Building robust deterministic neural networks remains a challenge. On the one hand, some approaches improve out-of-distribution detection at the cost of reducing classification accuracy in some situations. On the other hand, some methods simultaneously increase classification accuracy, uncertainty estimation, and out-of-distribution detection at the expense of reducing the inference efficiency. In this paper, we propose training deterministic neural networks using our DisMax loss, which works as a drop-in replacement for the usual SoftMax loss (i.e., the combination of the linear output layer, the SoftMax activation, and the cross-entropy loss). Starting from the IsoMax+ loss, we create each logit based on the distances to all prototypes, rather than just the one associated with the correct class. We also introduce a mechanism to combine images to construct what we call fractional probability regularization. Moreover, we present a fast way to calibrate the network after training. Finally, we propose a composite score to perform out-of-distribution detection. Our experiments show that DisMax usually outperforms current approaches simultaneously in classification accuracy, uncertainty estimation, and out-of-distribution detection while maintaining deterministic neural network inference efficiency. The code to reproduce the results is available at https://github.com/dlmacedo/distinction-maximization-loss.
Felipe Costa Farias, Teresa Bernarda Ludermir, Carmelo Jose Albanez Bastos-Filho
The definition of a Neural Network architecture is one of the most critical and challenging tasks to perform. In this paper, we propose ParallelMLPs. ParallelMLPs is a procedure to enable the training of several independent Multilayer Perceptron Neural Networks with a different number of neurons and activation functions in parallel by exploring the principle of locality and parallelization capabilities of modern CPUs and GPUs. The core idea of this technique is to use a Modified Matrix Multiplication that replaces an ordinal matrix multiplication by two simple matrix operations that allow separate and independent paths for gradient flowing, which can be used in other scenarios. We have assessed our algorithm in simulated datasets varying the number of samples, features and batches using 10,000 different models. We achieved a training speedup from 1 to 4 orders of magnitude if compared to the sequential approach.
Sergio F. Chevtchenko, Yeshwanth Bethi, Teresa B. Ludermir et al.
Reinforcement Learning (RL) provides a powerful framework for decision-making in complex environments. However, implementing RL in hardware-efficient and bio-inspired ways remains a challenge. This paper presents a novel Spiking Neural Network (SNN) architecture for solving RL problems with real-valued observations. The proposed model incorporates multi-layered event-based clustering, with the addition of Temporal Difference (TD)-error modulation and eligibility traces, building upon prior work. An ablation study confirms the significant impact of these components on the proposed model's performance. A tabular actor-critic algorithm with eligibility traces and a state-of-the-art Proximal Policy Optimization (PPO) algorithm are used as benchmarks. Our network consistently outperforms the tabular approach and successfully discovers stable control policies on classic RL environments: mountain car, cart-pole, and acrobot. The proposed model offers an appealing trade-off in terms of computational and hardware implementation requirements. The model does not require an external memory buffer nor a global error gradient computation, and synaptic updates occur online, driven by local learning rules and a broadcasted TD-error signal. Thus, this work contributes to the development of more hardware-efficient RL solutions.
Felipe Costa Farias, Teresa Bernarda Ludermir, Carmelo José Albanez Bastos-Filho
The model selection procedure is usually a single-criterion decision making in which we select the model that maximizes a specific metric in a specific set, such as the Validation set performance. We claim this is very naive and can perform poor selections of over-fitted models due to the over-searching phenomenon, which over-estimates the performance on that specific set. Futhermore, real world data contains noise that should not be ignored by the model selection procedure and must be taken into account when performing model selection. Also, we have defined four theoretical optimality conditions that we can pursue to better select the models and analyze them by using a multi-criteria decision-making algorithm (TOPSIS) that considers proxies to the optimality conditions to select reasonable models.
