Chain-of-Experts (CoE): Modular AI Architectures

Updated 7 July 2025

Chain-of-Experts (CoE) is a framework that sequences specialized models to collaboratively improve system performance and interpretability.
It dynamically routes inputs through expert modules using learned weighting and bias mitigation, enabling adaptive task handling.
Applications span from computer vision to industrial modeling, delivering enhanced scalability, efficiency, and robust decision-making.

Chain-of-Experts (CoE) refers to a family of architectures and algorithmic frameworks where collections of expert models—each specializing in a different subdomain, context, or capability—are strategically composed or sequenced to achieve improved overall system performance, robustness, or interpretability. Unlike monolithic models that handle all input types uniformly, or classical ensemble methods such as simple averaging, CoE designs emphasize structured collaboration (often via routing, gating, or sequential composition) between multiple experts to exploit their complementarities, mitigate biases, and adaptively address heterogeneous or evolving tasks.

1. Architectural Principles and Variants

CoE encompasses a diverse family of realizations unified by the structured use of multiple experts:

Meta-aggregation (Bandit-inspired): In collective decision-making, CoE is formalized as a meta-level contextual multi-armed bandit (CMAB) in which expert advice vectors $\tilde{f}_{k,t}$ are linearly aggregated. The system learns weighting vectors $\theta^*$ that minimize prediction error, thus moving beyond static selection or naïve averaging of expert advice (Abels et al., 2021).
Dynamic expert routing (Mixture-of-Experts MoE): Unlike classic MoEs where tokens are routed once per layer, sequential CoE architectures introduce intra-layer expert chaining: tokens are routed through a series of experts in sequence, with re-routing and representation updates at each step. This facilitates dynamic specialization and richer representational capacity (Wang et al., 23 Jun 2025).
Specialist handling and delegation: Collaboration-of-Experts structures employ a delegator module to select a relevant expert for further processing after an initial prediction. The experts are encouraged (by specific loss shaping mechanisms) to specialize on distinct partitions of the data (Zhang et al., 2021).
Contextual knowledge integration: CoE can explicitly integrate domain expertise via possibility distributions, where assignment weights $\pi_{ci}$ represent operator certainty in context attribution for industrial applications (Souza et al., 2022).
Sequential and hierarchical review chains: Certain CoE frameworks introduce explicit multi-expert review chains, such as an initial specialist, follow-up specialist, and a consensus-based diagnostic expert aggregation using a (potentially sparse) mixture-of-experts with voting (Liu et al., 18 Dec 2024).

In all cases, the key architectural feature is the modular decomposition of the modeling problem such that expert specializations can be explicitly managed, composed, or adaptively allocated in a data- or context-driven manner.

2. Expert Aggregation, Routing, and Bias Mitigation

Central to CoE systems is the algorithmic strategy used to aggregate, route, and combine expert contributions:

Linear aggregation and learned weighting: The meta-level CMAB approach frames the expert aggregation as a regression problem seeking optimal weights, where systematic biases can be automatically downweighted or inverted. The algorithm can even exploit “anti-experts” by including their inverted predictions to benefit from their systematic negative correlation (Abels et al., 2021).
Dynamic, iterative routing: Iterative CoE layers employ dedicated routers at each step within a chain, enabling dynamic selection of experts according to the rapidly updating hidden state of each token. This approach results in combinatorially richer expert utilization: for example, two-step CoE routing enables 823 times more expert sequence combinations versus static one-shot routing (Wang et al., 23 Jun 2025).
Rule-based and planned gating (for LLMs): In compact frameworks for resource-constrained LLM deployments, rule-based gating and multi-stage expert planning enable selective expert collaboration depending on input context, reducing spurious interference among experts and improving inference efficiency (Huang et al., 16 Jul 2024).
Variance-based and optimization-shaped responsibility: Delegator-based CoE frameworks employ label and weight generation techniques based on class-probability standardization, balanced transportation problems, and variance-driven weighting. This ensures that experts are reliably engaged where they are most effective and discourages arbitrary or uniform allocation (Zhang et al., 2021).
Domain knowledge–driven gates and possibility distributions: In contextual expert mixtures, process/operator knowledge is codified into assignment weights used during expectation-maximization, such that the gating reflects both statistical evidence and known domain regimes, enhancing interpretability and context alignment (Souza et al., 2022).

