PULSAR-Net: End-to-End Neural Pulsar Search

• PULSAR-Net is an end-to-end neural network pipeline that processes radio astronomy data to detect pulsars by effectively suppressing RFI and correcting for dispersion.
• The network architecture combines a dedispersion branch with dilated convolutional blocks and a multi-path classification branch using FFT, STFT, and FFA techniques.
• Empirical benchmarks show it operates ~200× real time on consumer GPUs with high accuracy (MCC ≳ 0.9) and a low false positive rate in real pulsar searches.

PULSAR-Net is an end-to-end neural network–based pipeline for conducting pulsar searches in time- and frequency-resolved radio astronomy data. The framework is designed to efficiently suppress a broad range of radio-frequency interference (RFI) and instrumental artifacts while simultaneously correcting for unknown interstellar dispersion, a crucial challenge in pulsar detection. After initial training, PULSAR-Net operates in real time on standard consumer-grade GPUs and integrates classical periodicity-search tools (FFT, STFT, FFA) within a deep learning context to classify pulsar candidates with high accuracy and extreme computational efficiency (Künkel et al., 2021).

1. Data Preprocessing

PULSAR-Net processes 8-bit filterbank data recorded with Arecibo/WAPP, consisting of 256 frequency channels across 100 MHz and 64 μs sampling over 268 s per beam. Data are first downsampled:

• Frequency: 256→16 channels (uniform averaging), followed by removal of the lowest and highest channel to result in 14 channels.
• Time: 64 μs is downsampled by a factor of 10 to 640 μs per sample, yielding 400,000 time steps.

The final preprocessed input tensor $x_0$ has the shape $(14, 400{,}000)$. Normalization is performed globally: $x' = (x - \mu) / \sigma$, with $\mu$ and $\sigma$ the mean and standard deviation over all elements. A fixed dropout rate $p=0.1$ is applied immediately after normalization to regularize the network.

2. Network Architecture

PULSAR-Net comprises two principal components: a dedispersion branch and a multi-path classification branch.

2.1 Dedispersion Branch

Modeled after temporal convolutional networks (TCNs), this branch converts the 2D spectrogram to one or two dedispersed 1D time series.

• Initial Downsampling Convolution: 1D conv with 14 input channels, 64 output channels, kernel size 4, stride 4, reducing time length to 100,000. ReLU activation and GroupNorm are applied.
• Dilated Convolutional Blocks: Two blocks of 5 layers each.
  • Block 1: Exponential dilations $d = 2^{\ell}$ ($\ell = 0 \ldots 4$), kernel size 4, 64 channels.
  • Block 2: $d = 4^{\ell}$ ($\ell = 0 \ldots 4$), otherwise same.
  • Each layer uses non-causal convolution, ReLU, GroupNorm, and a residual skip.
• Pointwise and Output Convs: 1×1 conv layers maintain/reduce channel dimensions (to $(14, 400{,}000)$0 or $(14, 400{,}000)$1 outputs; one- or two-channel model).

Output: $(14, 400{,}000)$2, a dedispersed time series for each output channel.

2.2 Classification Branch

Three parallel classifier modules operate on $(14, 400{,}000)$3, each producing a scalar pulsar "score". These scores are then linearly combined with learned weights and classified using a softmax. The classifiers are:

Branch	Input Features	Specialized Processing
FFT	Full-length dedispersed signal	Harmonic summing, 2D conv, max-pool
STFT	Time-chunked dedispersed signal	Multi-chunk FFT, harmonic summing, 2D conv, max-pool
FFA	Three period ranges	FFA (riptide), profile thresholding, conv, max-pool

• FFT Classifier: Computes the magnitude FFT ($(14, 400{,}000)$4 40,000 bins). Performs incoherent harmonic summing over 5 harmonics (stretching by 1, 2, 4, 8, 16), rescaled to equalize noise. Output features are processed by a small 2D conv net and global max-pooled.
• STFT Classifier: Splits $(14, 400{,}000)$5 into 1, 2, and 4 non-overlapping time segments, performs FFT on each, then applies the same harmonic summing as FFT classifier. 2D conv and pooling produce the final score.
• FFA Classifier: Uses "riptide" to apply the fast folding algorithm to $(14, 400{,}000)$6 over three period ranges:
  1. 0.03–0.12 s (bins 10–14)
  2. 0.12–0.48 s (bins 40–44)
  3. 0.48–1.1 s (bins 160–176) Each FFA output is mean-subtracted with threshold $(14, 400{,}000)$7 ($(14, 400{,}000)$8) and $(14, 400{,}000)$9. Profiles are concatenated, passed through a conv net and max-pooled.

Final logits: $x' = (x - \mu) / \sigma$0

$x' = (x - \mu) / \sigma$1

Softmax yields $x' = (x - \mu) / \sigma$2.

