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WisdomNet: trustable machine learning toward error-free classification

Truong X. Tran, Ramazan S. Aygun

arXiv:2610.15299v1cs.LGcs.AI

TL;DR

Misclassification can persist even in high-accuracy models, making their outputs difficult to rely on in consequential applications. The paper proposes WisdomNet, which uses a conjugate neuron to identify doubtful cases; across tested neural networks and data sets, it reports 0% error with reject rates under 10%.

  • Problem

    Even high-accuracy classifiers can make costly errors, and studying observed errors may miss correct predictions that are only ‘lucky’.

    Source: §1 · p. 1, §3 · p. 5

  • Method

    WisdomNet adds a conjugate neuron to a trained neural network and retrains using cases the base network misclassified, allowing doubtful cases to be rejected.

    Source: §6 · p. 14

  • Results

    0% error with reject rates under 10% was reported across tested data sets and multilayer perceptron, convolutional, and deep neural networks.

    Source: §6 · p. 14

  • Takeaways & Limitations

    WisdomNet can avoid critical misclassifications while giving experts an opportunity to study and analyze special cases.

    Source: §6 · p. 14

    The authors caution that they cannot claim all misclassifications can be detected for every problem, and reject rates may be high or missed cases may go undetected.

    Source: §6 · p. 15

Abstract

from arXiv · show

Misclassification is a critical problem in many machine learning applications. Since even the classifier models with high accuracy (e.g., > 95%) still introduce some misclassification error, it may not be possible to rely on the output of a classifier. In this paper, we introduce trustable learning, which prompts the learning model to yield only the true output, thus avoiding misclassifications. Whenever the model cannot decide the output accurately, the learning model should indicate that there could be a misclassification error if it is forced to classify, and hence, it should reject to make a decision or defer it to a human expert. Therefore, we develop a methodology for trustable learning and apply it to artificial neural networks and show that it is possible to develop a classifier with 0% misclassification error. We propose a novel neural network architecture named WisdomNet that could provide zero prediction error by introducing an additional neuron named as conjugate neuron that would indicate whether the network is able to classify the data correctly or not. The WisdomNet architecture can be applied to any previously built model, and we have evaluated WisdomNet with several network architectures such as multilayer perceptron, convolutional neural network, and deep network on different data sets. The results show that the WisdomNet is able to reduce the classification error rate to 0%, while labeling the data is difficult to classify as `reject' at a low percentage of within around 10%.

1 Introduction

In high-stakes settings, high accuracy and misclassification-cost adjustments may still leave errors, while manually reviewing every prediction undermines computer-assisted classification. The paper introduces WisdomNet, which adds a conjugate neuron to identify doubtful cases and reports reducing classification error to 0% while rejecting around 10%.

1 Introduction

  • High accuracy and misclassification-cost adjustments may still leave errors, while manually scanning predictions undermines computer-assisted learning.The paper frames these errors as especially consequential in applications such as medical diagnosis, disaster prediction, and fraud detection.Source: §1 · pp. 1–2
  • The approach aims to detect cases the model cannot classify properly without creating and labeling an additional difficult-data class.The introduction gives confusing handwriting examples such as ‘B’ and ‘8’.Source: §1 · p. 2
  • The proposed architecture uses a conjugate neuron to indicate whether the network can classify data correctly.Source: §1 · p. 2
  • WisdomNet is built from a trained neural network, adds a conjugate neuron for doubtful data, and trains on items the base network misclassified.It retains the base network’s weights and biases while initializing the conjugate neuron’s relevant parameters to zero.Source: §1 · p. 2
  • 0% classification error with around 10% of data labeled ‘reject’ is the reported WisdomNet result.The evaluation spans multilayer perceptron, convolutional, and deep networks on different data sets.Source: §1 · p. 2
  • The listed contributions include evaluating factors that affect WisdomNet performance across learning architectures.The contributions also include applying WisdomNet to multilayer perceptron and deep-learning architectures while keeping reject around 10%.Source: §1 · p. 2

2 Related work

The related work places trustable learning alongside approaches to accuracy, rejection, interpretability, and data quality, while distinguishing its aim of identifying predictions the model cannot reliably make. It also contrasts the proposed approach with multiclass labeling, transfer learning, and reinforcement learning.

