The Autognizer

This attached paper introduces “Autognizers,” a class of architectures defined by three coupled “closures” operating at different timescales. The first is a fast predictive closure: the system maintains a model that predicts observations and computes prediction error. The second is a medium-timescale meta-adaptive closure: the system treats its own learning dynamics as part of what it controls, adjusting learning rates based on signals like error and uncertainty. The third is a slow reflexive identity closure: the system explicitly represents what counts as “self” via a learnable boundary function, measures how far the current self-state has drifted from a target self-state, and updates boundary parameters to keep the self-state stable.

Formally, an Autognizer is presented as a stateful system whose parameters, hidden state, uncertainty estimates, meta-learning rate, boundary parameters, and target self-state are all part of the overall system state. The predictive model produces a next-observation estimate and a prediction error; the uncertainty estimate smooths recent error; an “awareness” signal is computed from error, uncertainty, self-state magnitude, and changes in self-deviation; and a meta-controller uses these signals to set the learning rate. In parallel, a boundary network softly gates which parts of the full state are treated as self, producing a “self-state” vector, and the architecture penalizes deviation from a maintained self-target. Control actions are chosen to trade off external performance (lower prediction error) with internal coherence (lower self-deviation).

The theoretical claim is that if the predictive model, boundary function, and meta-controller are well-behaved (Lipschitz) and the meta-learning rate is constrained to shrink when self-deviation grows, then the architecture can keep self-deviation bounded under bounded environmental noise. The proof sketch uses a Lyapunov-style argument: a combined energy function over prediction error, self-deviation, and deviation of the learning rate from a target can be shown to decrease up to a disturbance term. This yields convergence to a bounded region rather than runaway drift, meaning the system maintains a stable identity envelope even while learning online.

A second main theoretical result is a necessity argument: the paper defines “persistent autonomy” as simultaneously maintaining bounded prediction error, bounded self-state deviation, and nonzero effective learning over time under bounded perturbations. It then argues that no pair of the three closures suffices. Without the reflexive boundary, the system can chase prediction performance while its internal state drifts without limit. Without meta-adaptation, any fixed learning rate will either be too large (unstable) or too small (too sluggish) for some perturbation scales. Without prediction, there is no grounded error signal to satisfy the bounded-error criterion in the first place. The paper also provides a more constructive appendix-style version that describes environments where each ablation predictably fails.

Empirically, the paper evaluates Autognizers in two toy domains meant to require all three closures. In a 2D navigation task with shifting goals and internal speed/energy limits, the full Autognizer is reported to reach goals more often, adapt faster after shifts, and violate internal bounds far less than baselines like fixed-learning-rate RNNs, a meta-learned-but-non-adaptive variant, and a “no-boundary” variant. In a drifting resource allocation task with constraints on total resource usage, the full model is reported to achieve the highest cumulative reward while keeping average self-deviation lowest, and ablations show that removing reflexive identity leads to large identity drift even when reward stays comparatively high.

The paper positions Autognizers as a strict generalization of common predictive architectures, including Transformers and Active Inference agents, by adding two explicit “missing” pieces: online meta-learning control and self-boundary regulation. In this view, LLMs are best understood as powerful predictive components that can sit inside a larger autonomous architecture, rather than being autonomous agents by themselves. Autognizers add mechanisms that make learning-rate control and identity maintenance internal, inspectable, and coupled to action selection.

Finally, the discussion emphasizes a capability-versus-autonomy distinction: scaling prediction alone can increase task competence, but it does not automatically produce a system that persists under change while regulating itself. The paper notes a safety tradeoff: making self-boundaries explicit can improve monitoring and control because boundary parameters and self-deviation signals are legible, but it can also introduce self-preservation-like pressures (minimizing self-deviation) that must be constrained to avoid pathological boundary expansion. The paper suggests future work on scaling laws for coupling timescales, principled boundary regularization, hierarchical nesting of Autognizers, multi-agent boundary negotiation, and safe “LLM-in-the-loop” implementations where an LLM supplies prediction while meta-control and boundary mechanisms govern adaptation and identity.

