2.1. RFI detection with neural networks

The most popular base architecture for supervised RFI detection with neural networks is UNet, a neural network designed for image segmentation. Most works modify the original network design, improvements to the training routine, or both such as Yang et al. (Reference Yang, Yu, Xiao and Zhang2020). As is the case in all ML works, data is central to overall performance. Many works use simulated data for training, providing high confidence in the labels but limiting the model to the constraints of the simulator’s model. On the other hand, works using real data face a choice of using a traditional algorithm to generate training flags or using expertly labelled data. Using traditional algorithms to generate training masks on simulated or real data is straightforward. It yields abundant training data but constrains the ANN to learn from the behaviour of the traditional algorithm. Using expertly labelled data, arguably the most accurate by definition, is expensive, scarce, and, therefore, strains the training scheme. An alternate strategy is to train on simulated data and then perform transfer learning with small amounts of expertly labelled real data, aiming to combine the benefits of all worlds (e.g. Vafaei Sadr et al. Reference Vafaei Sadr, Bassett, Oozeer, Fantaye and Finlay2020) often termed Sim2Real. This Sim2Real method often struggles with a reality gap between the simulation behaviours and the real world, adding an additional challenge.

Mesarcik et al. (Reference Mesarcik, Boonstra, Ranguelova and van Nieuwpoort2022a) introduce a particularly interesting approach, where a traditional flagging algorithm generates flags with many false positives to select uncontaminated patches with high certainty, training an auto-encoder with these uncontaminated patches, then using this model to perform RFI detection as a downstream inference task, transforming the task from a semantic segmentation problem into an anomaly detection problem. By adopting this method, an abundance of training data is available, agnostic to the noise sources in the real data. This approach serves as the basis for our SNN conversion. However, the anomaly detection routine, which involves searching through latent representations of other examples, is iterated upon with our SNN approach while retaining the appealing innovations introduced by this method.

Developing a general-purpose model capable of producing RFI masks for any telescope across a wide range of frequencies and configurations remains a grand challenge in applying ML and NNs to RFI detection. Part of the enduring appeal of using traditional algorithmic approaches is their flexibility. Despite extensive efforts, currently, no method, traditional or NN-based, achieves an F1-score above $0.6$ on a real, representative dataset (Mesarcik et al. Reference Mesarcik, Boonstra, Ranguelova and van Nieuwpoort2022a). As we explore and develop new approaches, achieving better performance on real-world data becomes a crucial focus in advancing RFI detection techniques using ML and neural networks in radio astronomy.

2.2. Spiking Neural Networks

SNNs are ANNs that closely mimic the behaviour of biological neurons, enabling efficient and accurate processing of complex data sets. Unlike traditional ANNs, which use continuous activation functions, SNNs use discrete events called spikes. Incoming spikes contribute to a neuron’s membrane potential, and when the potential reaches a threshold, the neuron emits a spike. The precise mathematical behaviours of how the membrane potential increases with spike arrivals and decays over time hold much of the basis for SNNs and contemporary ANNs.

The leaky-integrate-and-fire (LiF) neuron is a simple yet accurate model of this biological process, resembling a low-pass filter circuit with a resistor R and capacitor C. The following RC circuit equation models the dynamics of the passive membrane potential for a single neuron subject to an input current I:

(1) \begin{equation} \tau\frac{dU(t)}{dt} = -U(t) + I_{in}(t)R,\end{equation}

where $\tau = RC$ is a fixed time constant. Abbott & Dayan (Reference Abbott and Dayan2001) provide a comprehensive derivation of spiking neuron dynamics and their relationship to ANNs.

SNNs’ close resemblance to biological neurons allows them to excel at tasks challenging for other neural network types as Deng et al. (Reference Deng2020) show, particularly real-time spatio-temporal data processing. It is precisely the time-varying nature of spiking neurons that contributes to their ability to capture time-varying details of ingested data. This spiking behaviour enables various information encoding techniques based on the timings of individual spikes or patterns of spikes, unlike artificial neurons in most contemporary deep learning approaches that operate only on an equivalent to rate-based encoding.

