Study on how noise and variation-norm regularisation help shallow ReLU networks use fewer neurons.
problem Understanding how shallow ReLU networks use a finite number of neurons in the infinitely wide limit.
method Analysis of two regularisation strategies: noise injection and variation-norm.
result Both regularisation methods minimize functions with a finite number of neurons, regardless of overparametrisation.
Simplified neural network EFTs reveal a single critical condition.
problem Understanding neuron statistics in neural networks at initialization.
method Diagrammatic approach to effective field theories (EFTs).
result A single condition governs criticality of all neuron preactivations.
Recurrent neural networks trained on regular languages exhibit stable states that can recover from noise.
problem Stability of internal states in recurrent neural networks trained on regular languages.
method Empirical study with analysis of network activation and transitions between states.
result Recurrent neural networks trained on regular languages can recover from random perturbations and maintain stable states.
Biological neurons learn tensor decompositions of higher-order correlations using nonlinear Hebbian plasticity.
problem Learning higher-order correlations in biological neurons.
method Introduce and study generalized nonlinear Hebbian learning rules.
result Neurons can learn tensor eigenvectors of higher-order input correlation tensors.
New method reduces over-parametrization in neural networks, ensuring sparsity and finite network size.
problem Over-parametrization leads to too many active neurons in neural networks, especially with large data.
method Investigates a nonconvex regularization method for shallow ReLU networks.
result Locally optimal networks are finite even with infinite data, maintaining approximation guarantees and network size bounds.
New neural stack and Turing Machine architectures prove stability and computational power.
problem Designing stable neural network architectures for Turing Machine simulation.
method Introducing neural stack and Turing Machine architectures, proving stability and computational equivalence.
result Differentiable nnTM with bounded neurons can simulate Turing Machine in real-time and is equivalent to UTM.
Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a higher dimensional manifold of the next layer as a curved submanifold, provided t…
In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This feature is inspired by the communication principles in the nervous system of small …
Neuron Shapley identifies key neurons in deep networks, improving model accuracy and fairness.
problem Identifying responsible neurons in deep networks for better model performance and fairness.
method Neuron Shapley framework quantifies neuron contributions, accounting for interactions.
result Removing just 30 critical filters can destroy model accuracy, revealing network function.
Describes explaining neurons in deep representations using compositional logical concepts.
problem Interpreting neuron behavior in deep neural networks.
method Identifying compositional logical concepts that closely approximate neuron behavior.
result Compositional explanations provide insights into model performance and allow for adversarial example creation.
SeReNe prunes neurons with low sensitivity to reduce network size.
problem Large neural networks consume too many resources on resource-constrained devices.
method Exploits neural sensitivity as a regularizer to prune neurons with low sensitivity.
result Pruning neurons with low sensitivity achieves competitive compression ratios.
Under-parameterized networks can either copy or average teacher weights, leading to universal optimal solutions.
problem Approximating a teacher network with an under-parameterized student network.
method Analyzing shallow neural networks with erf activation function and unitary teacher weights, proving copy-average configurations are critical points and finding the optimal solution.
result The optimal solution for under-parameterized networks has a universal structure, whether copying or averaging teacher neurons.
This research investigates selectively pruning hyper and hypo neurons to improve neural network generalization.
problem Improving neural network generalization to unseen data.
method Investigates pruning hyper and hypo neurons selectively in fully connected layers of CNNs.
result Selective pruning of hyper and hypo neurons improves model performance on out-of-domain data.
Modeling hidden neurons in SNNs using mesoscopic approximations.
problem Underconstrained problem of modeling unobserved neurons in SNNs.
method Coarse-graining and mean-field approximations to derive neuLVM.
result neuLVM can efficiently model large SNNs and recover connectivity parameters.
Topological methods improve neuron analysis and tracer injection summary.
problem Traditional methods fail to capture the tree-like structure of neurons.
method Discrete Morse (DM) Theory for neuron skeletonization and consensus tree summarization.
result Significant performance improvements over non-topological methods.
Inspired by complexity and diversity of biological neurons, our group proposed quadratic neurons by replacing the inner product in current artificial neurons with a quadratic operation on input data, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power o…
Simple neural networks approximate any continuous function with fixed neurons.
problem Approximating arbitrary continuous functions with limited neurons.
method Developed simple feed-forward neural networks with a specific activation function.
result Proven that networks with 36d(2d+1) neurons and depth 11 can approximate any continuous function.
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…
The paper introduces walks with jumps for modeling neuron activity in hyperbolic space.
problem Encoding neuron activity sequences in hyperbolic space.
method Introducing walks with jumps in hyperbolic geometry to model neuron activity.
result Endpoints of walks with jumps do not fully encode the sequence of jump times.
We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with thei…
SpaRCe optimizes reservoir computing by learning neuron thresholds to improve performance and prevent forgetting.
problem Improving performance and preventing forgetting in reservoir computing networks.
method Integrates neuron-specific learnable thresholds to optimize sparsity without altering dynamics, learning read-out weights and thresholds via gradient rule.
result Threshold learning improves performance and alleviates catastrophic forgetting.
It will be shown that according to theorems of K. Menger, every neuron grid if identified with a curve is able to preserve the adopted qualitative structure of a data space. Furthermore, if this identification is made, the neuron grid structure can always be mapped to a subset of a universal neuron grid which is constr…
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.
CHANI learns classification tasks with local transformations inspired by biology.
problem Proving neural networks can learn classification tasks with local transformations.
method CHANI uses spiking neurons modeled by Hawkes processes with expert aggregation for local learning.
result CHANI can learn and encode multiple classes, forming assemblies of neurons.
