Language Agents as Optimizable Graphs

1. Introduction

• GPTSwarm unifies language-agent systems by representing operations as graph nodes and information flow or communication as edges, with composite graphs modeling collaborating agents.The framework can express prompting approaches such as COT, TOT, and Self-Consistency as graphs.Source: §1 · p. 1, Figure 1 · p. 2
• Graph connectivity can self-improve online during task solving or when transferring a solution to another task.This enables the system to search for improved communication patterns among agents rather than relying only on fixed orchestration.Source: §1 · p. 2
• Automatic optimization improves both node-level prompts and edge-level communication or orchestration patterns.Node prompts can adapt from prior inputs and task feedback, while graph connectivity can be optimized through prompting, evolutionary methods, or reinforcement learning.Source: §1 · pp. 1–2
• The graph abstraction addresses disparate agent code bases by providing a common framework for constructing arbitrary systems from recombined fundamental operations.Prior multi-agent systems often required substantial human engineering to define prompting schemes and workflows.Source: §1 · pp. 1–2
• GPTSwarm validates its graph construction and automatic optimization framework on MMLU, Mini CrossWords, HumanEval, and GAIA.The stated emphasis is on the benefits of automatic graph optimization across these benchmarks.Source: §1 · p. 2

2.1. Language Agents as Graphs

• Language agents are graphs of functional nodes connected by execution edges, while swarms compose agent graphs with additional communication edges into a larger DAG.Nodes may query LLMs, use tools, call functions, or perform embodied actions; within-agent edges define execution, and cross-agent edges define collaboration.Source: §2.1 · p. 2, §2.2 · p. 3

2.2. Graph Definition

• A graph executes nodes in topological order, passing each node the task input and predecessor outputs, with the output node producing the task solution.Nodes without predecessors receive empty context, and routines may ignore the shared input when operating only on predecessor context.Source: §2.2 · pp. 2–3

2.3. Edge Optimization

• Edge optimization selects an acyclic pattern of inter-agent connections that maximizes a task-specific utility over the resulting composite graph.Potential edges form a binary configuration space, restricted to composite graphs that remain DAGs.Source: §2.3 · p. 3

2.3.1. PROBLEM REFORMULATION

• Because graph utilities are typically nondifferentiable and DAG choices are combinatorial, the method optimizes a parameterized distribution over feasible DAGs instead of directly searching discrete graphs.The distribution parameters define probabilities over candidate edges while preserving acyclicity.Source: §2.3.1 · p. 3

2.3.2. SOLUTION PARAMETERIZATION

• Candidate DAGs are sampled by considering potential edges sequentially, adding each with its parameterized probability unless doing so would create a cycle.The construction begins with required nodes and edges and rejects cycle-forming additions.Source: §2.3.2 · pp. 3–4

2.3.3. OPTIMIZATION ALGORITHM

• REINFORCE estimates the gradient of expected graph utility from sampled DAGs and updates the distribution parameters with gradient ascent.The estimator uses independently sampled graphs and unbiased utility estimates, with Algorithm 2 implementing iterative parameter updates.Source: §2.3.3 · p. 4

2.4. Node Optimization

• Node optimization improves each node’s prompt using its function description and execution history while holding the graph structure and other prompts fixed during each update.Each history records node inputs, predecessor context, and outputs; an improver then maps that history, the current prompt, and its description to an updated prompt.Source: §2.4 · p. 4

2.5. General Applicability

• GPTSwarm emphasizes reusable modular components, supporting capabilities such as file analysis, web search, and index-based memory within composable agent systems.The framework is presented as applicable to varied language-agent systems through recombinable nodes and agents.Source: §2.5 · pp. 4–5

3.1.2. COLLABORATIVE SETTING

• 2.1% ± 1.1% improvement over the single-agent baseline emerged when seven role-diverse IO agents were combined with adversarial agents and optimized over five seeds.Identically prompted IO agents produced no improvement over the single-agent baseline, motivating role diversity in the collaborative setting.Source: §3.1.2 · p. 5

3.2. Mini Crosswords

• On Mini Crosswords, edge probabilities changed chaotically early in optimization but became almost monotonic after iteration 6.The composite graph was optimized with REINFORCE using an initial edge probability of 10%, learning rate 0.4, and 20 sampled graphs per iteration.Source: Figure 3 · p. 6, §3.2 · p. 6
• 0.575(±0.0275) average accuracy after ten Mini Crosswords optimization iterations exceeded the initial distribution’s 0.465(±0.0509).A distribution with a similar expected edge count achieved 0.510(±0.0552), indicating that the gain was not explained by edge density alone.Source: §3.2 · p. 6
• 0.800(±0.0616) accuracy with GPT-4-Turbo exceeded Tree of Thought with GPT-4 at 0.675 on Mini Crosswords.The same optimized distribution scored 0.668 when Tree of Thought was implemented with GPT-4-Turbo.Source: §3.2 · p. 6, Figure 4 · p. 6

