Adaptive Memory Crystallization for Autonomous AI Agent Learning in Dynamic Environments

Rajat Khanda; Mohammad Baqar; Sambuddha Chakrabarti; Satyasaran Changdar

cs.LGApr 2, 2026

Adaptive Memory Crystallization for Autonomous AI Agent Learning in Dynamic Environments

Authors: Rajat Khanda, Mohammad Baqar, Sambuddha Chakrabarti, Satyasaran Changdar

Organizations: Supermicro San Jose, USA · Cisco Systems San Jose, USA · Princeton University New Jersey, USA · University of Copenhagen Copenhagen, Denmark

Abstract

Autonomous AI agents operating in dynamic environments face a persistent challenge: acquiring new capabilities without erasing prior knowledge. We present Adaptive Memory Crystallization (AMC), a memory architecture for progressive experience consolidation in continual reinforcement learning. AMC is conceptually inspired by the qualitative structure of synaptic tagging and capture (STC) theory, the idea that memories transition through discrete stability phases, but makes no claim to model the underlying molecular or synaptic mechanisms. AMC models memory as a continuous crystallization process in which experiences migrate from plastic to stable states according to a multi-objective utility signal. The framework introduces a three-phase memory hierarchy (Liquid--Glass--Crystal) governed by an Itô stochastic differential equation (SDE) whose population-level behavior is captured by an explicit Fokker--Planck equation admitting a closed-form Beta stationary distribution. We provide proofs of: (i) well-posedness and global convergence of the crystallization SDE to a unique Beta stationary distribution; (ii) exponential convergence of individual crystallization states to their fixed points, with explicit rates and variance bounds; and (iii) end-to-end Q-learning error bounds and matching memory-capacity lower bounds that link SDE parameters directly to agent performance. Empirical evaluation on Meta-World MT50, Atari 20-game sequential learning, and MuJoCo continual locomotion consistently shows improvements in forward transfer (+34--43% over the strongest baseline), reductions in catastrophic forgetting (67--80%), and a 62% decrease in memory footprint.

Figures & tables

Symbol	Meaning
$\mathcal{M}=(\mathcal{S},\mathcal{A},P,R,\gamma)$	MDP tuple
$e_{i}=(s,a,r,s^{\prime})$	Experience tuple
$c_{i}(t)\in[0,1]$	Crystallization state of $e_{i}$
$U_{i}(t)\in[0,1]$	Multi-objective utility of $e_{i}$
$\delta_{i}(t)$	Temporal-difference (TD) error
$N_{i}(t)$	State-action novelty

TABLE I: Notation used throughout the paper.

Property	Liquid	Glass	Crystal
$c_{i}$ range	$[0,\tau_{L})$	$[\tau_{L},\tau_{C}]$	$(\tau_{C},1]$
Eff. learning rate	$\eta_{\mathrm{base},t}$	${\sim}0.5\,\eta_{\mathrm{base},t}$	${\sim}0.09\,\eta_{\mathrm{base},t}$
Replay frequency	High	Medium	Low
Retention policy	Utility-FIFO	Priority	Indefinite
Interference resist.	Low	Medium	High
Buffer fraction †	62.5%	31.25%	6.25%

TABLE II: Memory Phase Properties

Method	AP $\uparrow$	FT $\uparrow$	BT $\uparrow$	ME $\uparrow$	Mem.
VR	62.3 $\pm$ 5.1	+3.2 $\pm$ 1.8	$-$ 31.4 $\pm$ 4.2	0.062	1000
PER	68.7 $\pm$ 4.3	+5.7 $\pm$ 2.1	$-$ 24.1 $\pm$ 3.9	0.069	1000
HER	71.2 $\pm$ 3.8	+8.4 $\pm$ 2.4	$-$ 21.3 $\pm$ 3.5	0.071	1000
NEC	64.5 $\pm$ 5.7	+4.1 $\pm$ 2.3	$-$ 28.7 $\pm$ 4.8	0.043	1500
PackNet	73.8 $\pm$ 3.2	+9.2 $\pm$ 1.9	$-$ 8.4 $\pm$ 2.1	0.015	5000
PNN	76.4 $\pm$ 2.9	+11.3 $\pm$ 1.7	$-$ 2.1 $\pm$ 1.3	0.015	5000