2 Related work

  • Prior rejection approaches include doubt regions, competing hypotheses, probability thresholds, and overlapping decision regions; the paper emphasizes reducing errors while limiting rejection.The cited discussion frames rejection as a trade-off between rejected cases and misclassifications.Source: §2 · p. 3
  • Other accounts of trustworthy learning emphasize properties including robustness, interpretability, fairness, accountability, and system transparency.The passage summarizes criteria from Sheshia et al., Kaul, Varshney, and a special issue.Source: §2 · p. 3
  • Interpretability and user feedback have been studied as ways to support trust, but increased user trust does not itself make a model correct.Examples include explanations for predictions, interactive learning, and visualizing training-data influence.Source: §2 · p. 3
  • Related work also addresses problematic training data and robustness to attacks, while expert feedback has been used to review partially tagged polyp detections.The passage describes approaches using verified examples, collaborative trusted instances [11], adversarial robustness, and attribution regularization [5]; Wang et al. report partially tagged polyps for expert review.Source: §2 · pp. 3–4
  • The paper distinguishes its method from adding an ‘unknown’ training class, transfer learning across domains, and reinforcement learning by trial and error.It also notes that multiclass training can suffer imbalance when misclassified samples are few.Source: §2 · p. 4
  • Prior zero-error work described in the section includes else-tree, which routes difficult samples to a virtual ‘undecided’ class on some data sets.Source: §2 · p. 4
  • The paper connects trust to detecting both incorrect and potentially lucky predictions, rather than relying only on observed errors or interpretability.It conjectures that some correct predictions by accurate models may be ‘lucky’ and seeks to determine what a model cannot learn.Source: §2 · p. 4

3 Trustable Learning

Trustable learning lets a model reject or defer cases it may misclassify; WisdomNet adds a conjugate neuron to flag such cases. The paper presents a motivating test example and theoretical claims about initialization and training.

3 Trustable Learning

  • Trustable learning labels cases likely to be misclassified as “reject,” allowing a model to defer a decision rather than force a classification.The paper notes that expert review can be costly, so the number of rejections should be kept minimal.Source: §3 · pp. 4–5

3.1 WisdomNet

  • WisdomNet adds a conjugate neuron to a trained base network and fine-trains it on misclassified training samples relabeled as reject.The authors caution that rejecting only those misclassified samples could overfit; the network may also identify lucky correct predictions that could fail in real scenarios.Source: §3 · p. 5, §3.1 · p. 6

3.2 Motivating Sample Scenario

  • 0 misclassifications with about 5% rejected samples on the motivating test set, compared with the base network’s about 98% accuracy.The WisdomNet rejection rate was slightly above the base network’s 2% test misclassification rate.Source: §3.2 · p. 7, Figure 2 · p. 7

3.3 Justification

  • At initialization, WisdomNet is equivalent to the base network because it preserves inherited parameters and keeps the conjugate neuron inactive.The paper states that this equivalence holds for every input in the domain.Source: §3.3 · p. 8
  • Zero training error on reject samples is claimed at differentiable local minima when |Sr| < nL−1nL−2; the stated test-set argument assumes training and test data share a distribution.Fine-training updates all parameters, so some previously correct samples may become rejects; the authors describe this as a way to identify lucky predictions.Source: §3.3 · pp. 8–9

4 Experiments and Results

Experiments evaluate WisdomNet across MLP, convolutional, and deep networks on varied datasets, then examine factors affecting rejection. In the reported tests, WisdomNet reaches zero classification error by rejecting some samples, with reject rates varying across settings.

4.1 Evaluation Measures

  • Evaluation counts rejects separately: N = TP + TN + FP + FN + R, and the WisdomNet confusion matrix includes a reject column.The paper also uses total error rate and reject rate as evaluation measures.Source: §4.1 · p. 9, Figure 3 · p. 9
  • 0% classification error across BN, IO, and BC, versus base MLP errors around 1%–3.71%; reject rates were around 1.5% (BN), 13.58% (IO), and 10.05% (BC).The WisdomNet results are reported in Table 3.Source: §4.2 · p. 10, Table 3 · p. 10