3.3. HumanEval

• 0.88(±0.007) HumanEval accuracy improved over 0.76 without optimization in online learning, with most gains occurring during the first five iterations.The node optimizer adds effective input-output demonstrations to prompts for a ReAct-style coding agent.Source: §3.3 · p. 7, Figure 5 · p. 7

3.4. GAIA

• GAIA performance significantly outperformed GPT-Series with plugins and AutoGPT baselines across several difficulty levels.The reported swarm used seven Tree of Thought agents with prompt-based self-consistency; Table 1 reports means and standard deviations across five runs.Source: §3.4 · p. 7, Table 1 · p. 7
• GAIA swarms improved as agent count and node-operation variety increased, while runtime grew approximately linearly with the number of agents.Web browsing was required for 43.9% of tasks, but the implementation only downloaded provided URLs or queried Google without further navigation; these experiments used no graph optimization.Source: §3.4 · pp. 7–8

4.1. LLM-based Autonomous Agents

• LLM agent research spans structured prompting methods, single-agent tool frameworks, and multi-agent systems with varied communication or role-based structures.Examples include Chain of Thought, ReAct, Reflexion, Tree of Thought, AutoGPT, LangChain, CAMEL, ChatDev, and AutoGen.Source: §4.1 · p. 8

4.2. Language Agents with Graphs

• GPTSwarm represents language agents as graphs that can compose hierarchically into swarms, extending graph-based prompting to external tools and agent collaboration.Nodes can represent prompting or other agent capabilities, while graph composition supports societies of agents.Source: §4.2 · p. 8
• Unlike approaches that describe components additively or use fixed collaboration schemes, GPTSwarm focuses on automatically optimizing agent nodes and edges for orchestration and routing.The framework applies prompt optimization at nodes and REINFORCE to potential edges between agents.Source: §4.2 · p. 8, §4.1 · p. 8

4.3. Optimizing LLM Inference and Self-Improvement

• Prompt and inference-structure optimization can be viewed as meta-learning because LLM prompting configures the effective inference procedure.Related methods include OPRO, PromptBreeder, DSPy, DyLAN, and STOP; GPTSwarm uses iterative node optimization and reinforcement learning over graph edges.Source: §4.3 · p. 9
• GPTSwarm addresses DSPy’s combinatorial optimization challenge by improving each node iteratively according to graph execution history and current prompts.This decomposes optimization across nodes rather than searching the Cartesian product of candidate solutions for the whole graph.Source: §4.3 · p. 9

• GPTSwarm constructs language agents from computational graphs and agent societies from graph compositions, enabling node-level prompt improvement and edge-level REINFORCE optimization.The framework supports implementation of existing methods from basic node operations and evaluates automatic optimization across several benchmarks.Source: §5 · p. 9

Impact Statement

• The impact statement identifies potential benefits in machine-learning efficiency and effectiveness alongside ethical, employment, bias, misuse, and oversight concerns from more autonomous LLM agents.The authors call for safeguards and ethical guidelines as these systems become more capable and automated.Source: Impact Statement · p. 9

A.1. The Vision

• GPTSwarm frames component integration as graph connectivity and uses edge optimization to learn agent orchestration and routing, especially as swarm size increases.The vision contrasts this with additive descriptions that list capabilities without specifying how components interact.Source: §A.1 · p. 13

A.2. Class Diagram

• GPTSwarm’s class structure separates graph objects, agent and operation types, LLM interfaces, dataset integration, prompt sets, and evaluation of node and edge optimization.The framework includes classes such as DirectAnswer, WebSearch, IO, TOT, Dataset, PromptSet, and Evaluator.Source: §A.2 · p. 13
• The implementation is extensible through additional LLM backends, datasets, prompt sets, agents, and nodes, and uses asynchronous computation for task parallelism.These design choices support customization of the framework beyond its included components.Source: §A.2 · p. 13

B. Swarm examples

• The supplementary examples illustrate a swarm combining Tree-of-Thought, Input-Output, and Decision agents, alongside visualizations of other agents and swarms.Figure 8 shows the three-agent example, while Figures 7 and 9 provide framework and agent-system visualizations.Source: Figure 7 · p. 14, B. Swarm examples · p. 15, Figure 8 · p. 15