TABLE III: Meta-World MT50 results. Mean

\pm

std over 50 seeds. Mem. in MB. Best result bolded . ‡ Memory-matched comparison: VR, PER, EWC run with 380 MB buffer (proportionally reduced from 1000 MB). AMC retains its advantage at equal budget. All AMC vs. best-baseline differences:

p<10^{-4}

, Holm–Bonferroni corrected.

Method	AP(%) $\uparrow$	FT $\uparrow$	BT $\uparrow$	$>$ Human
VR	124 $\pm$ 18	+2.1 $\pm$ 3.4	$-$ 47.3 $\pm$ 8.2	7/20
PER	142 $\pm$ 15	+8.3 $\pm$ 4.1	$-$ 38.6 $\pm$ 7.1	9/20
EWC	136 $\pm$ 17	+5.2 $\pm$ 3.8	$-$ 41.2 $\pm$ 7.8	8/20
PackNet	187 $\pm$ 12	+15.7 $\pm$ 3.2	$-$ 12.4 $\pm$ 4.3	14/20
AMC	201 $\pm$ 11	+22.4 $\pm$ 2.9	$-$ 9.7 $\pm$ 3.8	16/20

TABLE IV: Sequential Atari-20. AP as % of human-level performance.

Method	Avg. Return $\uparrow$	Task-1 Retention $\uparrow$
VR	3847 $\pm$ 312	25%
PER	4213 $\pm$ 278	41%
EWC	4567 $\pm$ 245	64%
AMC	5892 $\pm$ 198	86%

TABLE V: MuJoCo Continual Locomotion. Final average return

\pm

std.

Variant	AP $\uparrow$	BT $\uparrow$
AMC (full)	81.7 $\pm$ 2.4	$-$ 6.3 $\pm$ 1.8
No crystallization ( $c_{i}\equiv 0$ )	68.7 $\pm$ 4.3	$-$ 24.1 $\pm$ 3.9
No phase LR modulation	74.1 $\pm$ 3.1	$-$ 18.7 $\pm$ 3.2
No interference detection	77.3 $\pm$ 2.8	$-$ 12.4 $\pm$ 2.5
No novelty ( $w_{2}=0$ )	79.2 $\pm$ 2.6	$-$ 9.1 $\pm$ 2.2
No downstream val. ( $w_{3}=0$ )	80.1 $\pm$ 2.5	$-$ 7.8 $\pm$ 2.0

TABLE VI: Ablation on Meta-World MT50. Each row removes one AMC component.

Parameter	Values tested	AP range
$\alpha$	$\{0.005,0.01,0.05,0.1,0.5\}$	76.2–81.7
$\beta$	$\{0.0005,0.001,0.005,0.01,0.05\}$	77.4–81.7
$\sigma$	$\{0.001,0.005,0.01,0.05\}$	79.1–81.7
$\tau_{L}$	$\{0.1,0.2,0.3,0.4,0.5\}$	78.8–81.7
$\tau_{C}$	$\{0.5,0.6,0.7,0.8,0.9\}$	79.3–81.7
$w_{1}$	$\{0.3,0.4,0.5,0.6,0.7\}$	80.1–81.7

TABLE VII: Sensitivity of AP (Meta-World MT50) to AMC hyperparameters. Each row varies one parameter while holding others at default.

Fig. 1: t-SNE projection of AMC memory after 25 Meta-World tasks. Color encodes crystallization level $c_{i}$ (dark=high, light=low). Crystallized cluster centers correspond to shared motor primitives (grasping, collision avoidance) reused across tasks. Silhouette score for crystal vs. non-crystal separation: $0.61\pm 0.04$ (50 seeds; $>$ 0.5 indicates well-separated clusters).