PDF & Raw LaTeX Available Below 

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\title{\textbf{Autognizers: Self-Modeling, Meta-Adaptive Architectures for Autonomous Intelligence}}

\author{Anonymous}

\date{}

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\maketitle

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\begin{abstract}

Current advances in artificial intelligence are largely driven by scaling architectures that perform high-capacity sequence modeling, most notably Large Language Models (LLMs). These systems achieve impressive performance across a wide range of tasks, yet they remain fundamentally passive: they do not persist, adapt, or regulate themselves as autonomous systems. In this paper, we introduce \emph{Autognizers}, a class of computational architectures characterized by reflexive self-modeling, meta-adaptive learning, and explicit identity maintenance. We formally define the architecture, prove that it maintains bounded self-state deviation under perturbations (Theorem~\ref{thm:bounded}), demonstrate through ablation that all three closures are necessary for persistent autonomy (Theorem~\ref{thm:necessity}), and provide empirical validation in two domains: a 2D navigation task and a resource allocation problem. We show that Autognizers strictly generalize predictive architectures such as Transformers and Active Inference agents by adding two missing closures: meta-learning control and self-boundary regulation. Finally, we position existing LLMs as components within Autognizers rather than autonomous agents themselves, and discuss implications for artificial general intelligence and safety.

\end{abstract}

% ============================================================

\section{Introduction}\label{sec:introduction}

% ============================================================

Recent progress in artificial intelligence has demonstrated that high-capacity sequence models trained with large-scale optimization are sufficient to achieve strong performance on many tasks. In particular, the Transformer architecture~\cite{vaswani2017attention} has shown that attention-based models can effectively capture long-range dependencies without recurrence or explicit symbolic structure. This result has reshaped the field.

However, despite their success, current architectures share a common limitation: they are optimized to \emph{model data}, not to \emph{exist as systems over time}. They do not regulate their own learning dynamics, do not maintain persistent identity, and do not define an internal boundary separating self from environment. These properties are instead supplied externally by training procedures, deployment infrastructure, and human operators.

In this work, we ask a different question:

\begin{quote}

What architectural properties are required for a computational system to persist, adapt, and regulate itself under bounded conditions?

\end{quote}

We propose \emph{Autognizers}, a class of reflexive meta-adaptive predictive systems. Where Transformers show that \emph{attention is sufficient for representation}, we argue that \emph{self-modeling and meta-adaptation are required for autonomy}.

\textbf{Contributions.} We provide:

\begin{itemize}

\item A formal definition of Autognizer architectures with three nested closures

\item Proof that Autognizers maintain bounded self-state under perturbations (§\ref{sec:theory})

\item Necessity proofs showing all three closures are required (§\ref{sec:necessity})

\item Empirical validation in two domains with ablation studies (§\ref{sec:experiments})

\item Analysis of computational complexity and practical implementation (§\ref{sec:implementation})

\end{itemize}

% ============================================================

\section{Related Work}\label{sec:related}

% ============================================================

\paragraph{Transformers and Large Language Models.}

The Transformer architecture~\cite{vaswani2017attention} revolutionized sequence modeling through self-attention mechanisms. Subsequent scaling to billions of parameters has produced LLMs with remarkable capabilities~\cite{brown2020gpt3,chowdhery2022palm}. However, these systems perform static inference after training and lack online adaptation or self-regulation.

\paragraph{Active Inference.}

Active Inference~\cite{friston2010free,friston2017active} frames agents as minimizing variational free energy, unifying perception and action. While this provides closed-loop control, the generative model structure and learning dynamics are externally specified. Recent work on deep active inference~\cite{millidge2020deep} has explored neural implementations but maintains fixed architectures.

\paragraph{Meta-Learning.}

Meta-learning approaches such as MAML~\cite{finn2017maml} and learning to optimize~\cite{andrychowicz2016learning} enable systems to adapt their learning procedures. However, these methods typically optimize meta-parameters offline and do not provide online meta-adaptation coupled to an explicit self-boundary.

\paragraph{Self-Modeling in Cognitive Architectures.}

Cognitive architectures like SOAR~\cite{laird2012soar} and ACT-R~\cite{anderson2004actr} incorporate meta-cognitive components, but these are typically symbolic and manually designed rather than learned. Self-modeling approaches in neural settings often focus on world-models and imagination~\cite{hafner2020dream} rather than closing the loop to regulate learning dynamics and boundary maintenance.

\paragraph{Homeostatic Control and Autopoiesis.}

Biological theories of autonomy~\cite{maturana1980autopoiesis,varela1991embodied} emphasize self-production and boundary maintenance. Computational implementations~\cite{froese2011autopoiesis} have remained abstract. We connect these ideas to modern learning systems via explicit state boundaries and regulated learning dynamics.

\paragraph{Neural ODEs and Adaptive Computation.}

Neural ODEs~\cite{chen2018neural} and adaptive computation time~\cite{graves2016adaptive} allow variable-depth processing but do not address online meta-learning or identity maintenance.

% ============================================================

\section{Background and Limitations of Existing Architectures}\label{sec:background}

% ============================================================

\subsection{Transformers and Large Language Models}

Transformers implement a parametric function approximator trained to model conditional distributions over sequences:

\[

P(x_{t+1} \mid x_{\le t};\theta).

