Neural networks learn to mimic brain neurons with two-input activation functions, improving performance and robustness.
problem Training neural networks to mimic the complex interactions of brain neurons.
method Developed a network-in-network architecture with two-input activation functions, optimized hyperparameters, and compared to conventional ReLU networks.
result Two-input activation functions can learn soft XOR functions, improving network performance and robustness.
Study on neuron dynamics for XOR classification with zero-margin.
problem Understanding neural network training dynamics in zero-margin classification problems.
method Analysis of Gaussian XOR problem, focusing on neuron block dynamics and generalization without margin assumptions.
result Neurons cluster into four directions and block-level signals evolve coherently, essential for reliable prediction in the Gaussian setting.
SGD quickly learns a spurious XOR feature before the signal feature, revealing learning dynamics.
problem Over-reliance on spurious correlations in neural networks trained by SGD.
method Theoretical analysis of SGD on two-layer ReLU networks trained on XOR data.
result SGD learns the spurious feature first and exponentially fast, dominating the signal feature.
We show linear XOR classification is possible and propose equality separation for anomaly detection.
problem Linearly separating XOR data.
method Equality separation, adapting SVM objective for data within/outside margin.
result Equality separation can detect both seen and unseen anomalies.
FleXOR trains fractional quantization for neural networks, improving accuracy and size.
problem Quantization limits to integer bits restricts compression and accuracy.
method Encryption algorithm with XOR gates for fractional bits during inference.
result FleXOR achieves high accuracy with fractional sub-1-bit weights.
SGD efficiently learns the XOR function with near-optimal sample complexity.
problem Learning the XOR function with a 2-layer neural network.
method Minibatch SGD on a 2-layer neural network with ReLU activations, focusing on signal-finding and signal-heavy phases.
result Achieves population error o(1) with dextpolylog(d) samples. The exclusive or (xor) function is one of the simplest examples that illustrate why nonlinear feedforward networks are superior to linear regression for machine learning applications. We review the xor representation and approximation problems and discuss their solutions in terms of probabilistic logic and associative …
Training an artificial neural network involves an optimization process over the landscape defined by the cost (loss) as a function of the network parameters. We explore these landscapes using optimisation tools developed for potential energy landscapes in molecular science. The number of local minima and transition sta…
When applying Machine Learning techniques to problems, one must select model parameters to ensure that the system converges but also does not become stuck at the objective function's local minimum. Tuning these parameters becomes a non-trivial task for large models and it is not always apparent if the user has found th…
Empirical evidence suggests that neural networks with ReLU activations generalize better with over-parameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparameterized convolutional net…
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
Neural networks can overfit perfectly to noisy data and then grok near-optimal generalization.
problem Neural networks' ability to overfit perfectly to noisy data and then generalize near-optimally.
method Two-layer ReLU networks trained by gradient descent on XOR cluster data.
result Neural networks can achieve perfect fit to noisy training data and then grok near-optimal generalization.
This paper models the crowdsourced labeling/classification problem as a sparsely encoded source coding problem, where each query answer, regarded as a code bit, is the XOR of a small number of labels, as source information bits. In this paper we leverage the connections between this problem and well-studied codes with …
Study of eigenvalues in nonlinear kernels for classification of separable data.
problem Understanding the applicability of linear equivalents in nonlinearly separable data classification.
method Analysis of conjugate kernels and their quadratic equivalents for a canonical nonlinearly separable dataset (XOR problem).
result Identification of regimes where nonlinear kernels deviate from linear equivalents, leading to label-aligned eigenspaces.
Study of local optima in neural networks for feature interactions.
problem NNs struggle with local optima in feature interactions for small datasets.
method Proposed a node pruning and feature selection algorithm to improve NN performance.
result NNs have many non-equivalent local optima in XOR-like data with irrelevant variables.
New method disentangles feature importance scores in machine learning.
problem Misinterpretation of feature importance scores due to interactions and dependencies.
method Derive DIP (Disentangled Importance) decomposition of feature importance scores.
result DIP decomposition uniquely separates standalone contributions from interactions and dependencies.
Model compression techniques, such as pruning and quantization, are becoming increasingly important to reduce the memory footprints and the amount of computations. Despite model size reduction, achieving performance enhancement on devices is, however, still challenging mainly due to the irregular representations of spa…
New measure LMN explains neural network grokking.
problem Delayed generalization after memorization in neural networks.
method Defined LMN to measure network complexity, showing LMN correlates with test losses linearly.
result LMN reveals intriguing XOR network behavior and is a promising complexity measure.
We consider a query-based data acquisition problem for binary classification of unknown labels, which has diverse applications in communications, crowdsourcing, recommender systems and active learning. To ensure reliable recovery of unknown labels with as few number of queries as possible, we consider an effective quer…
Overparameterisation can limit the benefits of curriculum learning in neural networks.
problem The ineffectiveness of curriculum learning in deep learning applications.
method Analytical study connecting curriculum learning and overparameterisation in an online learning setting for a 2-layer network in the XOR-like Gaussian Mixture problem.
result High degree of overparameterisation can limit the benefit from curricula.
Study on neural networks forgetting in continual learning.
problem Forgetting in neural networks during continual learning.
method Gradient descent analysis on XOR-cluster datasets.
result Explicit bounds on forgetting rate and generalization gap.
Paper proposes GrokTransfer to eliminate delayed generalization in neural networks.
problem Delayed generalization in neural networks, compromising predictability and efficiency.
method Trains a smaller, weaker model to reach a nontrivial test performance, then uses its learned input embedding to initialize the stronger model.
result GrokTransfer enables the target model to generalize directly without delay, across various tasks.
