating to lower computational cost and enhanced agent focus.
• Comparative Superiority: Against both “full” and “partial” debate variants, CortexDebate provides higher accuracy-to-token efficiency, demonstrating that intelligent graph sparsity and trust-optimized communication surpass naive network designs.

5. Theoretical and Mathematical Foundations

CortexDebate rigorously formalizes agent selection and edge weighting via transparent mathematical modeling:

Formula	Description
$T = \frac{C \times R \times I}{S}$	McKinsey Trust Formula: weighted aggregate trust score.
$C = 1/L(N, M)$	Model competence from pretraining scaling law.
$R_d = \frac{R_{d-1} \times (d-1) + H_i^{d-1}}{d}$	Reliability from historic confidence.
$I_d = 1 - \text{mean cosine similarity}$	Intimacy (opinion collision/distance).
$S_d = (d-1) \times (n-1) - P_d$	Self-orientation from debate participation frequency.

These provide a mathematically grounded basis for connection pruning, agent selection, and collaborative optimization, directly addressing overconfidence and context explosion.

6. Practical Implications, Limitations, and Future Research

CortexDebate’s sparse, trust-informed debate structure yields immediate benefits for inference efficiency, agent diversity, and robustness to hallucinations, with direct applicability to any domain requiring collaborative LLM reasoning—mathematics, QA, multi-hop logic, and long-context tasks.

Recognized limitations include:

• Lower efficiency relative to single-agent methods (due to multi-agent orchestration).
• The residual gap between aggregate multi-agent intelligence and the innate reasoning deficit of contemporary LLMs.

Planned research extensions include scaling to larger agent pools, domain-specific expert deployment, and systematic analysis of the theoretical tradeoff between sparsity depth, trust diversity, and debate convergence.

7. Position Within Broader Debating Systems

CortexDebate’s advances complement and contrast with several contemporary works in the multi-agent debate literature. Whereas traditional MAD methods focus on either unrestricted agent-agent debate, majority-voting ensembles, or fixed communication topologies, CortexDebate’s distinguishing feature is its biologically-inspired, dynamically sparse, and trust-optimized debate graph.

Contrasted with works such as (Choi et al., 24 Aug 2025)—which attributes most gains in MAD to majority voting and presents a martingale analysis suggesting debates alone do not improve expectation of correctness—CortexDebate introduces explicit graph optimization to amplify beneficial information flow and mitigate majority or high-confidence suppression of diverse correct reasoning.

This model sets a new direction for research in multi-agent AI debate, emphasizing selective, transparent, and quantitatively justified information exchange, thereby enhancing both correctness and collaborative interpretability.