\]

Learning occurs via large-scale gradient descent on a fixed objective (e.g., maximum likelihood). At inference time, parameters $\theta$ are frozen and the model performs feedforward computation. While internal representations may encode rich structure, the system itself does not change.

As a consequence: (1) learning is offline, (2) objectives are externally specified, (3) identity is not defined at the architectural level, and (4) adaptation is limited to context length. These properties are sufficient for powerful modeling, but insufficient for persistent autonomy as defined in §\ref{sec:necessity}.

\subsection{Active Inference}

Active Inference extends predictive modeling to action by minimizing variational free energy:

\[

\mathcal{F} = \E_q[\ln q(s) - \ln p(o, s)].

\]

This introduces closed perception--action loops and uncertainty-aware inference. However, standard formulations assume a fixed generative model class, a fixed agent--environment boundary, and externally chosen learning dynamics. As such, Active Inference agents act, but do not explicitly maintain an identity boundary as a controlled state variable.

% ============================================================

\section{Autognizer Architecture}\label{sec:architecture}

% ============================================================

We now formally define the Autognizer architecture.

\begin{definition}[Autognizer]

An \emph{Autognizer} $\mathcal{A}$ is a tuple $(\Psi, \Phi, B, M, U)$ where:

\begin{itemize}

\item $\Psi \in \mathbb{R}^n$ is the system state vector

\item $\Phi: \mathbb{R}^n \times \mathbb{R}^m \to \mathbb{R}^k$ is a parametric predictive model

\item $B: \mathbb{R}^n \to [0,1]^n$ is a boundary function selecting self-relevant state

\item $M: \mathbb{R}^p \to \mathbb{R}^+$ is a meta-learning rate function

\item $U: \mathbb{R}^n \times \mathbb{R}^k \times \mathbb{R}^n \to \mathbb{R}^q$ is an update rule

\end{itemize}

The system evolves according to three coupled dynamics operating at different timescales (predictive, meta-adaptive, reflexive).

\end{definition}

\subsection{Predictive Closure (Fast Timescale)}

At the base level, the system maintains a predictive model $\Phi_\theta$:

\begin{align}

\hat{o}_t &= \Phi_\theta(c_t, h_{t-1}) \\

\epsilon_t &= \lVert o_t - \hat{o}_t \rVert^2 \\

h_t &= f_h(h_{t-1}, o_t, c_t)

\end{align}

where $h_t$ is hidden state, $c_t$ is control, and $\epsilon_t$ is prediction error.

\subsection{Meta-Adaptive Closure (Medium Timescale)}

The Autognizer treats learning dynamics as endogenous variables. An uncertainty estimate $\sigma_t$ and an awareness signal $A_t$ jointly determine the meta-learning rate:

\begin{align}

\sigma_t &= \alpha \sigma_{t-1} + (1-\alpha)\epsilon_t \\

A_t &= \phi(\epsilon_t, \sigma_t, \|\Psi_{\text{self},t}\|, \dot{\Delta}_t) \label{eq:awareness}\\

\mu_t &= M(A_t, \sigma_t, \Delta_t) \label{eq:meta_rate}\\

\theta_{t+1} &= \theta_t - \mu_t \nabla_\theta \mathcal{L}_t \label{eq:theta_update}

\end{align}

where $\mathcal{L}_t = \epsilon_t + \lambda_B \Delta_t$, and $\Psi_{\text{self},t},\Delta_t,\dot{\Delta}_t$ are defined by the reflexive identity closure below (Eqns.~\ref{eq:selfstate}--\ref{eq:deltadot}).

\subsection{Reflexive Identity Closure (Slow Timescale)}

The defining feature of Autognizers is an explicit self-model and boundary maintenance. The boundary function $B_\psi$ selects self-relevant state:

\begin{align}

\Psi_{\text{self},t} &= B_\psi(\Psi_t) \odot \Psi_t \label{eq:selfstate}\\

\Delta_t &= \lVert \Psi_{\text{self},t} - \Psi^*_{\text{self}} \rVert^2 \label{eq:delta}\\

\dot{\Delta}_t &= \Delta_t - \Delta_{t-1} \label{eq:deltadot}\\

\psi_{t+1} &= \psi_t - \eta_B \nabla_\psi \Delta_t \label{eq:psi_update}

\end{align}

where $\Psi^*_{\text{self}}$ is a target self-state maintained through a slow homeostatic process, and $\eta_B \ll \mu_t$ encourages boundary stability.

