CoEx: Diverse Innovations in AI and Beyond

Updated 3 July 2026

CoEx is a multifaceted concept spanning AI agent architectures, spectrum sharing, combinatorics, coded data exchange, and real-time vision with distinct technical innovations.
In AI, CoEx employs a hierarchical Planner–Actor–Memory framework that dynamically updates neurosymbolic memory to enhance exploration and achieve significant performance gains.
CoEx also covers cognitive beamforming for interference control, coalesced expert execution in MoE inference, and optimized protocols in combinatorial and medical data extraction.

CoEx encompasses a diverse range of technical meanings across artificial intelligence, computer networking, spectrum sharing, combinatorics, knowledge extraction, and computer vision. This article details major established definitions and results for CoEx in LLM-based hierarchical agents, spectrum coexistence, codegree extremal combinatorics, coded data exchange, medical information extraction, and real-time stereo vision, referencing the relevant foundational sources.

1. Hierarchical Co-evolution of World Models and Exploration in LLM Agents

CoEx, in the context of AI agents, refers to a hierarchical agent architecture facilitating co-evolving world-models and exploration within a persistent neurosymbolic belief state (Kim et al., 29 Jul 2025). The core innovation is a Planner–Actor–Memory decomposition:

Planner (LLM-based): Operates at the subgoal level, reasoning over a structured belief state $B_k = (m_k, l_k)$ , where $m_k$ denotes symbolic, object-oriented memory (Python sets/dicts) and $l_k$ holds an LLM-generated structured textual memory.
Actor: Executes low-level environment interactions to realize a specified subgoal $g_k$ , generating a trajectory $\varepsilon_k$ .
Adaptive Belief Update: After each subgoal, the memory is updated through (i) verification (LLM-driven Q&A to detect task status and errors) and (ii) synthesis (high-level summarization). All factual adaptation happens through in-place augmentation of the belief state, not parametric LLM retraining.

Formally, state updates are

$B_{k+1} = \mathcal{F}(B_k, g_k, \varepsilon_k),$

with symbolic and textual learning mechanisms specified as

$m_{k+1} = \mathrm{SymbolicUpdate}(m_k,\;\varepsilon_k),\quad l_{k+1} = \mathrm{Synthesis}(l_k,\;m_{k+1},\;\varepsilon_k,\;g_k).$

This persistent neurosymbolic memory allows systematic online assimilation of new environment knowledge.

The architecture allows hierarchical LLM planning (subgoal selection), coupled with grounded, code-controlled symbolic memory, enabling agents to dynamically adapt exploration, rapid error recovery, and effective handling of partial observability.

2. Formal Properties and Implementation Details

The CoEx agent instantiates neurosymbolic memory with:

Symbolic memory ( $m_k$ ): Object-predicate sets, “holding” dictionaries, agent locations, and step counters. Updates involve interpreting environment feedback with regular expressions and efficient set operations.
Structured textual memory ( $l_k$ ): JSON records encoding "status_line", "justification", and "learned_facts". Verification queries (LLM-prompted) validate subgoal outcomes; synthesis produces high-level summaries.

Subgoal planning leverages a prompted LLM to optimize (implicitly) a utility over candidate plans, balancing task progress, uncertainty reduction, and exploration. The agent’s adaptive loop is formalized as: $G_k = \arg\max_{G}\;U(G\mid B_k, H_k)$ with $m_k$ 0 the ordered subgoal sequence and $m_k$ 1 the utility defined by the LLM's plan-generation prompt.

All memory updates are online and nonparametric; the LLM’s parameters remain fixed during deployment. This yields sample efficiency and robustness against plan divergence in nonstationary environments.

3. Empirical Evaluation Across Benchmarks

CoEx was evaluated on ALFWorld (kitchen tasks), PDDL domains (Gripper/Blocksworld), and Jericho (text adventure games), demonstrating superior exploration and planning capability (Kim et al., 29 Jul 2025):

Suite	Baseline (Success %)	CoEx (Success %)	Progress (CoEx)
ALFWorld	ReAct 61.94, Reflexion 88.06, WALL-E 95.00, AdaPlanner 91.79	93.28	N/A
PDDL	ReAct 60.0, HiAgent 66.7	73.3	92.8
Jericho	10.0 (avg. success)	25.0	55.5

Ablation experiments show a $m_k$ 2 point improvement in success rate and $m_k$ 3 point improvement in progress rate on PDDL when shifting from a monolithic to a hierarchical Planner-Actor structure. CoEx was especially strong on composite “Picktwo” tasks, outperforming monolithic baselines by a large margin.

