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REVIEW 4 major objections 5 minor 97 references

Quantum-Cognitive Neural Networks: Assessing Confidence and Uncertainty with Human Decision-Making Simulations

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A quantum-tunnelling activation function yields a neural network that classifies images with human-like confidence and trains up to 50 times faster than a classical network.

desk verdict There is a real empirical kernel (QT-NN weights barely move during training) buried under unsupported headline claims about human-like decision-making and 50x faster training. read the letter →

arxiv 2412.08010 v1 pith:OM6QV5RK submitted 2024-12-11 cs.LG physics.soc-phquant-ph

Milan Maksimovic , Ivan S. Maksymov This is my paper · ORCID
classification cs.LGphysics.soc-phquant-ph
keywords quantumtunnellingneuralnetworkscognitiontheoryuncertaintyquantificationShannonentropyimageclassificationFashionMNISThumandecision-makingsimulationconfidenceestimation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that replacing a classical neural network's activation function with the quantum-tunnelling transmission coefficient yields a network that classifies images with human-like confidence and uncertainty. On the Fashion MNIST dataset, the quantum-tunnelling neural network (QT-NN) produces higher Shannon entropy for visually ambiguous categories such as T-shirt versus dress, where a human observer would hesitate, while a classical network is overconfident. The authors also report that the QT-NN trains up to 50 times faster than an otherwise identical classical network, because its probabilistic tunnelling activation barely moves the randomly initialised weights during training. If correct, this points to a cheaper way to build uncertainty-aware classifiers that signal doubt instead of failing silently.

What carries the argument

The central object is the quantum-tunnelling neural network (QT-NN), whose hidden-layer activation function $\phi_{QT}$ is the algebraic transmission coefficient $T$ of an electron penetrating a potential barrier, i.e., the solution of the Schrödinger equation for a particle incident on a barrier. This probabilistic activation, combined with white-noise weight initialisation, lets the network keep its weights spread across the full range of possible values instead of converging to fixed points, which the authors identify as the source of both faster training and human-like uncertainty. The analysis tools are Shannon entropy $H(p) = -\sum_i p(x_i)\log p(x_i)$ for measuring output uncertainty and the Jensen–Shannon divergence for comparing initial versus trained weight distributions. The barrier thickness acts as a hyperparameter that can be adjusted to control the model's confidence level.

What would settle it

Present human participants with the same Fashion MNIST images and record their category choices and confidence; if human uncertainty patterns (e.g., confusion between T-shirt and dress) do not match the QT-NN's softmax entropy ordering across categories, the human-likeness claim is falsified. Alternatively, test whether a classical network with a stochastic activation of similar shape reproduces the same entropy and speedup; if it does, tunnelling is not the active ingredient.

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Extended reading notes

Core claim

The paper's central claim is that a neural network whose hidden-layer activation is the transmission coefficient of an electron tunnelling through a potential barrier, computed from the Schrödinger equation, reproduces key features of human perception and judgment in image classification. On Fashion MNIST, the QT-NN and a classical MLP with identical architecture achieve broadly similar accuracies, but their output entropies differ: the QT-NN is markedly less certain on categories that look alike (T-shirt versus dress, shirt versus coat), which the authors take as evidence of ambiguity handling akin to human cognition. The supporting quantitative finding is that training barely changes the QT-NN's input-to-hidden weights (Jensen–Shannon divergence of $2.4\times10^{-7}$ from the initial random distribution), whereas the classical weights narrow into a tighter Gaussian; from this the authors conclude the QT-NN can be trained up to 50 times faster than the classical model.

Load-bearing premise

The claim that the network's behaviour mimics human cognition rests on the assumption that quantum tunnelling, as described by the Schrödinger equation, is a valid model of human perception and decision-making; the paper never measures human judgements, so this mapping is assumed rather than tested.