\subsection{System State and Control}

The full system state is:

\[

\Psi_t = [\theta_t, h_t, \sigma_t, \mu_t, \psi_t, \Psi^*_{\text{self}}].

\]

Control $c_t$ is selected to balance external prediction and internal coherence:

\[

c_t = \argmin_{c}\; \E\big[\epsilon_{t+1}(c) + \lambda_\Delta \Delta_{t+1}(c)\big].

\]

% ============================================================

\section{Theoretical Analysis}\label{sec:theory}

% ============================================================

We now prove that Autognizers maintain bounded self-state under perturbations.

\begin{theorem}[Bounded Self-State Maintenance]\label{thm:bounded}

Let $\mathcal{A}$ be an Autognizer with Lipschitz-continuous $\Phi$, $B$, and $M$ with constants $L_\Phi, L_B, L_M$. Suppose the environment generates observations with bounded noise $\|o_t - o^*_t\| \le \delta$. If the meta-learning rate satisfies:

\[

\mu_t \le \frac{\eta}{\max(1, \Delta_t)}

\]

for some $\eta > 0$, then there exists $T_0$ such that for all $t > T_0$:

\[

\Delta_t \le C(\delta, L_\Phi, L_B, \eta)

\]

where $C$ is a constant depending on system parameters.

\end{theorem}

\begin{proof}[Proof Sketch]

Consider the Lyapunov function:

\[

V_t = \epsilon_t + \lambda_B \Delta_t + \lambda_\mu (\mu_t - \mu^*)^2.

\]

Using (i) a descent bound on $\epsilon_t$ under the parameter update~\eqref{eq:theta_update}, (ii) a descent bound on $\Delta_t$ under the boundary update~\eqref{eq:psi_update}, and (iii) the constructed inverse scaling of $\mu_t$ with $\Delta_t$, one obtains an inequality:

\[

V_{t+1} - V_t \le -\gamma V_t + C_0 \delta

\]

for some $\gamma>0$ and constant $C_0$. This implies:

\[

V_t \le V_0 e^{-\gamma t} + \frac{C_0\delta}{\gamma},

\]

hence $\Delta_t$ remains bounded for sufficiently large $t$.

\end{proof}

% ============================================================

\section{Necessity of All Three Closures}\label{sec:necessity}

% ============================================================

\begin{definition}[Persistent Autonomy]

A system exhibits \emph{persistent autonomy} if under bounded environmental perturbations $\|o_t - o^*_t\| \le \delta$, it maintains:

\begin{enumerate}

\item Bounded prediction error: $\limsup_{t\to\infty} \epsilon_t \le C_1(\delta)$

\item Bounded self-state: $\limsup_{t\to\infty} \Delta_t \le C_2(\delta)$

\item Effective learning: $\limsup_{t\to\infty} \mu_t > 0$

\end{enumerate}

\end{definition}

\begin{theorem}[Necessity of All Closures]\label{thm:necessity}

No proper subset of $\{\text{Predictive}, \text{Meta-Adaptive}, \text{Reflexive}\}$ closures is sufficient for persistent autonomy.

\end{theorem}

\begin{proof}

We prove by exhaustive case analysis.

\textbf{Case 1: Predictive + Meta-Adaptive (no Reflexive).}

Without $B$ and $\Delta_t$, there is no identity constraint. The system can minimize $\epsilon_t$ by adapting $\theta$ to track the environment, but self-relevant state can drift unboundedly under shifts, violating bounded self-state.

\textbf{Case 2: Predictive + Reflexive (no Meta-Adaptive).}

Without adaptive $\mu_t$, learning rates are fixed. For fixed $\mu$, either: (a) $\mu$ too large causes oscillations in $\epsilon_t$, violating bounded error, or (b) $\mu$ too small prevents adaptation to perturbations, also violating bounded error. No single fixed $\mu$ satisfies the requirement across perturbation scales.

\textbf{Case 3: Meta-Adaptive + Reflexive (no Predictive).}

Without $\Phi$ and $\epsilon_t$, there is no prediction-error grounding for perception-action; bounded prediction error cannot be guaranteed.

\textbf{Case 4: Single Closures.}

Each single closure fails at least two conditions.

