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Towards Explainable Deep Neural Networks (xDNN)
Plamen Angelov, Eduardo Soares
TL;DR
The paper addresses deep learning's limited explainability and resource demands while retaining its accuracy and automatic feature extraction. It proposes xDNN, a prototype-based, non-iterative, non-parametric architecture whose prototypes are derived from training data. On iRoads and Caltech-256, the authors report better accuracy, training time, and explainability than other methods, including deep learning.
Problem
Traditional deep learning is criticized for black-box behavior and substantial labeled-data, computational-resource, and training-time requirements despite strong accuracy and automatic feature extraction.
Method
xDNN is a prototype-based, non-iterative, non-parametric architecture that derives typicality and data-density prototypes from training data and can use pretrained VGG–VD–16 features.
Results
On iRoads and Caltech-256, xDNN outperforms other methods, including VGG–VD–16, in accuracy and training time while providing a clearly explainable classifier.
Takeaways & Limitations
xDNN combines statistical learning and reasoning through viewable prototype-based IF...THEN rules and a transparent internal architecture.
Abstract
from arXiv · showhide
In this paper, we propose an elegant solution that is directly addressing the bottlenecks of the traditional deep learning approaches and offers a clearly explainable internal architecture that can outperform the existing methods, requires very little computational resources (no need for GPUs) and short training times (in the order of seconds). The proposed approach, xDNN is using prototypes. Prototypes are actual training data samples (images), which are local peaks of the empirical data distribution called typicality as well as of the data density. This generative model is identified in a closed form and equates to the pdf but is derived automatically and entirely from the training data with no user- or problem-specific thresholds, parameters or intervention. The proposed xDNN offers a new deep learning architecture that combines reasoning and learning in a synergy. It is non-iterative and non-parametric, which explains its efficiency in terms of time and computational resources. From the user perspective, the proposed approach is clearly understandable to human users. We tested it on some well-known benchmark data sets such as iRoads and Caltech-256. xDNN outperforms the other methods including deep learning in terms of accuracy, time to train and offers a clearly explainable classifier. In fact, the result on the very hard Caltech-256 problem (which has 257 classes) represents a world record.
I. INTRODUCTION
Traditional deep learning combines strong accuracy and automatic feature extraction with concerns about explainability, data, computation, and training time. The paper introduces xDNN as a prototype-based architecture intended to combine high explainability with top accuracy and efficient training.
- Motivation: Deep learning achieves highly accurate results and automates feature extraction, but is criticized as a black box requiring substantial data, computation, and training time.Automatic feature extraction remains attractive for complex image-processing applications where human expertise may be unavailable or expensive.
- Motivation: Feature extraction defines the data space and can influence accuracy, while transfer learning can reduce training time and improve model accuracy.The paper uses these properties of deep learning as foundations for its approach.
- Motivation: Interpretability and explainability are especially important in high-stakes applications such as autonomous driving, medical decisions, and court decisions.The paper highlights the need to understand why an autonomous car took a particular action, especially after an accident.
- Contribution: Existing classifiers trade higher explainability for lower accuracy or higher accuracy for lower explainability, whereas xDNN aims to provide both.The proposed approach is presented as a new deep learning method combining reasoning and learning.
- Contribution: xDNN uses prototypes, data density, and typicality in a non-iterative, non-parametric architecture that is intended to be understandable to human users.The paper reports evaluation on iRoads and Caltech-256, including a claimed world-record result on the 257-class Caltech-256 problem.
A. Architecture and Training of the proposed xDNN
xDNN combines feature extraction, density and typicality modeling, prototype identification, and MegaCloud merging in a per-class architecture designed for transparent incremental learning. Its prototypes are actual images that support interpretable similarity-based rules and online structural adaptation.
- Architecture: xDNN uses five layers: feature descriptor, density, typicality, prototypes, and MegaClouds.The architecture assigns each layer a distinct semantic or functional role, from defining the data space to merging same-class clouds for interpretability.
- Feature descriptor layer: The feature descriptor layer extracts image features using handcrafted descriptors or pretrained networks; this paper uses VGG-VD-16’s 1 × 4096 first fully connected layer.Features are standardized and normalized to [0;1], then processed separately for each class.
- Density and typicality layers: Density measures mutual proximity in feature space, while typicality provides an empirically derived pdf-like measure from the observed data.For Euclidean or Mahalanobis distances, the density has a Cauchy form and can be updated online.
- Prototypes layer: The prototypes layer identifies actual training images from the empirical distribution and represents each prototype with an interpretable similarity-based IF...THEN rule.Prototypes are independent, allowing new prototypes to be added without changing existing ones; the associated data clouds need not have regular geometric shapes.
- Incremental training: Samples are assigned to the nearest prototype, while outlying samples create new data clouds and otherwise update cloud parameters online.Calculations for each data cloud use only the samples associated with that cloud.
- MegaClouds layer: The MegaClouds layer merges neighboring prototype clouds with the same class label to facilitate human interpretability.The merged regions are represented by class-level OR rules over MegaCloud similarities.
