Bayesian active learning tackles nuisance parameters, leading to bias and dilemmas.
problem Bayesian active learning with nuisance parameters leads to bias and dilemmas.
method Characterizes and mitigates negative interference by accurately estimating nuisance parameters.
result The extent of negative interference can be extremely large, and accurate estimation of nuisance parameters is critical.
Bayesian adaptive designs can be biased by active learning, especially with misspecified models.
problem Active learning bias in Bayesian adaptive experimental designs.
method Analysis of linear and preference learning models, empirical testing.
result Model misspecification and noise influence active learning bias in Bayesian designs.
This paper studies activation sparsity in large language models, finding key trends and implications.
problem Activation sparsity in large language models (LLMs) can be improved for efficiency and interpretability.
method Proposes PPL-p% sparsity, analyzes trends with training data, width-depth ratio, and parameter scale. result ReLU is more efficient for sparsity than SiLU, and deeper architectures can improve sparsity.
Paper extends Chernoff sampling for active testing and parameter estimation, improving neural network and regression models.
problem Reducing sample complexity in hypothesis testing and model parameter estimation.
method Developed an extension of Chernoff sampling for active learning and parameter estimation.
result Non-asymptotic bounds for sample complexity and estimation error in active learning.
We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal description of the trad…
Deep neural networks with specific parameter sets can approximate smooth functions efficiently.
problem Approximating smooth functions with deep neural networks.
method Deep neural networks with ReLU activation and specific parameter sets {0,±21,±1,2} are used to approximate Cβ-smooth functions. result The constructed networks can approximate Cβ-smooth functions with parameters {0,±21,±1,2} efficiently, achieving the same convergence rate as sparse networks with parameters in [−1,1]. Many neural network architectures rely on the choice of the activation function for each hidden layer. Given the activation function, the neural network is trained over the bias and the weight parameters. The bias catches the center of the activation, and the weights capture the scale. Here we propose to train the netw…
Learning automatically the best activation function for the task is an active topic in neural network research. At the moment, despite promising results, it is still difficult to determine a method for learning an activation function that is at the same time theoretically simple and easy to implement. Moreover, most of…
Overfitting frequently occurs in deep learning. In this paper, we propose a novel regularization method called Drop-Activation to reduce overfitting and improve generalization. The key idea is to drop nonlinear activation functions by setting them to be identity functions randomly during training time. During testing, …
Study on rich regime training in deep learning, finding active parameters in bottom layers.
problem Understanding the practical success of deep learning models.
method Empirical study on rich regime training with benchmark datasets, re-initialization analysis, and probabilistic Layer-Wise Sparse SGD.
result Probabilistic Layer-Wise Sparse SGD matches vanilla SGD's generalization performance with improved efficiency.
Token-adaptive FFN design improves LLM expressivity.
problem Fixed activation functions limit FFN expressivity in LLMs.
method Mixture of Activations (MoA) and learnable activations (LA).
result MoA achieves lower terminal loss and better scaling than baselines.
Proposes a graph-based method for active learning in regression.
problem Active learning for regression is understudied and faces challenges with noisy labels and parameter uncertainty.
method Formulates active regression as a bipartite graph optimization problem.
result Demonstrates the effectiveness of the proposed graph-based approach on benchmark data sets.
Deep Neural Networks have been shown to be beneficial for a variety of tasks, in particular allowing for end-to-end learning and reducing the requirement for manual design decisions. However, still many parameters have to be chosen in advance, also raising the need to optimize them. One important, but often ignored sys…
This work simplifies Bayesian inference for neural networks by identifying influential parameter directions.
problem High computational complexity in Bayesian inference for neural networks due to high-dimensional parameter space.
method Constructing an active subspace of influential parameter directions to reduce dimensionality.
result Effective and scalable Bayesian inference achieved via reduced active subspace.
