Extreme Quantum Cognition Machines for Deliberative Decision Making

TL;DR

Hardware-compatible quantum implementations of the proposed framework are discussed, together with potential applications in symbolic inference, sequence analysis, anomaly detection, and automatic diagnosis, with direct relevance to domains such as biology, forensics, and cybersecurity.

Abstract

We introduce Extreme Quantum Cognition Machines, a class of quantum learning architectures for deliberative decision making that is tolerant to noisy and contradictory training data. Inspired by the quantum cognition paradigm, Extreme Quantum Cognition Machines are closely related to quantum extreme learning and quantum reservoir computing, where fixed quantum dynamics generates a nonlinear feature map and learning is confined to a linear readout. A dynamical attention mechanism, implemented through an input-dependent interaction term in the Hamiltonian, modulates the quantum evolution and biases the resulting feature embedding toward task-relevant correlations. The approach is validated on linguistic classification tasks, which serve as paradigmatic examples of deliberative inference. Hardware-compatible quantum implementations of the proposed framework are discussed, together with potential applications in symbolic inference, sequence analysis, anomaly detection, and automatic diagnosis, with direct relevance to domains such as biology, forensics, and cybersecurity.

Figures (4)

• Figure 1: Schematic representation of the Extreme Quantum Cognition Machine. Classical inputs $\boldsymbol{z}=(z_1,\dots,z_m)^{T}$, obtained after preprocessing of raw data, are mapped into a maximum-entropy density matrix $\rho_0(\boldsymbol{z})$, representing the initial mental state compatible with prescribed local expectation values. The state evolves unitarily under the Hamiltonian $H=H_0 + H_I(\boldsymbol{z})$, where $H_0$ models unguided (free-thinking) dynamics and $H_I$ encodes input-dependent dynamical attention, yielding $\rho(\boldsymbol{z};\tau)$. Expectation values of a fixed family of observables $\{Q_k\}_{k=1}^{M}$ define mental category features $f_k(\boldsymbol{z})=\mathrm{Tr}[Q_k \rho(\boldsymbol{z};\tau)]$. The final output (deliberative index) is obtained as a linear combination $y=\sum_k w_k f_k(\boldsymbol{z})$, where the weights $w_k$ are learned via ridge regression, while the quantum dynamical feature map remains fixed.
• Figure 2: Performance of the EQCM architecture on Task 1 (Italian vs random strings) with and without dynamical attention. Panels (a)–(c) correspond to the setting $\sigma = 0.1$, $\tau = 10$, $\lambda = 2\times 10^{-3}$, $g_1 = 0.1$, $g_2 = 0.4$, where $\sigma$ is the variance of the real-valued GOE Hamiltonian $H_0$ (zero mean), $\tau$ the dimensionless evolution time, and $g_{1,2}$ the coupling strengths controlling the interaction Hamiltonian $H_I$. In this regime dynamical attention is active. Panel (a) shows the learned weights $w_k$: only categories involving single-qubit observables and nearest-neighbour two-qubit correlators acquire significant amplitudes, indicating that attention effectively restricts learning to local two-letter structures. Panels (b) and (c) display the distribution of the continuous deliberative index $y$ for the training and test sets, respectively, with the corresponding confusion matrices shown as insets. For the training set, accuracy and balanced accuracy are both $0.9567$; for the test set, accuracy and balanced accuracy are $0.9625$, confirming excellent generalization. Panels (d)–(f) are obtained with identical hyperparameters but with $g_1 = g_2 = 0$, i.e. with attention switched off. In this case (d) shows that weights are distributed over a broader set of internal categories, including higher-order correlators. The corresponding histograms (e) and (f) reveal a moderate degradation of performance (training accuracy $0.9367$, test accuracy $0.9000$), indicating that dynamical attention enhances selectivity and improves generalization by biasing the dynamics toward task-relevant local structures.