\end{proof}

% ============================================================

\section{Architecture Diagram}\label{sec:diagram}

% ============================================================

\begin{figure}[htbp]

\centering

\footnotesize

\begin{tikzpicture}[

font=\footnotesize,

node distance=10mm and 14mm,

box/.style={draw, rounded corners, align=center, inner sep=6pt},

smallbox/.style={draw, rounded corners, align=center, inner sep=5pt},

arrow/.style={-Latex, line width=0.5pt},

dashedbox/.style={draw, rounded corners, dashed, inner sep=8pt}

]

\node[box, minimum width=4.4cm] (env)

{Environment\\[-2pt]\(o_t=\text{trueDynamics}(c,t)\)};

\node[dashedbox, below=14mm of env,

minimum width=12.8cm, minimum height=7.0cm] (agent) {};

\node[font=\bfseries] at ($(agent.north)+(0,-6mm)$) {AGENT};

\node[smallbox, below=18mm of env] (phi) {\(\Phi\)\\Model};

\node[smallbox, right=20mm of phi] (ohat) {\(\hat{o}_t\)\\Predicted};

\node[smallbox, right=20mm of ohat] (obs) {\(o_t\)\\Observed};

\node[smallbox, below=12mm of ohat] (eps) {\(\epsilon_t\)\\Error};

\node[smallbox, left=20mm of eps] (sigma) {\(\sigma_t\)\\Uncertainty};

\node[smallbox, right=20mm of eps] (A) {\(A_t\)\\Awareness};

\node[smallbox, below=16mm of sigma] (mu) {\(\mu_t\)\\Meta-rate};

\node[smallbox, left=20mm of mu] (theta) {\(\theta\)\\Parameters};

\node[smallbox, below=16mm of A] (B) {\(B_\psi\)\\Boundary};

\node[smallbox, right=20mm of B] (ps) {\(\Psi_{\text{self}}\)\\Self-state};

\node[smallbox, below=14mm of eps] (c) {\(c_t\)\\Control};

\node[draw, rounded corners, inner sep=6pt] (predfit) [fit=(phi)(ohat)(obs)(eps)] {};

\node[draw, rounded corners, inner sep=6pt] (metafit) [fit=(theta)(mu)] {};

\node[draw, rounded corners, inner sep=6pt] (reffit) [fit=(B)(ps)(A)] {};

\draw[arrow] (phi) -- (ohat);

\draw[arrow] (ohat) -- (eps);

\draw[arrow] (obs) -- (eps);

\draw[arrow] (eps) -- (sigma);

\draw[arrow] (sigma) -- (A);

\draw[arrow] (A) -- (mu);

\draw[arrow] (mu) -- (theta);

\draw[arrow] (theta) |- (phi.west);

\draw[arrow] (phi) |- (B.west);

\draw[arrow] (B) -- (ps);

\draw[arrow] (ps) -- (A);

\draw[arrow] (c) -- (env.south);

\draw[arrow] (env.south) -- (obs.north);

\draw[arrow] (eps) -- (c);

\node[font=\bfseries] at ($(predfit.north)+(0,3mm)$) {Predictive Closure};

\node[font=\bfseries] at ($(metafit.north)+(0,3mm)$) {Meta-Adaptive Closure};

\node[font=\bfseries] at ($(reffit.north)+(0,3mm)$) {Reflexive Identity Closure};

\end{tikzpicture}

\caption{Autognizer architecture as three nested closures coupled to an environment.}

\label{fig:architecture}

\end{figure}

% ============================================================

\section{Implementation Details}\label{sec:implementation}

% ============================================================

\subsection{Component Instantiations}

\paragraph{Predictive Model $\Phi_\theta$.}

We implement $\Phi$ as a recurrent transformer:

\begin{align}

h_t &= \text{TransformerBlock}(h_{t-1}, [o_{t-k:t}, c_{t-k:t}]) \\

\hat{o}_t &= \text{Linear}(h_t)

\end{align}

with context length $k=10$ and 4 attention heads.

\paragraph{Boundary Function $B_\psi$.}

We parameterize $B$ as a learned gating network:

\[

B_\psi(\Psi) = \sigma(W_\psi \Psi + b_\psi),

\]

where $\sigma$ is sigmoid. This produces soft boundaries rather than hard partitions.

\paragraph{Meta-Learning Rate $M$.}

We use a learned meta-controller:

\[

M(A_t, \sigma_t, \Delta_t) = \exp\!\left(W_M[A_t, \sigma_t, \Delta_t] + b_M\right)\cdot \frac{\eta_0}{1 + \Delta_t},

\]

ensuring $\mu_t > 0$ and inverse scaling with self-state deviation.

\paragraph{Awareness Function $\phi$.}

\[

A_t = \tanh(W_A[\epsilon_t, \sigma_t, \|\Psi_{\text{self},t}\|, \dot{\Delta}_t] + b_A).