Editorial extensions

If this is right

  • If the central claim holds, the QT-NN offers a drop-in replacement for the activation layer of a feedforward network that yields uncertainty-aware classifications without Bayesian inference or ensembles.
  • A network that barely moves its initial weights challenges the standard assumption that extensive weight updates are necessary for learning, implying that task-relevant structure can be exploited through stochastic activations alone.
  • The reported 50-fold training speedup would make quantum-cognition-inspired models practical for resource-constrained or real-time classification settings.
  • The entropy patterns on ambiguous Fashion MNIST categories suggest that QT-NN softmax outputs could be used directly as a confidence signal to trigger human review in safety-critical systems.
  • The framework extends naturally to hybrid quantum-Bayesian architectures, which the authors propose as a route to combine uncertainty quantification with fast tunnelling-based feature extraction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the human-likeness claim would present human participants with the same Fashion MNIST images and compare their category confusions and confidence ratings to the QT-NN's softmax entropy; the paper reports no such behavioural data, so this test is still open.
  • The 50x speedup is stated relative to a fixed training schedule (32 batches, 100 epochs each); a fairer comparison would train both models to convergence or to a target accuracy, which could change the magnitude of the advantage.
  • If the tunnelling activation is the active ingredient, a classical stochastic activation with a similarly shaped saturating curve should reproduce the entropy and speedup; if it does, the quantum-cognitive interpretation would not be needed to explain the results.
  • The barrier-thickness hyperparameter suggests a tunable confidence mechanism: varying it across a test set could reveal a calibration curve connecting the physics parameter to human agreement rates.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a quantum-tunnelling neural network (QT-NN) whose hidden-layer activation is derived from the Schrödinger transmission coefficient, and applies it to Fashion MNIST classification. It compares the QT-NN's output distributions and trained weight distributions with those of a classical multi-layer perceptron using Shannon entropy and Jensen–Shannon divergence, and claims that the QT-NN's output patterns replicate human-like decision-making and that it can be trained up to 50 times faster. The discussion connects the model to quantum cognition theory through a qualitative wave-packet tunnelling simulation and proposes future hybrid quantum-Bayesian architectures.

Significance. If the human-likeness and training-efficiency claims were established, this would be a notable contribution: a qubit-free quantum-inspired neural network with uncertainty-aware outputs and a claimed practical training speed advantage. The paper's use of Shannon entropy and Jensen–Shannon divergence as quantitative descriptors, and its choice of Fashion MNIST as a benchmark, are sensible and align with current interests in uncertainty quantification. However, the headline claims are not supported by the evidence presented: no human behavioural data are used, the 50-times-faster assertion is made without timing measurements, and the connection between Schrödinger tunnelling and human cognition is assumed from prior theory rather than tested. As it stands, the paper is a qualitative exposition with suggestive figures rather than a validated demonstration of human-like decision-making.

major comments (4)
  1. [Abstract; Section 3.1; Figure 4] The central claim that the QT-NN 'replicat[es] human-like decision-making' (Abstract) is not tested against any human data. Section 3.1 interprets category-level confusion and Shannon-entropy values as evidence of human-likeness, but there are no human participants, no human judgement dataset, and no behavioural comparison; the Institutional Review Board Statement 'Not applicable' and the Data Availability Statement 'no additional data' are consistent with this absence. Higher output entropy is not uniquely human-like: Figure 4 shows that for 'Coat' and 'Sandal' the classical model has higher SE than the QT-NN, so the argument that greater QT-NN uncertainty mimics human ambiguity is selective. A falsifiable test would be to compare the models' output distributions with human perceptual judgements on the same Fashion MNIST images or on stimuli with known ambiguity labels.
  2. [Section 3.2] The claim that 'the QT-NN can be trained up to 50 times faster than the classical model' is unsupported. No wall-clock training time, number of epochs to a target accuracy, or any other timing or convergence criterion is reported. The only quantitative evidence offered is JSD = 2.4e-7 between the initial and trained W1 weight distributions for the QT-NN, which shows that the weight distribution barely changes; this does not entail faster training. A direct speed comparison would require identical hardware, implementation, and stopping rules, together with measured epochs or seconds to a specified accuracy.
  3. [Section 2.1; Section 2.2] The manuscript does not give the algebraic form of the QT activation function \phi_QT, instead referring to Ref. [12] for the final ML-adopted forms. Since this activation is the defining ingredient of the model and the paper claims to assess its behaviour, the relevant expressions and the values of all free parameters (barrier thickness and height, learning rate, batch size, hidden-layer size, training schedule) should be specified. Without these, the experiments are not reproducible and the sensitivity of the conclusions to barrier geometry cannot be assessed.
  4. [Section 4.1; Figures 6-7] The wave-packet simulation in Figure 7 and the 'ball climbing a wall' analogy are not quantitatively linked to the classification results. The text asserts that the barrier thickness controls model confidence and that the QT-NN is 'inherently more adept at managing ambiguity', but no experiment varies the barrier or compares predicted ambiguity with human perception. The physical model is therefore illustrative rather than evidential for the human-likeness claim.
minor comments (5)
  1. [Section 2.1] The sentence 'Such a configuration has been shown to effectively predict MNIST images with an accuracy of less than 2% [66]' is self-contradictory; 'error rate of less than 2%' is presumably intended.
  2. [Section 2.1] There is a typo in 'Relevant information can be found in the the prior publications [12,53].'
  3. [Figure 3] The panels do not appear to have axis labels in the text description; the caption should clarify what the bar heights represent (e.g., mean softmax probability over the 50 test images) and how many independent training runs were averaged.
  4. [Section 3.1] The training protocol is described as '32 batches of training image sets, with 100 training epochs for each batch', but the batch size and whether this constitutes multiple passes over the full training set are not stated; please clarify.
  5. [References] Several references contain typos: Ref. [47] spells 'Neural Networks' as 'Neural Newt.', Ref. [72] spells 'Springer' as 'Spriger', and Ref. [9] should be checked for its volume and article-number formatting.