• Figure 3: Performance of the EQCM architecture on Task 2 (Italian vs English words) with dynamical attention active and identical hyperparameters as in Fig. \ref{['fig2']} ($\sigma = 0.1$, $\tau = 10$, $\lambda = 2\times10^{-3}$, $g_1 = 0.1$, $g_2 = 0.4$). Panels (a)–(c) correspond to the consonant–vowel encoding already employed in Task 1. Panel (a) shows the learned weights $w_k$, which concentrate on a restricted subset of internal categories. The corresponding training-set performance, shown in panel (b), yields $\mathrm{Accuracy} = 0.9600$ and $\mathrm{BA} = 0.9600$, with $\mathrm{Precision}_{\mathrm{IT}} = 0.9259$ and $\mathrm{Precision}_{\mathrm{ENG}} = 1.000$. On the test set (panel (c)), the model achieves $\mathrm{Accuracy} = 0.9625$ and $\mathrm{BA} = 0.9625$, confirming stable generalization across languages. Panels (d)–(f) report the results obtained using a two-bucket maximum-entropy encoding. In this case, the buckets are constructed in a label-aware fashion by estimating letter frequencies from the Italian portion of the training set and partitioning the alphabet accordingly. Panel (d) displays the corresponding learned weights, while panels (e) and (f) show the training and test performance, respectively. The training set yields $\mathrm{Accuracy} = 0.9533$ and $\mathrm{BA} = 0.9533$, with $\mathrm{Precision}_{\mathrm{IT}} = 0.9308$ and $\mathrm{Precision}_{\mathrm{ENG}} = 0.9789$. On the test set, the performance decreases to $\mathrm{Accuracy} = 0.8250$ and $\mathrm{BA} = 0.8250$, reflecting increased overlap between the class-conditional distributions of the deliberative index $y$. These results indicate that while both encodings allow the architecture to discriminate between Italian and English words with high training accuracy, the consonant–vowel partition provides superior robustness and generalization for this task. The label-aware maximum-entropy buckets, being constructed from empirical letter frequencies estimated on a finite Italian training subset of 150 words, inevitably reflect a sample-dependent approximation of the true dictionary-level statistics. As a consequence, the resulting frequent-symbol bucket may encode a slightly distorted version of the underlying Italian distribution, which reduces its transferability when confronted with a competing structured language such as English.
• Figure 4: Hardware-compatible implementation of the deliberative architecture for Task 2, consisting in the classification of seven-letter Italian and English words using the consonant--vowel encoding. For all the panels we used the following set of parameters: $J=-1$, $B_x=0.7$, $B_z=1.5$, $\tau=20$ and $\lambda=2 \cdot 10^{-3}$. First row (a-c): performance with attention active, $g_1 = g_2 = 2$. Second row (d-f): performance with attention switched off, $g_1 = g_2 = 0$. Panels (a,d) report the learned readout weights $w_k$ for the two configurations, showing comparable sparsity patterns and magnitude distributions, consistent with an analogous linear recombination of quantum features in both regimes. Panels (b,e) display the distributions of the deliberative index $y$ for the training set together with the corresponding confusion matrices. With attention active (b), the model achieves $\mathrm{TP}=150$, $\mathrm{TN}=136$, $\mathrm{FP}=14$, $\mathrm{FN}=0$, corresponding to an accuracy of $95.3\%$, precision of $91.5\%$, recall (sensitivity) of $100\%$, and specificity of $90.7\%$. In the absence of attention (e), we obtain $\mathrm{TP}=150$, $\mathrm{TN}=138$, $\mathrm{FP}=12$, $\mathrm{FN}=0$, yielding an accuracy of $96.0\%$, precision of $92.6\%$, recall of $100\%$, and specificity of $92.0\%$. Panels (c,f) show the corresponding test-set results. With attention active (c), the confusion matrix gives $\mathrm{TP}=40$, $\mathrm{TN}=38$, $\mathrm{FP}=2$, $\mathrm{FN}=0$, corresponding to an accuracy of $97.5\%$, precision of $95.2\%$, recall of $100\%$, and specificity of $95.0\%$. With attention switched off (f), we find $\mathrm{TP}=39$, $\mathrm{TN}=38$, $\mathrm{FP}=2$, $\mathrm{FN}=1$, corresponding to an accuracy of $96.3\%$, precision of $95.1\%$, recall of $97.5\%$, and specificity of $95.0\%$. Overall, the two configurations exhibit statistically indistinguishable performance on both training and test sets, indicating that, within this hardware-compatible implementation, the inclusion of the dynamical attention term does not produce a measurable advantage in terms of classification accuracy, precision, recall, or specificity.