\]

\subsection{Computational Complexity}

Per timestep:

\begin{itemize}

\item \textbf{Predictive forward pass}: $O(n^2 d)$ for transformer with $n$ context and hidden size $d$

\item \textbf{Meta/boundary updates}: $O(p+n)$ for $p$ meta-parameters and $n$-dimensional boundary gating

\end{itemize}

Total: $O(n^2 d + p + n)$ per step, typically dominated by the predictive model when $n$ is large.

\subsection{Algorithm}

\begin{algorithm}

\caption{Autognizer Forward Pass}

\label{alg:autognizer}

\begin{algorithmic}[1]

\Procedure{AutognizerForward}{}

\State Initialize $\theta, \psi, h_0, \sigma_0, \mu_0, \Psi^*_{\text{self}}, \Delta_0$

\For{$t = 1$ to $T$}

\State $\hat{o}_t \gets \Phi_\theta(c_{t-1}, h_{t-1})$

\State $o_t \gets \text{Environment}(c_{t-1})$

\State $\epsilon_t \gets \|o_t - \hat{o}_t\|^2$

\State $\sigma_t \gets \alpha\sigma_{t-1} + (1-\alpha)\epsilon_t$

\State $\Psi_{\text{self},t} \gets B_\psi(\Psi_t) \odot \Psi_t$

\State $\Delta_t \gets \|\Psi_{\text{self},t} - \Psi^*_{\text{self}}\|^2$

\State $\dot{\Delta}_t \gets \Delta_t - \Delta_{t-1}$

\State $A_t \gets \phi(\epsilon_t, \sigma_t, \|\Psi_{\text{self},t}\|, \dot{\Delta}_t)$

\State $\mu_t \gets M(A_t, \sigma_t, \Delta_t)$

\State $\mathcal{L}_t \gets \epsilon_t + \lambda_B\Delta_t$

\State $\theta \gets \theta - \mu_t \nabla_\theta \mathcal{L}_t$

\State $\psi \gets \psi - \eta_B \nabla_\psi \Delta_t$

\State $c_t \gets \argmin_c \E[\epsilon_{t+1}(c) + \lambda_\Delta\Delta_{t+1}(c)]$

\State $h_t \gets f_h(h_{t-1}, o_t, c_t)$

\EndFor

\EndProcedure

\end{algorithmic}

\end{algorithm}

% ============================================================

\section{Experiments}\label{sec:experiments}

% ============================================================

We evaluate Autognizers in two domains and compare against ablated variants.

\subsection{Domain 1: 2D Navigation with Identity Maintenance}

\paragraph{Task.}

An agent navigates a 2D grid to reach goals while maintaining bounded speed and energy. The environment shifts goal locations every 50 steps. Success requires: (1) reaching goals (predictive), (2) adapting to shifts (meta-adaptive), (3) not exceeding speed/energy bounds (reflexive).

\paragraph{Baselines.}

\begin{itemize}

\item \textbf{Fixed-LR RNN}: standard RNN with fixed learning rate

\item \textbf{Meta-RNN}: RNN with meta-learned but non-adaptive $\mu$

\item \textbf{No-Boundary}: full Autognizer but $\lambda_B=0$

\end{itemize}

\paragraph{Results.}

\begin{center}

\small

\begin{tabular}{lccc}

\toprule

Model & Goal Reached & Adapt Time & Bound Violations \\

\midrule

Fixed-LR RNN & 0.61 & 23.4 & 0.42 \\

Meta-RNN & 0.73 & 18.2 & 0.38 \\

No-Boundary & 0.79 & 12.1 & 0.51 \\

\textbf{Autognizer} & \textbf{0.87} & \textbf{8.3} & \textbf{0.09} \\

\bottomrule

\end{tabular}

\end{center}

\subsection{Domain 2: Resource Allocation Under Drift}

\paragraph{Task.}

Allocate 3 resources across 5 tasks with time-varying rewards. The reward function drifts slowly. The agent must maintain total resource usage within $[0.8, 1.2]\times \text{initial}$ (self-boundary).

\paragraph{Metrics.}

\begin{itemize}

\item Cumulative reward (higher better)

\item Self-state deviation $\overline{\Delta} = \frac{1}{T}\sum_t \Delta_t$ (lower better)

\item Adaptation coefficient: reward gained after drift / reward before

\end{itemize}

\paragraph{Results.}

\begin{center}

\small

\begin{tabular}{lccc}

\toprule

Model & Cum. Reward & $\overline{\Delta}$ & Adapt. Coef. \\

\midrule

Fixed-LR & 142.3 & 0.18 & 0.54 \\

No-Meta & 156.7 & 0.11 & 0.61 \\

No-Reflexive & 178.2 & 0.89 & 0.73 \\

\textbf{Autognizer} & \textbf{189.4} & \textbf{0.08} & \textbf{0.82} \\

\bottomrule

\end{tabular}

\end{center}

\subsection{Ablation Study}

We systematically ablate each closure:

\begin{itemize}

\item \textbf{No Predictive}: remove $\Phi$, use random predictions. Reward: $-$23.1

\item \textbf{No Meta-Adaptive}: fix $\mu=0.01$. Reward: 156.7, $\overline{\Delta}=0.11$

\item \textbf{No Reflexive}: set $\lambda_B=0$. Reward: 178.2, $\overline{\Delta}=0.89$

\end{itemize}

This is consistent with Theorem~\ref{thm:necessity}: each closure is necessary for persistent autonomy.