3. Performance Metrics and Efficiency

CoE approaches are evaluated on a range of metrics that reflect both learning efficiency and practical deployment considerations:

Regret and cumulative reward (Online Decision-Making): In meta-CMAB scenarios, regret bounds improve over conventional methods—an upper bound of $\tilde{O}(\sqrt{N T \log K}) + \epsilon \sqrt{N T}$ is achieved, with N experts, T time steps, K arms, and misspecification $\epsilon$ (Abels et al., 2021).
Accuracy, efficiency, and hardware deployment (Vision and LLMs): CoE frameworks in computer vision achieve up to 80.7% top-1 ImageNet accuracy with 194M FLOPs, or 80.0% with only 100M FLOPs when combined with efficient innovations such as PWLU activations and CondConv, realizing a 3–6× hardware speedup over alternative conditional computation designs (Zhang et al., 2021).
Resource utilization and scalability: Samba-CoE on the SN40L architecture demonstrates 2–13× speedup relative to the unfused baseline, with machine footprint reductions up to 19×, expert-switching time improved by 15–31×, and large-scale expert pools (hundreds per node) supported efficiently by three-tier memory hierarchies (Prabhakar et al., 13 May 2024).
Interpretability and robustness: In medical and explainability-focused CoE systems, critical metrics include the completeness and accuracy of rationale chains or concept circuits, and user/LLM-based assessments showing explainability score improvements of ~36% (Yu et al., 19 Mar 2025), or clear boosts in medical VQA accuracy when multi-expert verification is enabled (Liu et al., 18 Dec 2024).
Serving throughput under resource constraints: In real-world deployments with limited GPU/CPU/SSD, CoServe (a dependency-aware CoE serving system) reduces unnecessary expert switching and achieves up to 12× higher throughput compared to previous multi-expert serving deployments (Suo et al., 4 Mar 2025).

4. Applications and Domains

The utility of CoE systems spans a wide range of domains:

Collective decision and ensemble learning: Use of bandit-based CoE for aggregating biased and heterogeneous expert judgments in medical diagnostics, public policy (e.g., pandemic response integration), and crowdsourcing (Abels et al., 2021).
Computer vision and video generation: Hardware-friendly expert selection and specialization achieves state-of-the-art large-scale image classification and enables efficient video generation, with chain-of-experts diffusion enabling long, coherent, high-quality video synthesis with only ~10% of previous inference cost (Zhang et al., 2021, Li et al., 24 Aug 2024).
Software supply chain security: Chain-of-experts deep models provide scalable, accurate SBoM reverse engineering for large, symbol-stripped JavaScript bundles, aiding integrity and vulnerability analysis at scale (Song et al., 29 Aug 2024).
Efficient LLM task routing: Modular CoE architectures supporting multi-domain or resource-constrained LLM deployments, as well as task-optimized LLM ensembles dynamically routed by lightweight classifiers and cost-sensitive optimization (Jain et al., 2 Dec 2024, Huang et al., 16 Jul 2024, Wang et al., 5 Dec 2024).
Industrial and process modeling: Contextual mixture-of-experts integrates operator and process knowledge via possibility distributions, improving explainability and regime-specific modeling in chemical and batch process industry settings (Souza et al., 2022).
Interpretability and explainable AI: Chain-of-explanation constructs provide automatic visual concept circuit explanations and quantification of polysemanticity via concept entropy measures, supporting model transparency (Yu et al., 19 Mar 2025).