D.1. Comparing Our Method with Multiagent Debate and DYLAN on MMLU

• The MMLU experiment initializes equal numbers of truthful and adversarial agents and compares GPTSwarm with Multiagent Debate and DyLAN.DyLAN scores agents and prunes low-scoring agents, with results averaged across pruning settings from one to five agents.Source: §D.1 · p. 17
• DyLAN achieves a 0.0065 accuracy improvement over GPTSwarm on the MMLU adversarial-agent setup, while Multiagent Debate is less effective in this setting.The authors attribute DyLAN’s advantage to its more complex debate scheme and prompts, which also increase computational cost.Source: §D.1 · p. 17, Table 3 · p. 17

D.2. Applying Node Optimization after Edge Optimization

• 0.668(±0.0060) accuracy follows node optimization after edge optimization, improving from 0.575(±0.0275) after ten REINFORCE edge steps on Mini Crosswords.Node prompts are updated using demonstrations selected with UCB1 from executions on 20 Mini Crosswords problems.Source: §D.2 · p. 17

• A virtual agent aggregates multiple-agent outputs through majority vote or self-consistency and serves as the composite graph’s output node.Source: E. Experimental Details · p. 17

E.1. MMLU

• The 3T3A adversarial swarm’s train utility converges toward the baseline, with validation using the first 10% of the dataset, or 153 questions.The convergence is shown in Figure 10, which smooths the training score with an unbiased exponential moving average.Source: §E.1 · p. 18, Figure 10 · p. 18

E.1.1. HYPER-PARAMETERS & PROMPTS

• Adam updates edge logits with learning rate 0.1, while the adversarial-experiment prompts are collected in Table 5.Source: §E.1.1 · p. 18, Table 5 · p. 18

E.1.2. ADVERSARIAL SWARM OPTIMIZATION CASE STUDY

• Optimization prunes disconnected agents and edges, retaining only the connections realized after optimizing all potential edges in the 2T2A swarm.Figure 11 contrasts the pre-optimization swarm containing all potential edges with the post-optimization connected subgraph.Source: §E.1.2 · p. 19, Figure 11 · p. 19

E.1.3. SWARM ROLES

• The experiment randomly assigns input-output agent roles from the role list provided in Table 6.Source: §E.1.3 · p. 19, Table 6 · p. 19

E.2.1. AGENTS SETTING

• Mini Crosswords nodes return one or two conditionally independent updated or unchanged solutions, and the composite output node forwards all received solutions.Edges from every agent output node to the composite output node are required for integration.Source: §E.2.1 · p. 20

E.2.2. HYPER-PARAMETERS & PROMPTS

• The Tree of Thought agent searches a depth-eight perfect binary tree through eight branching nodes, each generating two solutions per input.This chain representation avoids explicitly constructing the tree’s 2^9 − 1 nodes; prompts are adapted from the original TOT work.Source: §E.2.1 · p. 20, §E.2.2 · p. 20

E.3.1. THE NODE OPTIMIZATION METHOD

• Every four problem executions, each node updates its demonstrations using recent positive and negative outcomes, retaining or randomly selecting up to four examples.The procedure considers the last ten node inputs and evaluates candidate demonstration sets by their program performance on unit tests.Source: §E.3.1 · p. 20
• Mini Crosswords utility is best-state word accuracy shifted by −0.4 to reduce REINFORCE gradient variance, yielding 0.6 for perfect and −0.4 for empty solutions.Source: §E.3.1 · p. 20

E.3.2. HYPER-PARAMETERS & PROMPTS

• The HumanEval node-optimization experiments use prompts following the ReAct principle, documented in Table 8.Source: §E.3.2 · p. 20, Table 8 · p. 22

E.4.1. AGENT SETTING

• The experiments design different agents and swarms for GAIA, using GPT-4-Turbo and distinct node operations to solve the tasks.GAIA task-solving prompts are provided in Tables 9 and 10.Source: §E.4.1 · p. 20, §E.4.2 · p. 20, Table 7 · p. 21

F. Resource Requirements

• Table 11 reports cost, token consumption, and time requirements for representative experiments.Source: F. Resource Requirements · p. 22

• The framework currently optimizes communication between agents rather than each agent’s internal node topology, which may matter for task planning.The authors propose dynamically changing internal topology as a direction for more extensive graph optimization.Source: G. Limitation and Future Work · p. 22
• Scaling beyond 100 agents is identified as a challenge because communication efficiency and system robustness become difficult to maintain.Source: G. Limitation and Future Work · p. 22