Circularity Check

2 steps flagged · score 6.0 of 10

Human-likeness conclusion rests on a self-citation chain and on defining human cognition as stochasticity, both of which the QT-NN satisfies by construction.

  1. self definitional [Section 1.1, paragraphs 'However, the QT-NN model is uniquely different…' and 'At the same time, akin to BNNs…']
    "Unlike classical models, which often rely on deterministic frameworks [57], QCT postulates that human behaviour and perception of the world are inherently probabilistic [56]. … At the same time, akin to BNNs [29,50], the QT-NN is a stochastic model that captures uncertainty through the probabilistic nature of its activation functions [12] as well as via the injection of white noise and its application for the initialisation of connection weights [53]."

    The claimed match to human perception is obtained by defining the relevant property of humans as 'inherently probabilistic' and then noting that the QT-NN is, by construction, a stochastic model (probabilistic activation plus injected noise). The paper then reads the resulting output entropy as human-like confidence. This makes the conclusion follow from the model's definition rather than from any measured correspondence to actual human judgments; no human subject or behavioural dataset is used anywhere in the paper.

  2. self citation load bearing [Section 1.1, paragraph 'The QT-NN model is based on the mathematical solution of the Schrödinger equation…']
    "Importantly, the effect of QT has been naturally integrated into the fundamental framework of QCT [53,60], facilitating neural network models capable of capturing the intricate features of human behaviour."

    Ref [53] is the present first author's prior paper (Maksymov, Algorithms 2024), which already assumed the quantum-tunnelling-to-cognition mapping; ref [92], later cited as showing the same numerical setup 'accurately model[s] problems related to human cognition,' is also first-authored by the present author. The paper's central claim that the QT-NN 'provides compelling evidence of its potential to replicate human-like decision-making' is therefore justified by the same author's earlier assertions rather than by an external, independently verified test.

full rationale

Most of the paper's directly measurable ML content—Fashion MNIST classification accuracies, Shannon entropies, JSD values, and weight-spectrum analyses—is self-contained and could in principle be reproduced from the described training setup, so those parts are not circular. The circularity lies in the interpretive layer. The QT-NN is built from a quantum-tunnelling activation imported from the first author's earlier paper [12], and the human-cognition link is asserted by citing the same author's prior work [12,53,92] and by defining the relevant aspect of human perception as 'inherently probabilistic'—a property the QT-NN possesses by construction. Under that definition, observing probabilistic outputs and calling them human-like is a restatement of the assumption, not a prediction validated against human data. The paper's own statements (Institutional Review Board Statement: 'Not applicable'; Data Availability: 'This article has no additional data') confirm that no human experiment provides external anchoring. The 'up to 50 times faster' claim is unsupported by timing or epoch-to-target measurements, but it is an empirical assertion rather than a fitted parameter renamed as a prediction, so it does not by itself count as circularity. Because the classification and weight-distribution results have independent content and are not derived from the target human-likeness claim, the score is 6 rather than 8 or 10.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on a quantum-cognition mapping that is assumed from prior literature (mostly by the same first author) rather than tested. The training comparison also depends on several hand-picked hyperparameters that are not fully reported.