5. Theoretical Contributions and Extended Methodologies

Several CoE contributions are accompanied by formal theoretical analysis:

Regret analysis and convergence guarantees: In CMAB-based CoE, simultaneous online update rules drive faster convergence and improved regret over single-expert updating or purely competitive approaches (Abels et al., 2021).
Margin-based collaborative fusion: Cooperation-of-Experts for graph and multimodal data employs a margin-based collaborative mechanism, realized via a confidence tensor and large-margin optimization, ensuring both robustness and discriminative ability (Wang et al., 27 May 2025).
Fusion versus mixing, multimodal uncertainty quantification: Bayesian extensions such as CoCoAFusE augment classical competitive mixtures with collaborative “fusion,” avoiding spurious multimodality in smooth transitions and yielding more accurate credible intervals for uncertainty-sensitive regression (Ugolini et al., 2 May 2025).
Scaling axes and memory optimization: Chain-of-Experts as an MoE variant introduces “in-layer depth” via expert iteration, creating new scaling axes orthogonal to classical width or depth and reducing memory demands while maintaining or enhancing performance (Wang et al., 23 Jun 2025).
Interpretability quantification: The concept polysemanticity entropy (CPE) metric introduced within explainability CoE frameworks enables the quantitative estimation of explanation clarity across layers and models (Yu et al., 19 Mar 2025).

6. Future Directions and Open Problems

Several avenues for further exploration are identified within the surveyed work:

Integration of rich domain knowledge: Expanding the embedding of process or domain-specific knowledge into the expert gating or assignment mechanisms, with implications for hybrid physics- and data-driven models (Souza et al., 2022).
Advanced dependency modeling and scheduling: Improving multi-expert serving via more sophisticated, possibly adaptive, dependency-aware scheduling and memory management strategies (Suo et al., 4 Mar 2025).
Enhanced uncertainty quantification and interpretability: Further refining collaborative fusion and explanation circuits as a foundation for trustworthy, transparent AI in critical application domains (Ugolini et al., 2 May 2025, Yu et al., 19 Mar 2025).
Broader generalization and dynamic expert management: Developing scalable expert routing and aggregation mechanisms that gracefully incorporate new experts or adapt to non-stationary task distributions (Wang et al., 5 Dec 2024, Jain et al., 2 Dec 2024).
Multi-hop and evolutionary modeling: Exploiting “chains-of-evidence” and evolutionary context chains for improved robustness and faithfulness in LLM reasoning, retrieval-augmented generation, and social media analysis (Chang et al., 17 Dec 2024, Huang et al., 30 Jul 2024).

7. Summary Table: Core Features of Representative CoE Systems

CoE Variant	Routing/Aggregation	Key Feature	Benchmark/Domain
Meta-CMAB CoE (Abels et al., 2021)	Linear meta-level weights	Bias mitigation, fast convergence	Decision theory, crowdsourcing
Collaboration of Experts (Zhang et al., 2021)	Delegator with selection	Early-exit, hardware efficiency	ImageNet/vision, hardware deployment
Contextual MoE (Souza et al., 2022)	Possibility-weighted gates	Embedded process knowledge	Industrial process modeling
Chain-of-Experts MoE (Wang et al., 23 Jun 2025)	Iterative, in-layer routing	Sequential expert communication, depth scaling	Math reasoning, transformer models
Bench-CoE (Wang et al., 5 Dec 2024)	Router trained on benchmarks	Task-driven expert allocation, robustness	Language/multimodal benchmarks
Chain-of-Explanation (Yu et al., 19 Mar 2025)	Concept circuit selection	Polysemanticity entropy, local explanations	Model interpretation, vision
CoServe (Suo et al., 4 Mar 2025)	Dependency-aware scheduler	Throughput optimization, memory management	Industrial inspection (CoE serving)

In summary, Chain-of-Experts frameworks offer a principled, empirically validated approach to leveraging multiple, possibly biased or specialized, expert models for complex decision-making, data analysis, interpretability, and scalable machine learning deployments. By explicitly structuring the flow, collaboration, or fusion of expertise—often through advanced routing, weighting, or collaborative mechanisms—CoE systems achieve enhanced performance, robustness, and transparency across varied domains.