It is worth noting that these two neural network models are equivalent, with ANNs better suited for implementation on existing computing hardware. The time-varying nature of SNNs requires specialised hardware to realise efficiently but consumes orders of magnitude less energy in the process, Schuman et al. (Reference Schuman2022) give a wide and long-range view of a future for neuromorphic computing. The equivalence rooted in the derivation of sigmoidal neurons found in ANNs from spiking neurons permits the conversion of trained ANNs back to an SNN as Rueckauer et al. (Reference Rueckauer, Lungu, Hu and Pfeiffer2016) summarise.

The development of neuromorphic hardware and SNNs has occurred alongside contemporary deep learning and ANN research. James et al. (Reference James2017) summarises the main developments throughout the last century. The increasing importance energy efficiency plays in modern computing reignites more widespread interest in SNNs. While energy improvements without rigorous benchmarking on real hardware are difficult, Lemaire et al. (Reference Lemaire, Tanveer, Agarwal, Ozawa, Ekbal and Jatowt2023) provide an analytical approach to estimate the energy use of equivalently sized ANNs and SNNs and show an improvement of six to eight times greater efficiency for SNNs on 45nm CMOS hardware.

The advancement in neuromorphic hardware and SNNs holds promise for tackling energy-intensive tasks while preserving the advantages of spiking behaviours inspired by biological neurons. Neuromorphic hardware combined with a suitable SNN-based technique would enable real-time and adaptable RFI detection, with orders of magnitude less power consumption than contemporary ANN and classical methods.

2.3. Anomaly detection with SNNs

Anomaly detection is a problem often encountered in time-varying domains. As such, there are several works exploring anomaly detection with SNNs. Notably, many anomaly detection works employing SNNs exist in sensor-based environments and on one-dimensional time-varying data streams. In healthcare, Bauer et al. (Reference Bauer, Muir and Indiveri2019) employ a recurrent SNN and custom neuromorphic processor to preprocess electrocardiograms for detecting anomalous behaviour. In industrial settings, Demertzis et al. (Reference Demertzis, Iliadis, Spartalis, Boracchi, Iliadis, Jayne and Likas2017) implement one-class anomaly detection with SNNs for industrial control systems, while Demertzis et al. (Reference Demertzis, Iliadis and Bougoudis2020) propose a semi-supervised one-class anomaly detection scheme using SNNs in industrial environments. Dennler et al. (Reference Dennler, Haessig, Cartiglia and Indiveri2021) design neuromorphic hardware for real-time detection of anomalous vibrations, applicable to various industrial settings.

The conversion of ANNs to SNNs for anomaly detection is also explored. Jaoudi et al. (Reference Jaoudi, Yakopcic and Taha2020) convert a traditional auto-encoder to an SNN to detect in-vehicle cyberattacks, achieving comparable performance to the original converted ANN in analysing one-dimensional, time-varying data. Paul et al. (Reference Paul, Tajin, Das, Mongan and Dandekar2022) convert a one-dimensional convolutional neural network to an SNN for anomaly detection in the breathing patterns of newborn infants.

Several studies present hardware implementations for real-time anomaly detection using SNNs. Chen & Qiu (Reference Chen and Qiu2017) propose a component library and design method for implementing real-time anomaly detection on IBM’s TrueNorth neuromorphic chip. Ronchini et al. (Reference Ronchini2022) develop wearable neuromorphic hardware for detecting anomalies in biological measurements in healthcare settings.

Other notable works include Chen et al. (Reference Chen2018) presenting an anomaly recognition and detection framework for incremental online learning from data streams, Stratton et al. (Reference Stratton, Wabnitz and Hamilton2020) performing anomaly detection on text streams with SNNs, Maciag et al. (Reference Maciag, Kryszkiewicz, Bembenik, Lobo and Del Ser2021) providing an online evolving SNN method for detecting anomalies in streaming data without supervision, Phusalculkajom et al. (Reference Phusalculkajom2022) using SNNs to generate fuzzy logic intervals for detecting anomalies in rail networks, and Baessler et al. (Reference Baessler, Kortus and Guehring2022) proposing a multivariate anomaly detection scheme based on SNNs.

