scholarly journals Sigmoidal NMFD: Convolutional NMF with Saturating Activations for Drum Mixture Decomposition

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 284
Author(s):  
Len Vande Veire ◽  
Cedric De Boom ◽  
Tijl De Bie
Keyword(s):  
Essential Role ◽  
Time Varying ◽  
Activation Functions ◽  
Local Minima ◽  
Sigmoidal Function ◽  
Regularization Term ◽  
Amplitude Factor ◽  
Mixture Decomposition ◽  
Component Amplitude ◽  
Percussive Instruments

In many types of music, percussion plays an essential role to establish the rhythm and the groove of the music. Algorithms that can decompose the percussive signal into its constituent components would therefore be very useful, as they would enable many analytical and creative applications. This paper describes a method for the unsupervised decomposition of percussive recordings, building on the non-negative matrix factor deconvolution (NMFD) algorithm. Given a percussive music recording, NMFD discovers a dictionary of time-varying spectral templates and corresponding activation functions, representing its constituent sounds and their positions in the mix. We observe, however, that the activation functions discovered using NMFD do not show the expected impulse-like behavior for percussive instruments. We therefore enforce this behavior by specifying that the activations should take on binary values: either an instrument is hit, or it is not. To this end, we rewrite the activations as the output of a sigmoidal function, multiplied with a per-component amplitude factor. We furthermore define a regularization term that biases the decomposition to solutions with saturated activations, leading to the desired binary behavior. We evaluate several optimization strategies and techniques that are designed to avoid poor local minima. We show that incentivizing the activations to be binary indeed leads to the desired impulse-like behavior, and that the resulting components are better separated, leading to more interpretable decompositions.

scholarly journals Evolution of subhalo orbits in a smoothly growing host halo potential

2021 ◽  
Vol 503 (1) ◽  
pp. 1233-1247
Author(s):  
Go Ogiya ◽  
James E Taylor ◽  
Michael J Hudson
Keyword(s):  
Spatial Distribution ◽  
Essential Role ◽  
Orbital Evolution ◽  
Observational Constraints ◽  
Time Varying ◽  
Cosmological Simulations ◽  
Orbital Parameters ◽  
The Impact ◽  
Spherical Potential ◽  
Radial Action

ABSTRACT The orbital parameters of dark matter (DM) subhaloes play an essential role in determining their mass-loss rates and overall spatial distribution within a host halo. Haloes in cosmological simulations grow by a combination of relatively smooth accretion and more violent mergers, and both processes will modify subhalo orbits. To isolate the impact of the smooth growth of the host halo from other relevant mechanisms, we study subhalo orbital evolution using numerical calculations in which subhaloes are modelled as massless particles orbiting in a time-varying spherical potential. We find that the radial action of the subhalo orbit decreases over the first few orbits, indicating that the response to the growth of the host halo is not adiabatic during this phase. The subhalo orbits can shrink by a factor of ∼1.5 in this phase. Subsequently, the radial action is well conserved and orbital contraction slows down. We propose a model accurately describing the orbital evolution. Given these results, we consider the spatial distribution of the population of subhaloes identified in high-resolution cosmological simulations. We find that it is consistent with this population having been accreted at $z \lesssim 3$, indicating that any subhaloes accreted earlier are unresolved in the simulations. We also discuss tidal stripping as a formation scenario for NGC 1052-DF2, an ultra diffuse galaxy significantly lacking DM, and find that its expected DM mass could be consistent with observational constraints if its progenitor was accreted early enough, $z \gtrsim 1.5$, although it should still be a relatively rare object.

Analysis and Design of Associative Memories Based on Recurrent Neural Networks with Linear Saturation Activation Functions and Time-Varying Delays

2007 ◽  
Vol 19 (8) ◽  
pp. 2149-2182 ◽  
Author(s):  
Zhigang Zeng ◽  
Jun Wang
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Activation Functions ◽  
Analysis And Design ◽  
Design Procedures ◽  
The Neural Network ◽  
Saturation Region ◽  
The Neural Networks

In this letter, some sufficient conditions are obtained to guarantee recurrent neural networks with linear saturation activation functions, and time-varying delays have multiequilibria located in the saturation region and the boundaries of the saturation region. These results on pattern characterization are used to analyze and design autoassociative memories, which are directly based on the parameters of the neural networks. Moreover, a formula for the numbers of spurious equilibria is also derived. Four design procedures for recurrent neural networks with linear saturation activation functions and time-varying delays are developed based on stability results. Two of these procedures allow the neural network to be capable of learning and forgetting. Finally, simulation results demonstrate the validity and characteristics of the proposed approach.

scholarly journals Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Huaiqin Wu ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang ◽  
Luying Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Activation Functions ◽  
Robust Exponential Stability ◽  
Discontinuous Activation ◽  
Interval Neural Networks ◽  
Discontinuous Activation Functions ◽  
Global Robust Exponential Stability

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

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