Current out-of-distribution detection approaches usually present special requirements (e.g., collecting outlier data and hyperparameter validation) and produce side effects (e.g., classification accuracy drop and slow/inefficient inferences). Recently, entropic out-of-distribution detection has been proposed as a seamless approach (i.e., a solution that avoids all previously mentioned drawbacks). The entropic out-of-distribution detection solution uses the IsoMax loss for training and the entropic score for out-of-distribution detection. The IsoMax loss works as a drop-in replacement of the SoftMax loss (i.e., the combination of the output linear layer, the SoftMax activation, and the cross-entropy loss) because swapping the SoftMax loss with the IsoMax loss requires no changes in the model's architecture or training procedures/hyperparameters. In this paper, we perform what we call an isometrization of the distances used in the IsoMax loss. Additionally, we propose replacing the entropic score with the minimum distance score. Experiments showed that these modifications significantly increase out-of-distribution detection performance while keeping the solution seamless. Besides being competitive with or outperforming all major current approaches, the proposed solution avoids all their current limitations, in addition to being much easier to use because only a simple loss replacement for training the neural network is required. The code to replace the SoftMax loss with the IsoMax+ loss and reproduce the results is available at https://github.com/dlmacedo/entropic-out-of-distribution-detection.
This work investigates the use of two-stage clustering methods. Four techniques were proposed: SOMK, SOMAK, ASCAK and SOINAK. SOMK is composed of a SOM (Self-Organizing Maps) followed by the K-means algorithm, SOMAK is a combination of SOM followed by the Ant K-means (AK) algorithm, ASCAK is composed by the ASCA (Ant System-based Clustering Algorithm) and AK algorithms, SOINAK is composed by the Self-Organizing Incremental Neural Network (SOINN) and AK. SOINAK presented a better performance among the four proposed techniques when applied to pattern recognition problems.
Neural Networks have been applied for time series prediction with good experimental results that indicate the high capacity to approximate functions with good precision. Most neural models used in these applications use activation functions with fixed parameters. However, it is known that the choice of activation function strongly influences the complexity and performance of the neural network and that a limited number of activation functions have been used. In this work, we propose the use of a family of free parameter asymmetric activation functions for neural networks and show that this family of defined activation functions satisfies the requirements of the universal approximation theorem. A methodology for the global optimization of this family of activation functions with free parameter and the weights of the connections between the processing units of the neural network is used. The central idea of the proposed methodology is to simultaneously optimize the weights and the activation function used in a multilayer perceptron network (MLP), through an approach that combines the advantages of simulated annealing, tabu search and a local learning algorithm, with the purpose of improving performance in the adjustment and forecasting of time series. We chose two learning algorithms: backpropagation with the term momentum (BPM) and LevenbergMarquardt (LM).
This works proposes a methodology to searching for automatically Artificial Neural Networks (ANN) by using Cellular Genetic Algorithm (CGA). The goal of this methodology is to find compact networks whit good performance for classification problems. The main reason for developing this work is centered at the difficulties of configuring compact ANNs with good performance rating. The use of CGAs aims at seeking the components of the RNA in the same way that a common Genetic Algorithm (GA), but it has the differential of incorporating a Cellular Automaton (CA) to give location for the GA individuals. The location imposed by the CA aims to control the spread of solutions in the populations to maintain the genetic diversity for longer time. This genetic diversity is important for obtain good results with the GAs.
Tarsicio Lucas, Teresa Ludermir, Ricardo Prudencio et al.
The optimization of Artificial Neural Networks (ANNs) is an important task to the success of using these models in real-world applications. The solutions adopted to this task are expensive in general, involving trial-and-error procedures or expert knowledge which are not always available. In this work, we investigated the use of meta-learning to the optimization of ANNs. Meta-learning is a research field aiming to automatically acquiring knowledge which relates features of the learning problems to the performance of the learning algorithms. The meta-learning techniques were originally proposed and evaluated to the algorithm selection problem and after to the optimization of parameters for Support Vector Machines. However, meta-learning can be adopted as a more general strategy to optimize ANN parameters, which motivates new efforts in this research direction. In the current work, we performed a case study using meta-learning to choose the number of hidden nodes for MLP networks, which is an important parameter to be defined aiming a good networks performance. In our work, we generated a base of meta-examples associated to 93 regression problems. Each meta-example was generated from a regression problem and stored: 16 features describing the problem (e.g., number of attributes and correlation among the problem attributes) and the best number of nodes for this problem, empirically chosen from a range of possible values. This set of meta-examples was given as input to a meta-learner which was able to predict the best number of nodes for new problems based on their features. The experiments performed in this case study revealed satisfactory results.