4.3 WisdomNet on Convolutional Neural Networks

  • On MNIST 4-9, WisdomNet reduced classification error to 0% with about 4.2% rejects; the base ConvNet had around 99.4% accuracy and about 0.6% classification error.The confusion matrices compare ConvNet and WisdomNet; WisdomNet rejected 84 digits, with zero false positives and false negatives.Source: §4.3 · p. 10, Figure 5 · p. 10
  • The dogs-cats ResNet50 experiment used 4,000 training and 400 validation images; fine-tuning updated the last residual block and classifier layers.The transfer-learning comparison extracted bottleneck features and trained a new top classifier.Source: §4.4 · p. 11
  • 0% misclassification error on dogs-cats validation data, with 6.5% rejects; deep transfer and fine-tuned models report 2.5% and around 2% error, respectively.The comparison is reported for three models; the rejected images are shown in Fig. 7.Source: §4.4 · p. 11, Table 4 · p. 12

4.5.1 Base Network Performance

  • Below 91% base accuracy on BN80, reject rate rose to 50%; below 89% on BN90, it exceeded 30%, while around 98% accuracy kept it under 10%.For higher-accuracy MLP base networks, the reject rate was around 1%.Source: §4.5.1 · p. 12

4.5.2 Similar Samples of Different Classes

  • Across ten MNIST digit-pair datasets, WisdomNet reduced error to zero; average reject rate was below 4%, peaking below 10% for MNIST(2-3).Reject rates varied across digit pairs despite similarly accurate base networks.Source: §4.5.2 · pp. 12–13, Figure 9 · p. 13

4.5.3 Noisy Data

  • At σ = 0.1, reject rates were about 4.5% (MOON), 5.9% (CIRCLE), and 5.4% (XOR); reject rates rose as noise increased.The tests used 1,000 training and 1,000 testing samples per dataset and noise condition.Source: §4.5.3 · p. 13

5 Discussion

For multiclass classification, one conjugate neuron was inadequate, while a multiple-neuron design produced a promising result on five MNIST digits. The discussion also considers probability-threshold rejection as an alternative under noisy inputs.

5 Discussion

  • With one conjugate neuron, more than 50% of the first five MNIST digits were rejected, showing that one neuron did not capture multiclass errors effectively.The authors describe multinomial classification as more challenging than binary classification.Source: §5 · p. 13
  • For multiclass classification, WisdomNet adds one conjugate neuron per class, doubling the base network’s output-neuron count.The conjugate neurons’ incoming weights and biases are initialized to zero.Source: §5 · p. 13
  • In the reported multinomial-classification experiment, multiple-conjugate-neuron WisdomNet reduced misclassification error to 0 and yielded a 9.8% reject rate; on 10-class MNIST, the reject rate was much higher.The base ConvNet obtained about 99.7% accuracy with 0.3% error.Source: §5 · pp. 13–14
  • Probability-threshold rejection can reject predictions within a chosen probability range, but high-confidence misclassifications may require wider ranges that substantially increase rejection.The passage gives 0.4–0.6 as an example range and notes that errors can occur above 0.95 confidence.Source: §5 · p. 14

6 Conclusion

Across the tested datasets and neural-network types, WisdomNet reported zero error while rejecting a minority of cases. The authors also identify limits in detection guarantees and in choosing when to stop fine-training.

6 Conclusion

  • WisdomNet builds on a trained base network, adds a conjugate neuron, and retrains on samples the base network misclassified.The authors say the approach is not restricted to a particular architecture, activation function, or network hyperparameter.Source: §6 · p. 14
  • 0% error was reported across diverse datasets and MLP, convolutional, and deep networks, with reject rates under 10%.For fairly accurate networks, the reject rate was under 5%.Source: §6 · p. 14
  • Under 10% rejection was still reported as noise or classification difficulty increased; rejected cases can be deferred to a human expert.The authors note that human review may offer a higher chance of a correct prediction, though rejection can be costly.Source: §6 · pp. 14–15
  • The method may also identify samples the base model classified correctly by chance and avoid potential misclassifications.The authors describe these as “lucky” cases.Source: §6 · p. 15
  • The authors do not claim that all misclassifications can be detected for every problem, and note risks of high rejection or missed errors.They specifically mention the possibility of failing to detect a single misclassified sample.Source: §6 · p. 15
  • The optimal stopping time for fine-training remains unresolved: training too long may reject all data, while stopping at zero training error may miss problematic test cases.The authors leave determining the optimum stopping time to future work.Source: §6 · p. 15

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