Researchers develop methods to learn neuron dynamics from colored noise.
problem Learning nonlocal stochastic neuron dynamics from colored noise.
method Proposed two methods for closing Fokker-Planck equations: nonlocal large-eddy-diffusivity closure and data-driven sparse regression.
result Mutual information and total correlation between stimulus and neuron states calculated for FHN neuron.
Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of the streamed data. …
Single neuron with ADA learns XOR and outperforms other functions.
problem Classifying linearly non-separable data.
method Proposed a new artificial neuron with apical dendrite activation.
result ADA function achieves 100% accuracy on XOR and superior performance on benchmark datasets.
Stable unactivated neurons reduce expressiveness in ReLU networks.
problem Reducing expressiveness in ReLU neural networks due to stably unactivated neurons.
method Investigated the probability of neurons being stably unactivated in ReLU networks with symmetric weight and bias distributions.
result Proved the probability of a neuron being stably unactivated in the second hidden layer of a ReLU network.
Deep neural networks (DNNs) are known for extracting useful information from large amounts of data. However, the representations learned in DNNs are typically hard to interpret, especially in dense layers. One crucial issue of the classical DNN model such as multilayer perceptron (MLP) is that neurons in the same layer…
Single-spike neurons can approximate as well as multi-spike neurons.
problem Limitation of single-spike neurons in spiking neural networks.
method Comparison of single-spike and multi-spike neural networks.
result Single-spike and multi-spike neural networks are equivalent in approximation capabilities.
The challenge of assigning importance to individual neurons in a network is of interest when interpreting deep learning models. In recent work, Dhamdhere et al. proposed Total Conductance, a "natural refinement of Integrated Gradients" for attributing importance to internal neurons. Unfortunately, the authors found tha…
Optimal neuron activation functions improve neural network performance.
problem Limited expressive power of standard neuron activation functions in neural networks.
method Additive Gaussian process regression to construct individual neuron activation functions.
result Optimal neuron activation functions lead to better performance and reduced overfitting.
The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to 2nd order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear qu…
Novel 'strong neuron' improves deep learning efficiency and robustness.
problem Improving deep learning efficiency and robustness against adversarial attacks.
method Introducing a novel 'strong neuron' model and a constructive training algorithm.
result Achieved 10x-100x reduction in operations count and hardware requirements.
The practical success of widely used machine learning (ML) and deep learning (DL) algorithms in Artificial Intelligence (AI) community owes to availability of large datasets for training and huge computational resources. Despite the enormous practical success of AI, these algorithms are only loosely inspired from the b…
Paper proves hardness of learning various complex models under local pseudorandom generators.
problem Hardness of learning various complex models.
method Existence of local pseudorandom generators.
result Proves hardness of learning shallow ReLU neural networks and other models.
With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or express in simple terms. The approach we propose in this paper is to characterize t…
Single ReLU neuron's gradient dynamics reveal support vectors as key to generalization.
problem Understanding the generalization capability of ReLU networks.
method Examined gradient flow dynamics and support vectors in single ReLU neuron training.
result Support vectors play a crucial role in the generalization of ReLU networks.
We view a neural network as a distributed system of which neurons can fail independently, and we evaluate its robustness in the absence of any (recovery) learning phase. We give tight bounds on the number of neurons that can fail without harming the result of a computation. To determine our bounds, we leverage the fact…
This paper presents a new artificial neuron model capable of learning its receptive field in the topological domain of inputs. The model provides adaptive and differentiable local connectivity (plasticity) applicable to any domain. It requires no other tool than the backpropagation algorithm to learn its parameters whi…
Novel method decorrelates neurons for better deep learning model generalization.
problem High correlations between neurons limit deep learning model generalization.
method Regularization terms from minimum spanning tree of neuron cliques, using correlation dissimilarities.
result Our regularizers outperform existing methods and minimize neuron redundancies.
A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of …
Sometimes it is not enough for a DNN to produce an outcome. For example, in applications such as healthcare, users need to understand the rationale of the decisions. Therefore, it is imperative to develop algorithms to learn models with good interpretability (Doshi-Velez 2017). An important factor that leads to the lac…
New training method for ReLU networks achieves optimal weight size for memorization.
problem Approximate memorization of arbitrary real labels with neural networks.
method Complex recombination training procedure for ReLU networks.
result Approximate memorization with nearly optimal weight size and neuron count.
Improved Bayesian inference for neuronal ensemble inference reduces computational cost.
problem Efficient inference of neuronal ensembles from activity data.
method Modified MCMC algorithm with simulated annealing for hyperparameter control.
result Our method reduces computational cost while maintaining or improving inference accuracy.
Gradient descent struggles with learning a single neuron with bias.
problem Learning a single neuron with a bias term in the realizable setting with ReLU activation.
method Theoretical study using gradient descent, characterizing critical points, and providing convergence guarantees.
result Gradient descent faces significant challenges in learning a single neuron with bias, unlike the bias-less case.
Over-parametrization speeds up learning a single neuron model.
problem Understanding why over-parametrization accelerates learning in neural networks.
method Studied a simple model of a single teacher neuron with quadratic activation, showing how over-parametrization can lead to faster convergence.
result Over-parametrization helps gradient descent enter the neighborhood of a global optimal solution faster.
Neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for the favorable training properties of "overparameterized" models. In this regime, gradient descent obeys a deterministic partial differential equation (PDE) that converges to a glo…