free parameters (4)
  • Barrier thickness = not specified
    Described as a hyperparameter controlling model confidence (Section 4.1). It directly affects the QT-NN's output and therefore the 'human-like uncertainty' claim.
  • Hidden layer size N = 800
    Architecture choice stated in Section 2.1. The central results depend on this capacity.
  • Training schedule = 32 batches x 100 epochs
    Called 'an optimal training strategy we identified' in Section 3.1. Hand-picked; the 50x faster claim depends on how many epochs the classical model is given.
  • Learning rate alpha = not reported
    Appears in the weight update rule (Section 2.1) but its value is never given, so the comparison between models is not fully specified.
assumptions (4)
  • domain assumption Quantum cognition theory: human perception and decision-making are inherently probabilistic and can be modelled by quantum mechanics.
    Invoked in Section 1.1 with refs [1,54-56]. This is the bridge that turns QT-NN outputs into 'human-like' evidence.
  • domain assumption The tunnelling transmission coefficient expressions from ref [12] are correct and valid as a neural activation function.
    Section 2.1 states these are 'well-established' and defers to [12]. The results depend entirely on this mapping.
  • domain assumption A single-layer MLP with ReLU is a representative 'traditional ML algorithm' baseline.
    Section 2.1 introduces the generic algorithm as a reference framework. The outperform claim is relative to this one baseline.
  • ad hoc to paper Wave-packet dynamics are equivalent to connection-weight behaviour in the trained network.
    Section 4.1 asserts that probability densities computed in Figure 7 'correspond to the connection weights'. No formal equivalence is derived.

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Cite this review

Pith. "Pith review of Quantum-Cognitive Neural Networks: Assessing Confidence and Uncertainty with Human Decision-Making Simulations." pith.science (2026). https://pith.science/paper/OM6QV5RK

@misc{pith2026241208010,
  author       = {Pith},
  title        = {Pith review of: Quantum-Cognitive Neural Networks: Assessing Confidence and Uncertainty with Human Decision-Making Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OM6QV5RK}},
  note         = {Machine review of arXiv:2412.08010}
}
read the original abstract

Modern machine learning (ML) systems excel in recognising and classifying images with remarkable accuracy. However, like many computer software systems, they can fail by generating confusing or erroneous outputs or by deferring to human operators to interpret the results and make final decisions. In this paper, we employ the recently proposed quantum-tunnelling neural networks (QT-NNs), inspired by human brain processes, alongside quantum cognition theory, to classify image datasets while emulating human perception and judgment. Our findings suggest that the QT-NN model provides compelling evidence of its potential to replicate human-like decision-making and outperform traditional ML algorithms.

Figures

Figures reproduced from arXiv: 2412.08010 by the authors.

Figure 1
Figure 1. Uncertainty in detecting fresh produce items at a supermarket self-checkout equipped with a machine vision system. Left: The system analysed a transparent plastic bag containing truss tomatoes and identified two possible categories: truss tomato and gourmet tomato, leaving the final selection to the customer. Right: In another test with a bag of Amorette mandarins, the system suggested three potential options: Delit… view at source ↗
Figure 2
Figure 2. Schematic representation of the QT-NN architecture. The inset illustrates the effect of quantum tunnelling that is employed as an activation function of the network. that is crucial for capturing complex patterns in classical systems [13], are not directly implementable in quantum circuits [43]. However, a number of strategies have been devised to simulate nonlinear processes through measurement and interference pro… view at source ↗
Figure 3
Figure 3. Outputs generated by the QT-NN (red) and the classical neural network model (blue). The insets show the representative testing images for each classification category [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: JSD and SE figures-of-merit for the QT-NN and the classical model for each item category. Note that the classical SE is zero (to machine accuracy) for the ‘Ankle Boot’ category. like ‘Coat’ and ‘Sandal’ yield higher SE values for the classical model, suggesting that th…
Figure 5
Figure 5. Figure 5: (a, b) Distributions of weights between the input layer and the hidden layer (denoted as W1 in the main text), plotted as a function of training iterations for the QT-NN model and the classical model (labelled as ’Class.’), respectively. (c, d) Results of the JSD cross…
Figure 6
Figure 6. Figure 6: Schematic illustration of the training process of (a) the classical model and (b) the QT-NN model, inspired by the discussion in Ref. [79]. The coloured lines illustrate the possible pathways of neural connection formation. Note that the additional hidden layers of neu…
Figure 7
Figure 7. Figure 7: (a–d) Instantaneous snapshots of an energy wave packet modelling the tunnelling of an electron through a potential barrier (depicted by a white rectangle). The false-colour scale of the images encodes the computed probability density values. Within the framework of the…

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.