Anderson P. da Silva, Teresa B. Ludermir, Leandro M. Almeida
This paper describes a method that automatically searches Artificial Neural Networks using Cellular Genetic Algorithms. The main difference of this method for a common genetic algorithm is the use of a cellular automaton capable of providing the location for individuals, reducing the possibility of local minima in search space. This method employs an evolutionary search for simultaneous choices of initial weights, transfer functions, architectures and learning rules. Experimental results have shown that the developed method can find compact, efficient networks with a satisfactory generalization power and with shorter training times when compared to other methods found in the literature.
Training of Artificial Neural Networks is a complex task of great importance in supervised learning problems. Evolutionary Algorithms are widely used as global optimization techniques and these approaches have been used for Artificial Neural Networks to perform various tasks. An optimization algorithm, called Group Search Optimizer (GSO), was proposed and inspired by the search behaviour of animals. In this article we present two new hybrid approaches: CGSO-Hk-WD and CGSO-Sk-WD. Cooperative GSOs are based on the divide-and-conquer paradigm, employing cooperative behaviour between GSO groups to improve the performance of the standard GSO. We also apply the weight decay strategy (WD, acronym for Weight Decay) to increase the generalizability of the networks. The results show that cooperative GSOs are able to achieve better performance than traditional GSO for classification problems in benchmark datasets such as Cancer, Diabetes, Ecoli and Glass datasets.
Dusan Stosic, Darko Stosic, Teresa B. Ludermir et al.
Distance metric learning has attracted a lot of interest for solving machine learning and pattern recognition problems over the last decades. In this work we present a simple approach based on concepts from statistical physics to learn optimal distance metric for a given problem. We formulate the task as a typical statistical physics problem: distances between patterns represent constituents of a physical system and the objective function corresponds to energy. Then we express the problem as a minimization of the free energy of a complex system, which is equivalent to distance metric learning. Much like for many problems in physics, we propose an approach based on Metropolis Monte Carlo to find the best distance metric. This provides a natural way to learn the distance metric, where the learning process can be intuitively seen as stretching and rotating the metric space until some heuristic is satisfied. Our proposed method can handle a wide variety of constraints including those with spurious local minima. The approach works surprisingly well with stochastic nearest neighbors from neighborhood component analysis (NCA). Experimental results on artificial and real-world data sets reveal a clear superiority over a number of state-of-the-art distance metric learning methods for nearest neighbors classification.
David Macêdo, Pedro Dreyer, Teresa Ludermir et al.
Proper optimization of deep neural networks is an open research question since an optimal procedure to change the learning rate throughout training is still unknown. Manually defining a learning rate schedule involves troublesome time-consuming try and error procedures to determine hyperparameters such as learning rate decay epochs and learning rate decay rates. Although adaptive learning rate optimizers automatize this process, recent studies suggest they may produce overffiting and reduce performance when compared to fine-tuned learning rate schedules. Considering that deep neural networks loss functions present landscapes with much more saddle points than local minima, we proposed the Training Aware Sigmoidal Optimizer (TASO), which consists of a two-phases automated learning rate schedule. The first phase uses a high learning rate to fast traverse the numerous saddle point, while the second phase uses low learning rate to slowly approach the center of the local minimum previously found. We compared the proposed approach with commonly used adaptive learning rate schedules such as Adam, RMSProp, and Adagrad. Our experiments showed that TASO outperformed all competing methods in both optimal (i.e., performing hyperparameter validation) and suboptimal (i.e., using default hyperparameters) scenarios.