Analysis of world model evolution shows stepwise correction and adaptation—mistaken picks, replanning, constraint awareness, and successful strategic shift—encoded into neurosymbolic memory.

4. Spectrum Coexistence and Signal Processing: CoEx via Beamforming

In wireless networks, CoEx also designates harmonious coexistence of heterogeneous networks on shared spectrum without cross-technology signaling (Bertizzolo et al., 2020). The CoBeam architecture employs cognitive beamforming to maximize secondary network throughput while satisfying per-user interference constraints for primary networks.

Key properties include:

Programmable Physical Layer (P PHY): Supports multistandard demodulation and legacy MAC reuse.
Cognitive Sensing Engine (CSE): Blind channel-state estimation from overheard preambles, enabling instantaneous adaptation without protocol modification.
Beamforming Engine (BFE): Adaptive switching between maximum-ratio transmission (MRT) and zero-forcing (ZF) precoders based on traffic metrics.
Closed-form SINR expressions for both secondary and primary receive users embody the trade-off:

$m_k$ 4

Field deployments show up to $m_k$ 5 aggregate throughput gain and strict interference control without negotiation, validating that spatial signal processing alone can realize CoEx in practice.

5. Coalesced Expert Execution (CoEx) in MoE Inference

Within Mixture-of-Experts (MoE) architectures, CoEx (Coalesced Expert Execution) describes batching strategies and hardware orchestration to maximize inference throughput by eliminating micro-batching-induced stalls and balancing CPU–GPU compute (Son et al., 18 May 2026).

Coalescing-Aware Orchestration: Executes all expert FFNs over the full batch (never micro-batched), maximizing operational GEMM intensity and enabling high AMX utilization on CPUs.
Static Expert-Aware Stratification: Pre-assigns top-routed experts to GPU (Exp_R), mid-tail to prefetch (Exp_M), and the remainder to CPU (Exp_C) under VRAM and PCIe limits.
AMX-Enabled Parallelism: Applies large-batch GEMMs on Intel AMX CPUs in parallel with CUDA GPU compute, overlapping PCIe transfers with computation.

Empirical results manifest $m_k$ 6– $m_k$ 7 overall throughput gains versus FlexGen and MoE-Lightning across multiple LLMs, with ablations attributing $m_k$ 8 of this to coalesced expert execution and AMX acceleration. EAS (stratification) alone yields up to $m_k$ 9 further improvement by boosting GPU hit ratio.

6. CoEx in Combinatorics and Coded Data Exchange

In extremal combinatorics, CoEx denotes the codegree extremal function, $l_k$ 0, for hypergraphs: the maximal pair codegree in an $l_k$ 1-vertex 3-graph that is $l_k$ 2-free (Falgas-Ravry, 2013, Falgas-Ravry et al., 2013). For families $l_k$ 3, the limit

$l_k$ 4

gives the codegree density. For instance, for $l_k$ 5, the complete 3-graph on $l_k$ 6 vertices, the lower bound

$l_k$ 7

is tight for infinitely many $l_k$ 8, and the extremal constructions include random edge-colorings and blow-ups via Steiner triple systems. For “independent neighborhoods” ( $l_k$ 9), one has $g_k$ 0, and all near-extremal graphs are close to cyclic 3-partite configurations.

For network coding, CoEx denotes the minimal-transmission cooperative data exchange protocol enabling universal packet recovery in multihop settings (Courtade et al., 2012, Heidarzadeh et al., 2015). The optimal schedule is characterized by cut-set inequalities and can be computed via submodular function minimization in the fully connected case. The model extends to unreliable clients, where the robust minimum transmission schedule is given (with high probability) by a closed-form LP solution, with exact formulas for $g_k$ 1 and vanishing approximation error for general $g_k$ 2.

7. CoEx in Medical Knowledge Extraction and Real-Time Stereo Matching

CoEx-BERT defines a parameter-sharing, joint entity and relation extraction model for Uyghur (and Mongolian) medicine deployed on edge devices (Lu et al., 2024); the architecture combines a shared BERT encoder with twin heads, one for entity prediction and one for subject-conditional relation-object extraction. This allows accurate inference of overlapping relational triples and achieves $g_k$ 3 F1, with low (65 ms) edge-device latency.

Finally, “Correlate-and-Excite” (CoEx) gives an efficient stereo-matching network utilizing Guided Cost-volume Excitation and top- $g_k$ 4 soft-argmin disparity regression (Bangunharcana et al., 2021). CoEx achieves $g_k$ 5 EPE on SceneFlow and $g_k$ 6 KITTI 2012 3px error at 27 ms runtime (37 FPS), with channel-wise excitation yielding high accuracy at minimal cost compared to spatially varying architectures.