Transition	AMC	Biological	Ratio
Liquid $\to$ Glass	$\sim$ 1k steps	1–3 h	$\approx$ 18 $\times$
Glass $\to$ Crystal	$\sim$ 10k steps	6–24 h	$\approx$ 10 $\times$
Full crystallization	$\sim$ 50k steps	Days–wks	$\approx$ 30 $\times$

TABLE VIII: AMC vs. biological consolidation timescales.

Setting	Fast-change	Moderate	Slow-change
	(Robotics)	(Games)	(Navigation)
$\alpha$	0.10	0.05	0.01
$\beta$	0.02	0.005	0.001
$\sigma$	0.01	0.005	0.002
$\tau_{L}$	0.25	0.30	0.35
$\tau_{C}$	0.65	0.70	0.80

TABLE IX: Recommended AMC settings by deployment scenario.

Operation	Complexity	$N\!=\!10^{5}$	$N\!=\!10^{6}$
FAISS index build	$O(N\log N)$	50 ms	0.5 s
kNN query (single)	$O(\log N)$	$<$ 1 ms	$<$ 1 ms
Full batch ( $N$ queries)	$O(N\log N)$	0.8 s	8.2 s

TABLE X: kNN runtime complexity. Empirical times on A100 GPU.

Benchmark	AP gain	FT gain	Forgetting red.
Meta-World MT50	$+6.9$ pp	$+34.5\%$	$67\%$ vs. best
Atari-20	$+7.5\%$	$+42.7\%$	$22\%$ vs. PackNet
MuJoCo Locomotion	$+29\%$	—	$80\%$ vs. VR

TABLE XI: Summary of AMC improvements over the strongest per-benchmark baseline.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Result	Key assumption	Implication
Thm. III.4 : Well-posedness	$U_{i},I_{i}$ bounded, measurable	SDE ( 5 ) has unique strong solution on $[0,1]$
Thm. III.8 : Fokker–Planck	Time-averaged $\bar{U},\bar{I}$	Population density $p(c,t)$ evolves as PDE ( 8 )
Thm. III.9 : Beta stationary dist.	$\sigma>0$ , $A,B>0$	$p_{\infty}=\mathrm{Beta}(A,B)$ ; mean $=\alpha\bar{U}/(\alpha\bar{U}+\beta\bar{I})$
Thm. III.12 : Exp. mean convergence	Constant $U_{i},I_{i}$	$\|\mathbb{E}[c_{i}]-c_{i}^{}\|\leq\|c_{i}(0)-c_{i}^{}\|e^{-\lambda_{i}t}$
Thm. III.13 : Forgetting bound	$c_{i}(0)>\tau_{C}$	$\mathbb{P}[\text{forget}]\leq e^{-2\lambda_{i}(c_{0}-\tau_{L})^{2}/(\sigma^{2}T)}\cdot e^{-\lambda_{i}T/2}$
Thm. V.7 : Q-learning convergence	Lipschitz $Q^{*}$ , sufficient exploration	Error $\leq O(\beta\bar{I}/(\alpha\bar{U}{+}\beta\bar{I})/\sqrt{N_{C}})$

Appendix

TABLE XII: Summary of theoretical results. All theorems are proved in full in Section III and Section V .

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An agent that operates sequentially must incorporate new experience without forgetting old experience, under a fixed memory budget. We propose a framework in which memory is not a parameter vector but a stochastic process: a Bridge Diffusion on a replay interval

[0,1]

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K

d

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L

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O(LKd^2)

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a_{1/2}\approx c\,L

with a constant

c>1

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c

admits an information-theoretic interpretation analogous to the Shannon channel capacity. The stochastic process underlying the bridge provides temporally coherent

movie'' replay -- compressed narratives of the agent's history, demonstrated visually on an MNIST latent-space illustration. The framework provides a fully analytical

Ising model'' of continual learning in which the mechanism, rate, and form of forgetting can be studied with mathematical precision.

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