A new method reduces high-dimensional parameter spaces for faster numerical tasks.
problem Efficiently reducing high-dimensional parameter spaces for numerical tasks.
method Local Active Subspaces (LAS) combining active subspaces with clustering techniques.
result Significant speed-up in numerical tasks through efficient dimension reduction.
Researchers use active subspaces to quantify uncertainty in deep generative models for molecular design.
problem Uncertainty quantification in deep generative models for molecular design due to high parameter space.
method Leveraging active subspaces to approximate posterior distribution over low-dimensional parameters.
result The proposed UQ scheme effectively estimates epistemic uncertainty in high-dimensional parameter space without altering model architecture.
Bayesian calibration improves ABMs for predicting travel patterns.
problem Calibrating ABMs for accurate travel pattern predictions.
method Gaussian Process emulator with deep learning dimensionality reduction for high-dimensional, non-stationary data.
result Improved accuracy in predicting travel patterns using traffic flow data.
New active learning algorithm adapts to data without strict assumptions.
problem Efficiently label data with expensive labeling costs.
method Nonparametric adaptive active learning under local smoothness condition.
result Achieves minimax rate of convergence, performs almost as well as best non-adaptive algorithms.
In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…
Extracting and detecting spike activities from the fluorescence observations is an important step in understanding how neuron systems work. The main challenge lies in that the combination of the ambient noise with dynamic baseline fluctuation, often contaminates the observations, thereby deteriorating the reliability o…
Improved bounds on neural network regions using activation histograms.
problem Bounding the number of affine regions in ReLU networks.
method Analysis of algebraic topology problem, extension of framework to subnetwork composition.
result Slightly tighter bounds and insights into parameter initialization.
Neural networks cannot approximate certain functions in Sobolev spaces, leading to unbounded parameter growth.
problem Non-closedness of sets of neural networks in Sobolev spaces.
method Construction of sequences of neural networks whose realizations converge to functions not realizable by neural networks.
result Sets of realized neural networks are not closed in order-(m−1) Sobolev spaces Wm−1,p for p∈[1,∞]. Active subspace is a model reduction method widely used in the uncertainty quantification community. In this paper, we propose analyzing the internal structure and vulnerability and deep neural networks using active subspace. Firstly, we employ the active subspace to measure the number of "active neurons" at each inter…
Optimized neural network approximates high-dimensional functions with minimal parameters.
problem Achieving optimal approximation of high-dimensional continuous functions with minimal parameters.
method Developed a neural network with a specific activation function and architecture to achieve super approximation property.
result A composed network with at most 10889d + 10887 nonzero parameters achieves super approximation property, suggesting optimality in parameter growth.
This research improves neural network performance with adaptive activation functions in sparse data settings.
problem Limited data availability in scientific and engineering problems.
method Investigation of two types of adaptive activation functions with individual trainable parameters.
result Adaptive activation functions, especially with individual trainable parameters, enhance prediction accuracy and confidence in sparse data settings.
LSQ+ improves quantization of neural nets with Swish activations, achieving state-of-the-art results.
problem Quantization of neural nets with Swish activations, especially negative activations, leads to significant performance loss.
method Introduces learnable scale and offset parameters for asymmetric quantization, and uses MSE-based initialization for quantization parameters.
result Significantly outperforms LSQ for low-bit quantization of neural nets with Swish activations, achieving up to 5.6% gain with W2A2 quantization of EfficientNet-B0.
Maxout networks show similar complexity issues as ReLU networks.
problem Understanding the complexity of maxout networks and decision boundaries.
method Analyzing the parameter space and decision boundaries, obtaining lower bounds, and investigating initialization procedures.
result Maxout networks exhibit a wide range of complexity, similar to ReLU networks.
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization.…
Proposes EPIG for active learning to improve predictive performance.
problem Suboptimal predictive performance of traditional active learning methods.
method Introduces EPIG, a new acquisition function measuring information gain in the space of predictions.
result EPIG leads to stronger predictive performance compared to BALD across various datasets and models.
