Beyond Episodic AI: Cognitive Field Networks for Biologically Inspired Persistent Cognition

Byung Gyu Chae

Figure 1: Cognitive Field Network (CFN): self-reentrant architecture and learning for persistent cognition. (a) Transition from episodic inference to self-reentrant cognitive dynamics. The hidden field

\Phi_{t}

generated during one computational cycle is retained and re-entered into the subsequent cycle, yielding the state-dependent evolution

\Phi_{t+1}=F_{\theta}(X_{t+1},\Phi_{t})

. (b) Decoder-style CFN implementation used in this work. The current token sequence follows the ordinary causal Transformer pathway, while the complete token-resolved hidden field

\Phi_{t-1}

from the preceding cycle is supplied as unmasked cross-attention memory to every Transformer layer, with learnable recurrent coupling

g

. After the final layer,

\Phi_{t}=H_{t}^{(L)}

provides both the internal field retained for the next cycle and the hidden representation from which the language-model output is read out. (c) Learning and experimental analysis of self-reentrant cognitive dynamics. The architecture makes field re-entry available without prescribing its functional role. Task-driven learning can organize this pathway into persistent, content-dependent recurrent computation. The recurrent hidden field can be directly accessed and experimentally manipulated, enabling causal tests of memory persistence and the functional contribution of self-reentry across successive computational cycles. The framework also provides a basis for quantitative dynamical analysis through Jacobian spectra, relaxation-mode distributions, memory kernels, and collective response observables.

Component	Specification
Backbone	GPT-NeoX decoder Transformer
Number of Transformer blocks	$6$
Hidden dimension $d$	$512$
Attention heads	$8$
Feed-forward dimension	$2048$
Positional representation	Rotary positional embedding (RoPE)

Table 1: Architecture of the decoder-style Cognitive Field Network used in this work. The final token-resolved hidden field from each computational cycle is retained and supplied as unmasked recurrent cross-attention memory to every Transformer layer of the subsequent cycle.

Figure 2: Learning dynamics of recurrent field re-entry during language-model pretraining. (a) Training and validation cross-entropy losses for the GPT-NeoX-based CFN trained on WikiText-103. Both losses decrease rapidly during early training, followed by a slower late-training regime. (b) Evolution of the learnable re-entry coupling

g

(green) and the recurrent-field strength

R_{\rm field}

measured on the training (blue) and validation (orange) sets. The recurrent quantities exhibit an initial decrease, followed by recovery and gradual stabilization.

Figure 3: Learning-induced reorganization of the relaxation spectrum. Time-scale density of states (TDOS) obtained from the local Jacobian of the

H^{(4)}\rightarrow H^{(5)}

layer map at successive language-model pretraining checkpoints. A fixed probe sequence of length

T=8

yields a

4096\times 4096

Jacobian, with relaxation rates defined as

\lambda_{\alpha}=-\ln|\mu_{\alpha}|

, where

\mu_{\alpha}

are the Jacobian eigenvalues. For each checkpoint, the upper panel shows the full stable relaxation spectrum, and the lower panel shows the infrared region

0<\lambda<0.2

. The dashed vertical line indicates the reference cutoff

\lambda_{c}=0.05

. The infrared spectral weight increases rapidly during early training and subsequently decreases as the spectrum broadens.

Figure 4: Infrared self-energy and inverse-gap proxies during learning. (a) Normalized infrared self-energy proxy

\Sigma_{\epsilon}^{\rm norm}(0)

. (b) Corresponding inverse-self-energy proxy

r_{\rm gap}^{\rm proxy}=1/\Sigma_{\epsilon}^{\rm norm}(0)

. Both quantities are computed from the stable relaxation spectrum of the

H^{(4)}\rightarrow H^{(5)}

Jacobian at successive pretraining checkpoints, using a fixed probe sequence of length

T=8

and an infrared regulator

\epsilon=10^{-3}

.