B. Architecture and Validation of the proposed xDNN
The xDNN validation process uses sequential feature, prototype-similarity, local decision, and global decision layers to assign labels to validation images.
- The validation architecture comprises feature descriptor, similarity, local decision-making, and global decision-making layers.The architecture is illustrated in Figure 7.
- Similarity and local decisions: Similarity degrees to the nearest prototypes are extracted for each unlabeled validation image.Similarity is denoted by S and is evaluated per class.
- Similarity and local decisions: Local per-class decisions use a winner-takes-all principle.
- Global decision-making: The global layer assigns validation-image labels by comparing prototype similarities and determining the winning class.The overall satisfaction degree is obtained from the maximum of the local per-class winners.
III. EXPERIMENTAL DATA
The proposed xDNN was validated on complex, well-known image-classification benchmarks, including iRoads and Caltech-256.
- xDNN was validated using several complex, well-known image-classification benchmark datasets.
- The validation datasets included iRoads.
- The validation datasets included Caltech-256.
A. iRoads dataset
The iROADS dataset contains 4,656 image frames recorded from moving vehicles across diverse road scenes and conditions.
- 4,656 image frames in iROADS were recorded from moving vehicles on diverse road scenes.The dataset includes varying times, weather, and lighting conditions.
- Lighting conditions: 903 iROADS images were recorded in daylight, while 1,050 were recorded at night.
- Weather conditions: 1,049 rainy-day images and 431 rainy-night images are included in iROADS.
- Scene conditions: 569 snowy images, 307 sun-stroke images, and 347 tunnel images are included in iROADS.
B. Caltech-256
Caltech-256 contains 30,607 images organized into 257 object categories, including a background category.
- 30,607 images are divided into 257 object categories in Caltech-256.One category is background.
- Caltech-256 includes a background category among its 257 categories.
- The dataset is organized around object-category classification.
C. Performance Evaluation
The evaluation defines classification accuracy and specifies the computing setup and cross-validation protocol used for experiments.
- Accuracy is defined as the proportion of correct predictions among true and false positives and negatives.The metric is expressed using TP, FP, TN, and FN.
- Experiments used MATLAB 2018a on a 1.8 GHz Intel Core i5 computer with 8-GB RAM and MacOS.
- Classification experiments used 10-fold cross-validation with an 80% training and 20% testing split.
IV. RESULTS AND ANALYSIS
The study uses computational simulations to compare xDNN’s accuracy with other state-of-the-art approaches.
- Computational simulations assessed xDNN’s classification accuracy against other state-of-the-art approaches.
A. iRoads Dataset
On iRoads, xDNN is presented as accurate, efficient, compact, and explainable through prototypes, rules, MegaClouds, Voronoi tessellations, and typicality.
- xDNN provides the best reported combination of classification accuracy, time/complexity, and model simplicity on iRoads.Its model parameters are derived from data, and its top layer contains 27 MegaClouds, averaging 4 per class.
- 27 MegaClouds at the top layer make xDNN easier to explain and visualize than the 521 prototypes produced by DRB.The comparison reports averages of 4 MegaClouds per class for xDNN and 75 prototypes per class for DRB.
- MegaClouds can be visualized using prototype-based IF...THEN rules and Voronoi tessellations.The rules are illustrated in Figure 8, while Voronoi tessellation is illustrated in Figure 9.
- Typicality is shown for the iRoads night-scene and snow-scene classes.The figure presents typicality for two classes in a two-dimensional representation.
- Typicality corresponds to the probability density function and can express how likely an image is to represent particular driving conditions.The image is represented by a standardized and normalized 4096-dimensional feature vector.
B. Caltech-256 Dataset
On Caltech-256, xDNN is reported to achieve the best classification result while retaining an explainable and computationally efficient representation.
- 75.41% is reported as the best classification result worldwide for the complex Caltech-256 problem.
- xDNN surpasses all competitors on Caltech-256 in accuracy while providing a clearly explainable model.
- 721 MegaClouds, averaging 3 per class, provide an explainable representation for Caltech-256.
- Across challenging datasets, xDNN is reported to surpass state-of-the-art methods and produce interpretable outputs as rules, Voronoi tessellations, or typicality.The approach is also described as enabling computationally efficient implementations through its recursive, non-iterative, and non-parametric form.
V. CONCLUSION
xDNN is a prototype-based, explainable deep neural architecture designed to address traditional deep learning’s computational and interpretability bottlenecks. It uses a non-iterative, non-parametric approach and reports superior benchmark performance, including a claimed world record on Caltech-256.
- xDNN uses prototypes, typicality, and data density to combine reasoning with learning in an explainable architecture.Its generative model is derived automatically from training data in closed form.
- No GPUs and training times in the order of seconds reduce xDNN’s computational requirements.The paper attributes efficiency to its non-iterative and non-parametric design.
- xDNN derives its model entirely from training data without user- or problem-specific thresholds, parameters, or intervention.
- On iRoads and Caltech-256, xDNN outperforms other methods, including state-of-the-art deep learning approaches, in accuracy and training time while providing an explainable classifier.
- 257 classes on Caltech-256 constitute a result the paper describes as a world record.