Recurrent Network Topology Research Articles

Scaling Up Wave Calculations with a Scattering Network

Wave scattering is a challenging numerical problem, yet it is central to fields as diverse as seismology, fluid dynamics, acoustics, and photonics. Complex structures scatter waves in random yet deterministic ways. Advances in our understanding and control of scattering are key to applications such as deep-tissue microscopy. However, computing the internal fields on a scale relevant to microscopy remains excessively demanding for both conventional methods and physics-based neural networks. Here, we show how coherent scattering calculations can be scaled up to 21 × 10 6 cubic wavelengths by mapping the physics of multiple scattering onto a deterministic neural network that efficiently harnesses publicly available machine learning infrastructure. We refer to this as a scattering network. Memory usage, an important bottleneck to scaling beyond (10 μm)³, is kept to a minimum by the recurrent network topology and the convolutional derivatives it embodies. Tight integration with an open-source electromagnetic solver enables any researcher with an internet connection to compute complex light-wave scattering throughout volumes as large as (130 μm)³ or 25 mm 2 .

Unveiling the alterations in the frequency-dependent connectivity structure of MEG signals in mild cognitive impairment and Alzheimer’s disease

Mild cognitive impairment (MCI) and dementia due to Alzheimer’s disease (AD) are neurological disorders that affect cognition, brain function, and memory. Magnetoencephalography (MEG) is a neuroimaging technique used to study changes in brain oscillations caused by neural pathologies. However, MEG studies often use fixed frequency bands, assuming a common frequency structure and overlooking both subject-specific variations and the potential influence of pathologies on frequency distribution. To address this issue, a novel methodology called Connectivity-based Meta-Bands (CMB) was applied to obtain a subject-specific functional connectivity-based frequency bands segmentation. Resting-state MEG activity was acquired from 161 participants: 67 healthy controls, 44 MCI patients, and 50 AD patients. The CMB algorithm was used to identify “meta-bands” (i.e., recurrent network topologies across frequencies). The meta-bands were used to extract an individualised frequency band segmentation. The network topology of the meta-bands and their sequencing were analysed to identify alterations associated with MCI and AD in the underlying frequency-dependent connectivity structure. We found that MCI and AD alter the neural network topology, leading to connectivity patterns both more widespread in the frequency spectrum and heterogeneous. Furthermore, the meta-band frequency sequencing was modified, with MCI and AD patients exhibiting sequences with increased complexity, suggesting a progressive dilution of the frequency structure. The study highlights the relevance of considering the impact of neural pathologies on the frequency-dependent connectivity structure and the potential bias introduced by using fixed frequency bands in MEG studies.

Neural mechanism of activity spread in the cat motor cortex and its relation to the intrinsic connectivity

Motor cortical points are linked by intrinsic horizontal connections having a recurrent network topology. However, it is not known whether neural activity can propagate over the area covered by these intrinsic connections and whether there are spatial anisotropies of synaptic strength, as opposed to synaptic density. Moreover, the mechanisms by which activity spreads have yet to be determined. To address these issues, an 8 × 8 microelectrode array was inserted in the forelimb area of the cat motor cortex (MCx). The centre of the array had a laser etched hole ∼500 μm in diameter. A microiontophoretic pipette, with a tip diameter of 2-3 μm, containing bicuculline methiodide (BIC) was inserted in the hole and driven to a depth of 1200-1400 μm from the cortical surface. BIC was ejected for ∼2min from the tip of the micropipette with positive direct current ranging between 20 and 40 nA in different experiments. This produced spontaneous nearly periodic bursts (0.2-1.0 Hz) of multi-unit activity in a radius of about 400 μm from the tip of the micropipette. The bursts of neural activity spread at a velocity of 0.11-0.24 ms⁻¹ (mean=0.14 mm ms⁻¹, SD=0.05)with decreasing amplitude.The area activated was on average 7.22 mm² (SD=0.91 mm²), or ∼92% of the area covered by the recording array. The mode of propagation was determined to occur by progressive recruitment of cortical territory, driven by a central locus of activity of some 400 μm in radius. Thus, activity did not propagate as a wave. Transection of the connections between the thalamus and MCx did not significantly alter the propagation velocity or the size of the recruited area, demonstrating that the bursts spread along the routes of intrinsic cortical connectivity. These experiments demonstrate that neural activity initiated within a small motor cortical locus (≤ 400 μm in radius) can recruit a relatively large neighbourhood in which a variety of muscles acting at several forelimb joints are represented. These results support the hypothesis that the MCx controls the forelimb musculature in an integrated and anticipatory manner based on a recurrent network topology

Learning Beyond Finite Memory in Recurrent Networks of Spiking Neurons

We investigate possibilities of inducing temporal structures without fading memory in recurrent networks of spiking neurons strictly operating in the pulse-coding regime. We extend the existing gradient-based algorithm for training feedforward spiking neuron networks, SpikeProp (Bohte, Kok, & La Poutré, 2002), to recurrent network topologies, so that temporal dependencies in the input stream are taken into account. It is shown that temporal structures with unbounded input memory specified by simple Moore machines (MM) can be induced by recurrent spiking neuron networks (RSNN). The networks are able to discover pulse-coded representations of abstract information processing states coding potentially unbounded histories of processed inputs. We show that it is often possible to extract from trained RSNN the target MM by grouping together similar spike trains appearing in the recurrent layer. Even when the target MM was not perfectly induced in a RSNN, the extraction procedure was able to reveal weaknesses of the induced mechanism and the extent to which the target machine had been learned.

Learning Beyond Finite Memory in Recurrent Networks of Spiking Neurons

We investigate possibilities of inducing temporal structures without fading memory in recurrent networks of spiking neurons strictly operating in the pulse-coding regime. We extend the existing gradient-based algorithm for training feedforward spiking neuron networks, SpikeProp (Bohte, Kok, & La Poutré, 2002), to recurrent network topologies, so that temporal dependencies in the input stream are taken into account. It is shown that temporal structures with unbounded input memory specified by simple Moore machines (MM) can be induced by recurrent spiking neuron networks (RSNN). The networks are able to discover pulse-coded representations of abstract information processing states coding potentially unbounded histories of processed inputs. We show that it is often possible to extract from trained RSNN the target MM by grouping together similar spike trains appearing in the recurrent layer. Even when the target MM was not perfectly induced in a RSNN, the extraction procedure was able to reveal weaknesses of the induced mechanism and the extent to which the target machine had been learned.