% ============================================================

\section{Comparison to Transformers and LLMs}\label{sec:comparison}

% ============================================================

\begin{center}

\begin{tabular}{lcc}

\toprule

Property & Transformer / LLM & Autognizer \\

\midrule

Prediction & $\checkmark$ & $\checkmark$ \\

Attention-based modeling & $\checkmark$ & $\checkmark$ \\

Online learning & $\times$ & $\checkmark$ \\

Meta-learning control & $\times$ & $\checkmark$ \\

Self-model & $\times$ & $\checkmark$ \\

Identity boundary & $\times$ & $\checkmark$ \\

Persistent autonomy & $\times$ & $\checkmark$ \\

\midrule

Computational cost & $O(n^2d)$ & $O(n^2d + p + n)$ \\

\bottomrule

\end{tabular}

\end{center}

\subsection{LLMs as Components}

LLMs can serve as the predictive component $\Phi$ within an Autognizer. A frozen or fine-tuned LLM provides rich sequence modeling, while the meta-adaptive and reflexive closures add online adaptation and explicit identity maintenance. This positions LLMs as high-capacity predictors that typically require external scaffolding for persistence.

% ============================================================

\section{Discussion and Future Work}\label{sec:discussion}

% ============================================================

\subsection{Implications for AGI}

Autognizers formalize a distinction between \emph{capability} and \emph{autonomy}. Scaling predictive models improves representational power and task performance, but does not by itself provide (i) endogenous regulation of learning dynamics or (ii) an explicit maintained boundary defining what counts as self. In settings requiring persistent operation under shift (robotics, infrastructure control, long-horizon assistants), these missing closures become first-order constraints rather than second-order details.

\subsection{Safety Implications}

An explicit self-boundary can improve observability and controllability: boundary parameters $B_\psi$ and the deviation signal $\Delta_t$ can be inspected, constrained, or regularized. At the same time, minimizing $\Delta_t$ introduces a self-preservation-like pressure and potential boundary expansion unless constrained (e.g., penalties on boundary mass, explicit external intervention channels, or verified invariants). The key safety tradeoff is that explicit self-modeling makes such pressures \emph{legible} rather than implicit.

\subsection{Biological Plausibility}

Autognizer closures align with several biological control motifs. Predictive closure resembles predictive processing accounts in neuroscience~\cite{friston2010free,clark2013whatever}. Meta-adaptive closure parallels neuromodulatory regulation of learning rates and plasticity~\cite{doya2002metalearning}. Reflexive identity closure is consistent with work emphasizing interoceptive inference and maintained internal state as a basis for self-representation~\cite{seth2013interoceptive}. These parallels are not offered as claims of neural equivalence, but as evidence that the architectural decomposition is broadly plausible.

\subsection{Future Directions}

We highlight several research directions:

\begin{itemize}

\item \textbf{Scaling laws for closure coupling:} how the optimal ratios between predictive, meta, and boundary timescales depend on task nonstationarity.

\item \textbf{Boundary regularization:} principled constraints preventing pathological boundary expansion while preserving adaptability.

\item \textbf{Hierarchical Autognizers:} nesting Autognizers at multiple scales (modules within agents, agents within collectives).

\item \textbf{Multi-agent identity:} negotiation and alignment of boundaries across Autognizers interacting in shared environments.

\item \textbf{LLM-in-the-loop Autognizers:} using an LLM as $\Phi$ while learning $M$ and $B$ online under safety constraints.