Our approach uniquely sits as a conversion of an existing auto-encoder performing anomaly detection on two-dimensional spectrograms.

2.4. Auto-encoders with SNNs

Auto-encoders are a neural network architecture designed to extract signals from high-dimensional feature space without supervision. The encoder compresses raw input data into a latent space, and the decoder reconstructs the original input data from this latent representation. Training an auto-encoder minimises the difference between the reconstruction and input data, enabling it to learn an efficient representation of the input data.

Efforts have been made to craft SNN-based auto-encoders to achieve energy-efficient and sparse latent representations. For instance, Alom & Taha (Reference Alom and Taha2017) trains an auto-encoder for detecting anomalous network packets, converting it to an SNN using discrete vector factorisation, which is then simulated and executed on IBM TrueNorth hardware. Yin & Gelenbe (Reference Yin and Gelenbe2019) combine an auto-encoder architecture with a spiking random neural network. Their approach performs well on typical image datasets. Roy et al. (Reference Roy, Panda and Roy2019) develop a spiking auto-encoder to synthesise audio inputs into image outputs. Stratton et al. (Reference Stratton, Wabnitz and Hamilton2020) perform anomaly detection on text streams using an SNN auto-encoder. Kamata et al. (Reference Kamata, Mukuta and Harada2022) present a fully spiking variational auto-encoder, enabling variational learning through random sampling of the latent space. Stewart et al. (Reference Stewart, Danielescu, Shea and Neftci2022) create a hybrid SNN auto-encoder specialised in encoding event-based data from vision sensors.

In our work, we leverage the time-varying nature of the latent state built by an SNN during inference to simplify the downstream anomaly detection scheme.

4.1. Tabascal

We additionally create and publish openly a new dataset generated using the Tabascal simulator written by Finlay et al. (Reference Finlay, Bassett, Kunz and Oozeer2023) and emulating the MeerKAT telescope. The main focus of this dataset is to provide a large-array mid-frequency dataset that includes moving low-orbit satellite RFI sources, which are expected to become increasingly troublesome in the coming years. The majority of simulation parameters come from Finlay et al. (Reference Finlay, Bassett, Kunz and Oozeer2023) which are in turn derived from MeerKAT documentation. We simulate for 512, two second integration steps over 512 frequency channels from $1.227$ to $1.334$ GHz of 209 KHz width, average the visibility amplitude over 16 samples per integration and finally sample 512 baselines to produce $512 \times 512 \times 512 \times 1$ datasets. The resulting spectrograms contain RFI localised in narrow frequency bands but present for the entire simulation duration. While this dataset is not truly indicative of practical observation, and in practice, these frequencies may be removed entirely without the need for more sophisticated methods, it creates a difficult task for ML methods to distinguish the fine boundary between the contaminated and uncontaminated region precisely.

Table 2 contains the size of each dataset and the proportion of RFI contamination.

Table 2. Description of each dataset used for training and testing. We reproduce values for the HERA and LOFAR datasets from Mesarcik et al. (Reference Mesarcik, Boonstra, Ranguelova and van Nieuwpoort2022a).

Tabascal’s architecture produces sky and RFI visibilities separately, which we then use to produce input and label data. Access to machine-precision ground truth in the RFI visibilities introduces an interesting problem; the vast majority of affected pixels are perturbed by incredibly small values close to zero. Therefore, we can threshold the ground-truth data to provide the same dataset at several difficulty levels. Our uploaded datasets contain the original RFI visibility data, masks without thresholds, with thresholds of 0, 1, 2, 4, 8, 16 and finally thresholded above the median value of the sky visibilities, as a rough analogue of human perception. We use a simulation containing two satellite sources similar to GPS and GLONASS satellites and three static ground-based RFI sources.

The resulting dataset exhibits RFI strongly localised in time but over all frequencies and thus provides a challenge for the NLN method, which will never be exposed to heavily contaminated data during training.