RBMs model binary interactions with hidden node activation effects.
problem Understanding how RBM hidden node activation affects binary variable distributions.
method Investigated RBM marginal distributions with different hidden node activation functions.
result Found exact expressions for RBM marginals as interacting binary variables.
Improves decentralized learning by teleporting active nodes for better convergence.
problem Decentralized learning's convergence rate degrades with large node numbers.
method Activates a subset of nodes, fetches parameters from previous active nodes, updates, and performs gossip averaging on a small topology.
result Teleportation completely alleviates convergence rate degradation with proper node activation.
Paper optimizes neural network initialization using SMT solvers.
problem Improving neural network performance through better initialization.
method Reduces initialization to SMT problem solving.
result Proposed method achieves better performance than random initialization.
Quantized neural networks can represent all fixed-point functions under certain conditions.
problem Expressive power of quantized neural networks under fixed-point arithmetic.
method Analyzing necessary and sufficient conditions for quantized networks to represent all fixed-point functions.
result Various popular activation functions satisfy the sufficient condition for representing all fixed-point functions.
Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we continue this thread in two parts by exploiting these relations for the first time …
Uncertainty estimation in deep neural networks is essential for designing reliable and robust AI systems. Applications such as video surveillance for identifying suspicious activities are designed with deep neural networks (DNNs), but DNNs do not provide uncertainty estimates. Capturing reliable uncertainty estimates i…
We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this sett…
Mean field theory has been successfully used to analyze deep neural networks (DNN) in the infinite size limit. Given the finite size of realistic DNN, we utilize the large deviation theory and path integral analysis to study the deviation of functions represented by DNN from their typical mean field solutions. The para…
DMLE improves active learning by correcting MLE for sample dependencies.
problem Dependencies among samples in active learning affect model parameter estimation.
method Dependency-aware Maximum Likelihood Estimation (DMLE).
result DMLE achieves superior performance across multiple benchmark datasets.
Spark Transformer achieves high sparsity in FFN and attention without sacrificing model quality.
problem Inactivity of most neurons in FFN of Transformers, leading to inefficiency.
method Top-k masking, statistical top-k algorithm, and predictor for activated entries.
result Only 8% of FFN neurons are activated, achieving up to 2.5x wall-time speedup.
The Heston model optimizes portfolio management based on real market data.
problem Choosing between active and passive investment strategies.
method Calibrated Heston model to real stock market data.
result Passive strategy can outperform active strategy depending on market parameters.
This paper proposes LDM for efficient deep active learning.
problem Improving model performance by selecting informative unlabeled data.
method Least Disagree Metric (LDM) and its estimator for deep learning models.
result LDM-based active learning achieves state-of-the-art performance.
The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep learning, it becomes important to look at the non linear component of NNs more careful…
AReLU uses attention-based rectification to improve neural network performance.
problem Improving neural network performance through better activation functions.
method Integrates attention mechanism with rectified linear unit (ReLU) to learn and scale feature maps.
result AReLU significantly boosts performance of most network architectures with minimal changes.
We propose a new generic type of stochastic neurons, called q-neurons, that considers activation functions based on Jackson's q-derivatives with stochastic parameters q. Our generalization of neural network architectures with q-neurons is shown to be both scalable and very easy to implement. We demonstrate expe…
Study on neural networks' storage capacity and solution space structure.
problem Understanding the storage capacity and solution space structure of neural networks.
method Replica method from statistical physics.
result Storage capacity per parameter remains finite even with infinite width and weights exhibit negative correlations.
New algorithm trains deep neural networks without global optimization.
problem Training deep neural networks efficiently and without global optimization.
method Uses random complex exponential activation functions and Markov Chain Monte Carlo sampling.
result Consistently attains theoretical approximation rate for residual networks.
A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accura…
Bayesian active learning method improved for censored regression data.
problem Challenges in estimating BALD for censored regression data.
method Derived entropy and mutual information for censored distributions, developed C-BALD objective, proposed novel modelling approach. result Demonstrated C-BALD outperforms other methods in censored regression.