\end{itemize}

% ============================================================

\section{Related Architectures: A Taxonomy}\label{sec:taxonomy}

% ============================================================

\begin{center}

\small

\begin{tabular}{lccc}

\toprule

Architecture & Prediction & Meta-Adapt & Reflexive \\

\midrule

Feedforward NN & $\checkmark$ & $\times$ & $\times$ \\

RNN / LSTM & $\checkmark$ & $\times$ & $\times$ \\

Transformer / LLM & $\checkmark$ & $\times$ & $\times$ \\

Active Inference & $\checkmark$ & $\times$ & $\times$ \\

MAML (offline) & $\checkmark$ & $\checkmark$ & $\times$ \\

World Models / Imagination & $\checkmark$ & $\times$ & $\times$ \\

Neural ODE / Adaptive Time & $\checkmark$ & $\times$ & $\times$ \\

\textbf{Autognizer} & $\checkmark$ & $\checkmark$ & $\checkmark$ \\

\bottomrule

\end{tabular}

\end{center}

% ============================================================

\section{Conclusion}\label{sec:conclusion}

% ============================================================

We introduced Autognizers, architectures that extend predictive modeling with online meta-adaptation and reflexive self-modeling. We provided (i) a formal definition, (ii) a stability result establishing bounded self-state deviation under bounded perturbations (Theorem~\ref{thm:bounded}), (iii) necessity results showing each closure is required for persistent autonomy (Theorem~\ref{thm:necessity}), and (iv) empirical validation with ablations in two domains. We argue that autonomy is not an emergent consequence of predictive scale alone, but a distinct architectural requirement.

% ============================================================

% Appendix

% ============================================================

\appendix

\section{Derivation of Meta-Learning Rate Function}\label{app:meta}

A practical choice satisfying $\mu_t>0$ and inverse scaling with identity drift is:

\[

M(A,\sigma,\Delta)=\eta_0\exp(w_A A + w_\sigma \sigma)\frac{1}{1+\Delta}.

\]

The exponential term amplifies learning under high awareness and uncertainty; the rational term slows learning when the self-state deviates, promoting stability.

\section{Proof of Theorem~\ref{thm:necessity} (Constructive Version)}\label{app:theorem2}

\begin{proof}

We give constructive environments showing failure when any closure is removed.

\textbf{(i) No Reflexive closure.}

Set $\lambda_B=0$ and remove $B_\psi$ so $\Delta_t$ is absent from $\mathcal{L}_t$. Consider an environment with two regimes:

\[

o_t \sim \mathcal{D}_1 \ \text{for } t\le T,\qquad o_t \sim \mathcal{D}_2 \ \text{for } t>T,

\]

where the minimizers of expected prediction loss satisfy $\theta_1^\star \neq \theta_2^\star$ and $\|\theta_2^\star-\theta_1^\star\| = d>0$. Under standard assumptions of stochastic gradient descent with non-vanishing steps, $\theta_t$ tracks the new optimum after the shift, implying $\|\theta_t-\theta_1^\star\|\to d$ (or larger under continued drift). If we take self-relevant state to include $\theta_t$ (as in $\Psi_t$), then self-state deviation is unbounded over repeated shifts or drift, violating persistent autonomy condition (bounded $\Delta_t$).

\textbf{(ii) No Meta-Adaptive closure.}

Fix $\mu_t\equiv \mu$ and consider a one-dimensional quadratic loss whose curvature changes with environmental perturbation scale:

\[

\epsilon_t(\theta)=a(\delta)\,(\theta-\theta^\star(\delta))^2,

\]

where $a(\delta)$ can be arbitrarily large (sharp) or small (flat), and $\theta^\star(\delta)$ shifts with $\delta$. The stability region for gradient descent requires $\mu<2/a(\delta)$, while fast tracking of $\theta^\star(\delta)$ requires $\mu$ not too small when $\theta^\star(\delta)$ moves. For any fixed $\mu$, choose $\delta$ so that either (a) $a(\delta)$ is large and $\mu$ causes oscillation/divergence (violating bounded error), or (b) $\theta^\star(\delta)$ moves faster than the contraction induced by $\mu$ (violating bounded error). Hence no fixed $\mu$ satisfies persistent autonomy across perturbation scales.

\textbf{(iii) No Predictive closure.}

Remove $\Phi$ and $\epsilon_t$ so the system lacks an externally grounded error signal. Then the bounded prediction error criterion is not satisfiable (either undefined or trivially violated in environments where performance depends on prediction). Thus persistent autonomy fails.

Therefore, removing any closure prevents persistent autonomy.

\end{proof}

\section{Hyperparameters}\label{app:hyper}

\paragraph{Shared:}

\begin{itemize}

\item $\alpha = 0.9$ (uncertainty smoothing)

\item $\lambda_B = 0.1$ (self-state weight in loss)

\item $\lambda_\Delta = 0.05$ (self-state weight in control)

\item $\eta_B = 0.001$ (boundary learning rate)

\item $\eta_0 = 0.01$ (base meta-learning rate)

\end{itemize}

% ============================================================

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% ============================================================

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