Figure 5: Cross-cycle protocol for learning content-specific memory and selective retrieval. During the source (WRITE) cycle

n

, the CFN receives a sequence containing

N

randomly generated entity–attribute bindings (illustrated for

N=2

) and produces the token-resolved recurrent field

\Phi_{n}=H_{n}^{(L)}

. During the subsequent QUERY cycle

n+1

, the source text is no longer available, and the field

\Phi_{n}

is re-entered through recurrent cross-attention. Independent single-query inputs retrieve different attributes from the same preceding field

\Phi_{n}

. Training uses full backpropagation through both cycles, with answer supervision applied only during the QUERY cycle.

Figure 6: Learning dynamics of selective retrieval from the re-entered cognitive field. Validation exact-match accuracy during cross-cycle retrieval training for memory loads

N=1,2,4,8,

and

16

, where

N

denotes the number of entity–attribute bindings presented during the source cycle. The

N=1

task reaches near-perfect accuracy rapidly, whereas larger memory loads exhibit distinct learning trajectories. For

N=2

, accuracy remains near

0.5

before rising sharply toward unity. The

N=8

and

N=16

conditions also show abrupt improvements, while

N=4

exhibits greater fluctuations before reaching high retrieval accuracy.

Memory load	$C_{\rm EM}$	$W_{\rm EM}$	$O_{\rm EM}$	$C-W$	$C-O$
$N=1$	1.0000	0.0275	0.0350	0.9725	0.9650
$N=2$	0.9975	0.0150	0.0354	0.9825	0.9621
$N=4$	0.9760	0.0131	0.0185	0.9629	0.9575
$N=8$	0.9988	0.0160	0.0167	0.9827	0.9821
$N=16$	0.9976	0.0140	0.0193	0.9835	0.9783

Table 2: Causal intervention on the recurrent field during selective retrieval.

C

,

W

, and

O

denote the correct-field, wrong-field, and state-off conditions, respectively. Subscript EM denotes exact-match accuracy. The differences

C-W

and

C-O

quantify the retrieval advantage of the correct field over the controls.

Figure 7: Experimental protocol for persistent memory through recurrent cognitive-field dynamics. (a) Cross-cycle memory protocol without context replay. During the WRITE cycle, the CFN receives an entity–attribute binding and generates the recurrent field

\Phi_{0}

. The original context is then removed, while the field propagates through

d-1

bridge cycles with unrelated inputs

X_{1},\ldots,X_{d-1}

. At cycle distance

d

, a QUERY retrieves the original attribute from the propagated field

\Phi_{d-1}

. (b) Causal intervention on the recurrent field. For the same query and matched intervening inputs, retrieval is evaluated using the correct field

\Phi_{C}

, an unrelated field

\Phi_{W}

, or disabled re-entry

\Phi_{\rm off}

. Content-specific retrieval is assessed through

P(A\mid Q,\Phi_{C})\gg P(A\mid Q,\Phi_{W})\simeq P(A\mid Q,\Phi_{\rm off})

. (c) Schematic illustration of learning-dependent memory persistence for training distances

d_{\rm train}=1,2,4,

and

8

. Larger training distances correspond to longer illustrated retention horizons.

Figure 8: Long-horizon persistence of content-specific information in the recurrent cognitive field. Exact-match retrieval for the CFN trained at cycle distance

d_{\rm train}=8

and evaluated without further optimization or replay of the original WRITE context. The vertical dashed line indicates the training distance. (a) Teacher-forced exact-match accuracy under the correct-field (

C

), wrong-field (

W

), and state-off (

O

) conditions. Correct-field retrieval remains near perfect beyond the trained distance before gradually declining, while the wrong-field and state-off controls remain near background levels. (b) Content-specific retrieval signals measured by the exact-match differences

C-W

and

C-O

. Both differences remain large beyond the trained distance and decrease at longer cycle distances.