Felipe Farias, Teresa Ludermir, Carmelo Bastos-Filho
We propose a Similarity-Based Stratified Splitting (SBSS) technique, which uses both the output and input space information to split the data. The splits are generated using similarity functions among samples to place similar samples in different splits. This approach allows for a better representation of the data in the training phase. This strategy leads to a more realistic performance estimation when used in real-world applications. We evaluate our proposal in twenty-two benchmark datasets with classifiers such as Multi-Layer Perceptron, Support Vector Machine, Random Forest and K-Nearest Neighbors, and five similarity functions Cityblock, Chebyshev, Cosine, Correlation, and Euclidean. According to the Wilcoxon Sign-Rank test, our approach consistently outperformed ordinary stratified 10-fold cross-validation in 75\% of the assessed scenarios.
Nicolas M. de Oliveira, Lucas P. de Albuquerque, Wilson R. de Oliveira et al.
The advancement of technology in Quantum Computing has brought possibilities for the execution of algorithms in real quantum devices. However, the existing errors in the current quantum hardware and the low number of available qubits make it necessary to use solutions that use fewer qubits and fewer operations, mitigating such obstacles. Hadamard Classifier (HC) is a distance-based quantum machine learning model for pattern recognition. We present a new classifier based on HC named Quantum One-class Classifier (QOCC) that consists of a minimal quantum machine learning model with fewer operations and qubits, thus being able to mitigate errors from NISQ (Noisy Intermediate-Scale Quantum) computers. Experimental results were obtained by running the proposed classifier on a quantum device and show that QOCC has advantages over HC.
David Macêdo, Tsang Ing Ren, Cleber Zanchettin et al.
In this paper, we argue that the unsatisfactory out-of-distribution (OOD) detection performance of neural networks is mainly due to the SoftMax loss anisotropy and propensity to produce low entropy probability distributions in disagreement with the principle of maximum entropy. Current out-of-distribution (OOD) detection approaches usually do not directly fix the SoftMax loss drawbacks, but rather build techniques to circumvent it. Unfortunately, those methods usually produce undesired side effects (e.g., classification accuracy drop, additional hyperparameters, slower inferences, and collecting extra data). In the opposite direction, we propose replacing SoftMax loss with a novel loss function that does not suffer from the mentioned weaknesses. The proposed IsoMax loss is isotropic (exclusively distance-based) and provides high entropy posterior probability distributions. Replacing the SoftMax loss by IsoMax loss requires no model or training changes. Additionally, the models trained with IsoMax loss produce as fast and energy-efficient inferences as those trained using SoftMax loss. Moreover, no classification accuracy drop is observed. The proposed method does not rely on outlier/background data, hyperparameter tuning, temperature calibration, feature extraction, metric learning, adversarial training, ensemble procedures, or generative models. Our experiments showed that IsoMax loss works as a seamless SoftMax loss drop-in replacement that significantly improves neural networks' OOD detection performance. Hence, it may be used as a baseline OOD detection approach to be combined with current or future OOD detection techniques to achieve even higher results.
Adenilton J. da Silva, Teresa B. Ludermir, Wilson R. de Oliveira
In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator.
Adenilton J. da Silva, Wilson R. de Oliveira, Teresa B. Ludermir
Training artificial neural networks requires a tedious empirical evaluation to determine a suitable neural network architecture. To avoid this empirical process several techniques have been proposed to automatise the architecture selection process. In this paper, we propose a method to perform parameter and architecture selection for a quantum weightless neural network (qWNN). The architecture selection is performed through the learning procedure of a qWNN with a learning algorithm that uses the principle of quantum superposition and a non-linear quantum operator. The main advantage of the proposed method is that it performs a global search in the space of qWNN architecture and parameters rather than a local search.