Field-Theoretic Memory for AI Agents: Continuous Dynamics for Context Preservation

TL;DR

A memory system for AI agents that treats stored information as continuous fields governed by partial differential equations rather than discrete entries in a database is presented, showing near-perfect collective intelligence (>99.8%) through field coupling.

Abstract

We present a memory system for AI agents that treats stored information as continuous fields governed by partial differential equations rather than discrete entries in a database. The approach draws from classical field theory: memories diffuse through semantic space, decay thermodynamically based on importance, and interact through field coupling in multi-agent scenarios. We evaluate the system on two established long-context benchmarks: LoCoMo (ACL 2024) with 300-turn conversations across 35 sessions, and LongMemEval (ICLR 2025) testing multi-session reasoning over 500+ turns. On LongMemEval, the field-theoretic approach achieves significant improvements: +116% F1 on multi-session reasoning (p<0.01, d= 3.06), +43.8% on temporal reasoning (p<0.001, d= 9.21), and +27.8% retrieval recall on knowledge updates (p<0.001, d= 5.00). Multi-agent experiments show near-perfect collective intelligence (>99.8%) through field coupling. Code is available at github.com/rotalabs/rotalabs-fieldmem.

Figures (6)

• Figure 1: Field evolution over time. Left: initial memory injection creates localized peaks. Center: diffusion spreads activation to semantically related regions while decay reduces low-importance areas. Right: after multiple evolution steps, important memories form stable peaks while less important information has faded.
• Figure 2: Quality comparison across benchmarks. The field-theoretic approach shows largest gains on multi-session and temporal reasoning tasks where field dynamics preserve cross-session relationships.
• Figure 3: Multi-agent field coupling. Each agent maintains its own field, with coupling terms driving convergence toward shared knowledge. The coupling strength $k_{ij}$ controls the rate of knowledge transfer between agents.
• Figure 4: Performance scaling with memory count. The sparse field representation keeps evolution time sub-linear in the number of memories, remaining practical even at 100k+ memories.
• Figure 5: Ablation study showing component contributions. Field evolution and thermodynamic decay are the most critical components; removing either substantially degrades performance.