Figure 9: Learning-dependent temporal persistence of the recurrent cognitive field. (a) Content-specific retention measured by the correct–wrong exact-match difference

\mathcal{M}(d)

for training distances

d_{\rm train}=1,2,4,

and

8

. The vertical dashed lines indicate the corresponding training distances. The retention curves shift toward longer cycle distances as

d_{\rm train}

increases. (b) Retention half-distance

d_{1/2}

, defined by

\mathcal{M}(d_{1/2})=\mathcal{M}_{0}/2

, as a function of

d_{\rm train}

. The measured values are

d_{1/2}\simeq 1.52,\,4.55,\,11.59,

and

23.02

for

d_{\rm train}=1,2,4,

and

8

, respectively. The dashed line indicates the reference

d_{1/2}=d_{\rm train}

.

Figure 10: Learning-dependent displacement of long-horizon memory retention under semantic continuation. Teacher-forced exact-match accuracy as a function of cycle distance

d

for CFN models trained at

d_{\rm train}=2,4,

and

8

using semantic-continuation bridges. Symbols represent measured retention values, and solid curves denote four-parameter logistic fits. The fitted midpoints are

d_{50}=6.84

,

11.43

, and

26.63

for

d_{\rm train}=2,4,

and

8

, respectively. The retention curves shift toward longer cycle distances as the training distance increases.

Figure 11: Approximate temporal scaling collapse of learned recurrent-memory retention under semantic continuation. Normalized correct-field retention,

\widetilde{P}=(P-P_{\infty})/(P_{0}-P_{\infty})

, is plotted against the rescaled cycle distance

u=d/d_{\rm train}

for CFN models trained at

d_{\rm train}=2,4,

and

8

. Symbols represent measured teacher-forced exact-match retention, and solid curves denote the corresponding logistic fits. The three retention profiles exhibit an approximate collapse in the transition region, with modest differences in the rescaled midpoints

d_{50}/d_{\rm train}

.

$d_{\rm train}$	$d_{50}$	$s$	$\Delta d_{90\rightarrow 10}$	$d_{50}/d_{\rm train}$	$s/d_{\rm train}$
2	6.84	1.21	5.32	3.42	0.605
4	11.43	2.40	10.54	2.86	0.600
8	26.63	4.99	21.95	3.33	0.624

Table 3: Logistic characterization of long-horizon correct-field retention under semantic continuation. The midpoint

d_{50}

and transition scale

s

are obtained from Eq. ( 72 ). The transition width is

\Delta d_{90\rightarrow 10}=2s\ln 9

. The last two columns show the fitted midpoint and transition scale normalized by the training distance.

Figure 12: Representation-sensitive renewal of recurrent-memory retention under periodic source re-exposure. Teacher-forced exact-match accuracy as a function of cycle distance

d

for a CFN trained with semantic continuation at

d_{\rm train}=4

. Periodic re-exposure presents either the exact original source or a near-paraphrased version of the same episode, without supplying the target answer through intervening bridges. Exact source re-exposure produces repeated recovery of correct-field retrieval, whereas near-paraphrased re-exposure yields substantially weaker recovery. Wrong-field and recurrent-field-off controls remain near background accuracy.

Figure 13: Long-horizon recurrent-memory retention under periodic content-matched source re-exposure. Teacher-forced exact-match accuracy for a CFN trained at

d_{\rm train}=4

, with the original source re-presented every eight recurrent cycles. The vertical dotted lines indicate source re-exposure events. Correct-field retrieval exhibits repeated recovery followed by gradual decay between successive re-exposure events, producing a sawtooth trajectory. After an initial transient, the peak–trough envelope approaches an approximately stationary nonzero regime over the 128-cycle evaluation window. Wrong-field and recurrent-field-off controls remain near background accuracy.

Beyond Episodic AI: Cognitive Field Networks for Biologically Inspired Persistent Cognition

Abstract

Figures & tables

Computational Cognitive Modeling

Continuous Memory Machines

Persistent Memory Through Triple-Loop Consolidation Under Stochastic Unit Turnover

Information as Structural Alignment: A Dynamical Theory of Continual Learning

Abstract

Computational Cognitive Modeling

Explore similar work

Continuous Memory Machines

Persistent Memory Through Triple-Loop Consolidation Under Stochastic Unit Turnover

Information as Structural Alignment: A Dynamical Theory of Continual Learning