3. Training Procedures and Loss Functions

3.1 Dataset Construction

The training set combines 529 PALFA/WAPP beams devoid of any known pulsars (noise) with 8,620 simulated injections of pulsar signals covering uniform periods (30–650 ms, DM from 80 to 700 pc cm⁻³). Amplitudes are capped to avoid unrealistic pulse strength. The test set includes 24 real pulsar beams and 81 noise beams.

3.2 Labeling and Augmentation

Half of training samples are pure noise (label 0), half are noise plus a simulated pulsar (label 1). Pulsar injections use: $x' = (x - \mu) / \sigma$3 where $x' = (x - \mu) / \sigma$4, with $x' = (x - \mu) / \sigma$5 rising during training.

3.3 Optimization Objectives

• Reconstruction Loss:

$x' = (x - \mu) / \sigma$6

where $x' = (x - \mu) / \sigma$7 is a Gaussian-convolved pulse train, $x' = (x - \mu) / \sigma$8 is the output channel number. For two-channel models, $x' = (x - \mu) / \sigma$9 assigns pulses differentially by DM.

• Classification Loss: Cross-entropy for each branch and for the combined output,

$\mu$0

• Total Loss:

$\mu$1

3.4 Three-Stage Training

1. Stage 1 (Warm-up): Input downsampling to 100,000, $\mu$2 from 0.9 to 15, $\mu$3, $\mu$4 (no FFA).

2. Stage 2 (Full-length): Restore full input, $\mu$5 from 15 to 35, $\mu$6, dedisp branch frozen for 2 epochs.
3. Stage 3 (FFA Integration): Add FFA classifier, fix $\mu$7, dedisp branch frozen, retrain only classifier weights.

Optimizer: Adam (lr$\mu$8$\mu$9), batch size 15. Five-fold cross-validation, 80/20 split. Training durations: ≲3 h (Stage 1), ≲13 h (Stage 2), ≲50 h (Stage 3) on Nvidia V100.

4. RFI Suppression and Dispersion Correction

No explicit RFI-masking layers are used. The dedispersion branch, trained end-to-end via reconstruction and classification objectives, is incentivized to both reconstruct clean pulse trains and ignore noise-only (including RFI) inputs. GroupNorm and dropout add regularization, mitigating overfitting to specific RFI patterns.

RFI suppression results in a lower FFA noise floor compared to standard dedispersion methods, even with classical zero-DM filtering, yielding boosted pulsar S/N. Dispersion correction is achieved by the TCN's large receptive field, so a range of DMs is handled in one forward pass—avoiding brute-force shift-and-sum strategies. The two-channel output structure specializes in low- vs. high-DM responses: $\sigma$0 where $\sigma$1 is the dispersion delay between channels $\sigma$2 and $\sigma$3 at dispersion measure DM.

5. Integration with Classical Periodicity Search Methods

Dedispersed output is passed directly to periodicity search modules (FFT, STFT, FFA), embedded in the PyTorch framework. Harmonic summing, time-window splitting, and FFA period-range searches are constructed as differentiable modules, except for the wrapped "riptide" FFA whose gradients are not propagated. The final decision combines the three classifiers' scores via a linear model and softmax.

6. Empirical Performance and Benchmarks

On 105 test beams (469 minutes), PULSAR-Net processes data in approximately 29 s (no FFA) or 105 s (with FFA), constituting $\sigma$4200× real time on a consumer GPU. In held-out real data, the two-channel model (ensemble of 5 cross-validated nets over 5 overlapping segments) identified 22/24 real pulsars with only 1 false positive in 81 noise beams (false positive rate $\sigma$51.2%). Matthews correlation coefficient (MCC) reaches $\sigma$60.9 in Stages 2 and 3. FFA S/N metrics for real pulsars show the PULSAR-Net output's median S/N matches or exceeds dedispersion at the true DM, attributed to effective RFI suppression.

7. Ablation Studies and Limitations

Two-channel dedispersion improves FFA S/N for high-DM pulsars. End-to-end training (joint reconstruction and classification) outperforms two-step training for faint signals, and removing classification loss degrades the utility of $\sigma$7 for weak pulses. Limitations:

• Detects only the strongest pulse train per beam (no support for multiple candidates).
• FFA gradients are not propagated, slowing Stage 3.
• Not evaluated on accelerated (binary) pulsars.
• Full-resolution input exceeds common GPU memory limits; longer-term solutions may require time/frequency splitting.
• Retraining is needed for each survey's specifics (band, resolution, RFI environment).

PULSAR-Net demonstrates that a dilated-convolutional dedispersion network, coupled with integrated periodicity-search classifiers, can achieve high-throughput, low-false-positive pulsar searches with competitive or superior RFI rejection and S/N recovery relative to conventional approaches (Künkel et al., 2021).