Related papers: Strong noise sensitivity and random graphs
With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known…
Graph neural networks (GNNs) learn node representations by passing and aggregating messages between neighboring nodes. GNNs have been applied successfully in several application domains and achieved promising performance. However, GNNs…
Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…
The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…
We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell\_p$ ball for $p \in [1, \infty]$ and Gaussian noise with an arbitrary covariance matrix. We…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will…
Deep Neural Networks (DNNs) are a revolutionary force in the ongoing information revolution, and yet their intrinsic properties remain a mystery. In particular, it is widely known that DNNs are highly sensitive to noise, whether adversarial…
In many applications of classifier learning, training data suffers from label noise. Deep networks are learned using huge training data where the problem of noisy labels is particularly relevant. The current techniques proposed for learning…
In a recent paper by Jonasson and Steif, definitions to describe the volatility of sequences of Boolean functions, \( f_n \colon \{ -1,1 \}^n \to \{ -1,1 \} \) were introduced. We continue their study of how these definitions relate to…
Items in a test are often used as a basis for making decisions and such tests are therefore required to have good psychometric properties, like unidimensionality. In many cases the sum score is used in combination with a threshold to decide…
Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…
We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external Poissonian shot noise. The asymmetry of the noise induces an effective nonlinearity in the potential, which…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
During the past 15 years, several extensions of the concepts noise sensitivity and noise stability, first coined in~\cite{schramm2000}, has been studied. The purpose in this paper is to give definitions of this concepts in the setting of…
We find that sensory noise delivered together with a weak periodic signal not only enhances nonlinear response of neuronal networks, but also improves the synchronization of the response to the signal. We reveal this phenomenon in neuronal…
Neurons in the central nervous system are affected by complex and noisy signals due to fluctuations in their cellular environment and in the inputs they receive from many other cells 1,2. Such noise usually increases the probability that a…
We show that on every product probability space, Boolean functions with small total influences are essentially the ones that are almost measurable with respect to certain natural sub-sigma algebras. This theorem in particular describes the…
Neural correlations play a critical role in sensory information coding. They are of two kinds: signal correlations, when neurons have overlapping sensitivities, and noise correlations from network effects and shared noise. In experiments…
The statistical properties of nonlinear phase noise, often called the Gordon-Mollenauer effect, is studied analytically when the number of fiber spans is very large. The joint characteristic functions of the nonlinear phase noise with…