Employers actively look for talents having not only specific hard skills but also various soft skills. To analyze the soft skill demands on the job market, it is important to be able to detect soft skill phrases from job advertisements automatically. However, a naive matching of soft skill phrases can lead to false pos…
Soft labeling impacts OOD detection in neural networks.
problem Impact of soft labeling on OOD detection in deep neural networks.
method Empirical analysis of how soft labeling affects OOD detection performance.
result Soft labeling can either improve or deteriorate OOD detection performance.
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.
problem Creating space-filling shapes without sharp corners.
method Edge bending algorithm to deform polyhedral tilings into soft tilings.
result Soft tilings derived from minimal surfaces can be continuously transformed into one another.
Explaining neural network computation in terms of probabilistic/fuzzy logical operations has attracted much attention due to its simplicity and high interpretability. Different choices of logical operators such as AND, OR and XOR give rise to another dimension for network optimization, and in this paper, we study the o…
ASBART accelerates Soft BART for faster Bayesian regression.
problem Slow computation in Soft BART.
method Proposed ASBART, a variant of Soft BART.
result ASBART is about 10 times faster than Soft BART with similar accuracy.
Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid l…
New method improves stability of soft FQI for offline RL.
problem Stability issues in soft FQI under function approximation.
method Stationary reweighting to align operator norms.
result Local linear convergence proved under certain conditions.
Generalizes soft noncommutative schemes to flag varieties.
problem Applying soft noncommutative schemes to flag varieties.
method Generalization via toric geometry and distinguished affine charts.
result Soft noncommutative schemes can be applied to flag varieties.
Paper proposes a new loss function for conditional models using soft targets.
problem Improving generalization performance of deep neural networks on supervised classification tasks.
method Introduces a new loss function compatible with soft targets, based on noise contrastive estimation.
result Soft target InfoNCE loss performs on par with cross-entropy baselines and outperforms other losses.
Introduces Soft-SVM for binary classification bridging logistic and SVM.
problem Data separability issues in binary classification.
method Soft-SVM regression using convex relaxation of hinge loss with softness and class-separation parameters.
result Soft-SVM performs well in classification and prediction errors.
Deep model learns from labeled and unlabeled data for industrial soft sensing.
problem Lack of data limits soft sensor development in industrial processes.
method Hierarchical, generative deep latent variable model for semi-supervised multi-unit soft sensing.
result Model outperforms current methods for soft sensing in industrial processes.
This paper introduces TNTK to study infinite soft tree ensembles.
problem Understanding the behavior of infinite soft tree ensembles.
method Introduced Tree Neural Tangent Kernel (TNTK) to analyze infinite soft tree ensembles.
result Identified several non-trivial properties of infinite soft tree ensembles.
Improves deep neural networks using soft labels through alternating minimization.
problem Improving deep neural networks training with soft labels.
method Co-Learns DNNs and soft labels via Alternating Minimization of two objectives.
result COLAM achieves improved performance on many tasks with better testing classification accuracy.
The paper develops a multi-unit soft sensing model for virtual flow meters that improves few-shot learning.
problem Improving soft sensor performance for new wells with limited data.
method Formulates a probabilistic, hierarchical model using a deep neural network for multi-unit soft sensing.
result Multi-unit models trained on many wells can perform well on new wells with just a few data points.
In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the p…
Recently, deep learning becomes the main focus of machine learning research and has greatly impacted many important fields. However, deep learning is criticized for lack of interpretability. As a successful unsupervised model in deep learning, the autoencoder embraces a wide spectrum of applications, yet it suffers fro…
Proposes a new method for deep ensembles that improves accuracy and calibration.
problem Improving accuracy and calibration of deep ensembles.
method Estimates confusion matrices of ensemble members and weighs them according to their inferred performance.
result Empirically shows superiority of soft Dawid Skene over ensemble averaging.
Bayesian neural networks update beliefs with soft evidence, improving accuracy and calibration.
problem Updating neural network weights with uncertain or soft evidence.
method Developed two algorithms to approximate Jeffrey's rule for updating neural network weights.
result Jeffrey-based methods outperform traditional approaches in accuracy and calibration, especially in noisy data.
A method for selecting pseudo-labeled data in semi-supervised learning using generalized Bayes and soft revision.
problem Selecting pseudo-labeled data for semi-supervised learning with robustness to uncertainty.
method Using credal sets and the Gamma-Maximin method with soft revision to update priors and select pseudo-labeled data.
result The Gamma-Maximin method with soft revision can achieve promising results, especially in scenarios with low labeled data proportions.
For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (ap…
Floer homology is a good example of homological invariants living in the infinite dimension. We suggest a way to construct this kind of invariants using only soft essentially finite-dimensional tools; no hard analysis or PDE is involved. This work is partially inspired by the M. Gromov's survey ``Soft and hard symplect…
MSLG generates soft labels to improve DNN performance on noisy datasets.
problem Significant performance degradation of DNNs due to noisy labels.
method Meta-learning techniques to estimate optimal label distribution and iteratively update soft labels.
result MSLG outperforms state-of-the-art methods by a large margin on various datasets.
Constructs noncommutative spaces for D-branes on complex algebraic spaces.
problem Mathematical model for D-branes on noncommutative spaces.
method Toric geometry, Azumaya schemes, invertible sheaves.
result Embeds algebraic Calabi-Yau spaces into soft noncommutative schemes.
In industrial systems, certain process variables that need to be monitored for detecting faults are often difficult or impossible to measure. Soft sensor techniques are widely used to estimate such difficult-to-measure process variables from easy-to-measure ones. Soft sensor modeling requires training datasets includin…
HyperFair integrates fairness in recommender systems using probabilistic soft logic.
problem Ensuring fairness in recommender systems across diverse domains.
method Soft fairness constraints integrated as regularization in a joint inference objective function.
result HyperFair improves fairness of predictions from black-box models and hybrid systems.