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CMU DeepLens: Deep Learning For Automatic Image-based Galaxy-Galaxy Strong Lens Finding
Francois Lanusse, Quanbin Ma, Nan Li, Thomas E. Collett, Chun-Liang Li, Siamak Ravanbakhsh, Rachel Mandelbaum, Barnabas Poczos
TL;DR
Large surveys are expected to contain many galaxy-scale strong lenses, creating a need for efficient and quantifiable detection despite challenging imaging trade-offs. CMU DeepLens uses supervised deep residual networks to learn lens-relevant features from training data. On simulated LSST exposures, it reaches 90% completeness at 99% non-lens rejection for lenses above the stated size and signal-to-noise thresholds.
Problem
Large surveys are expected to contain unprecedented numbers of galaxy-scale strong lenses, making efficient detection and an easily quantifiable selection function important.
Source: §1 · pp. 1–2Method
CMU DeepLens is a supervised lens finder based on deep residual networks that learns relevant detection features from training data.
Source: §1 · p. 2Results
At a 99% rejection rate of non-lenses, completeness is 90% for lenses with Einstein radii larger than 1.43′′ and lensed-image S/N larger than 20 on single LSST exposures.
Source: §7 · p. 11Takeaways & Limitations
Given realistic simulations, fully automated lens-finding methods have selection functions that are easier to quantify.
Source: §7 · p. 11The simulations omit likely contaminants and cannot distinguish models of very different complexity, so reported performance is optimistic for real data.
Source: §6 · p. 9, §7 · p. 11
Abstract
from arXiv · showhide
Galaxy-scale strong gravitational lensing is not only a valuable probe of the dark matter distribution of massive galaxies, but can also provide valuable cosmological constraints, either by studying the population of strong lenses or by measuring time delays in lensed quasars. Due to the rarity of galaxy-scale strongly lensed systems, fast and reliable automated lens finding methods will be essential in the era of large surveys such as LSST, Euclid, and WFIRST. To tackle this challenge, we introduce CMU DeepLens, a new fully automated galaxy-galaxy lens finding method based on Deep Learning. This supervised machine learning approach does not require any tuning after the training step which only requires realistic image simulations of strongly lensed systems. We train and validate our model on a set of 20,000 LSST-like mock observations including a range of lensed systems of various sizes and signal-to-noise ratios (S/N). We find on our simulated data set that for a rejection rate of non-lenses of 99%, a completeness of 90% can be achieved for lenses with Einstein radii larger than 1.4" and S/N larger than 20 on individual $g$-band LSST exposures. Finally, we emphasize the importance of realistically complex simulations for training such machine learning methods by demonstrating that the performance of models of significantly different complexities cannot be distinguished on simpler simulations. We make our code publicly available at https://github.com/McWilliamsCenter/CMUDeepLens .
1 INTRODUCTION
Large surveys will contain many galaxy-scale strong lenses, but their imaging presents trade-offs that make efficient, quantifiable detection challenging. CMU DeepLens applies supervised deep residual networks to lens finding, learning relevant features from training data rather than relying on predefined features or physical models.
1 INTRODUCTION
- Strong lensing probes massive galaxies’ gravitational potential and can constrain cosmology through lensed-quasar time delays or lens populations.The introduction cites ensemble constraints on massive elliptical galaxies’ total matter profiles from SLACS lenses.Source: §1 · p. 1
- LSST is low resolution despite six photometric bands, while Euclid offers higher resolution in only one optical passband; neither provides high-resolution multicolor imaging.WFIRST near-infrared multiband data are closer to the stated ideal, though they may probe different galaxy populations.Source: §1 · p. 2
- Automated lens searches have used arc or ring morphology, lens-light subtraction, or physical lens modeling, but galaxy light can obscure galaxy-scale arcs.The approaches include multi-band differencing, PCA-based lens-light subtraction, and fitting source and deflector models.Source: §1 · p. 2
- Prior automated searches can leave substantial review workloads: ARCFINDER produced about 1,000 candidates per square degree, while RingFinder produced 18.The cited estimates imply substantial human-time demands if such inspection rates scale to LSST or Euclid survey areas.Source: §1 · p. 2
- Crowdsourced visual inspection found 59 candidates missed by robotic searches and missed 20 known lenses, indicating complementarity between the approaches.The project involved 430,000 CFHTLS images reviewed by 37,000 citizen scientists.Source: §1 · p. 2
- Deep learning is promising for this challenging image-classification task, with potential to reduce reliance on non-expert visual inspection in future surveys.The paper situates lens finding among deep-learning applications in galaxy morphology, star-galaxy classification, photometric redshifts, and galaxy-image generation.Source: §1 · p. 2
- CMU DeepLens uses deep residual networks for lens finding, and its supervised approach learns relevant features from training data rather than assuming specific features or physical models.The authors also report that it outperformed most CNN-based lens finders in a blind Euclid challenge.Source: §1 · p. 2
2 DEEP LEARNING BACKGROUND
The background introduces neural networks, convolutional image processing, and residual learning as the foundations for DeepLens. It explains how these architectures address image structure and the training difficulties of deep networks.
2.1 The Deep Learning Revolution
- A fully connected layer combines outputs from the preceding layer using learned weights and biases, then applies an activation function; training adjusts parameters by stochastic gradient descent and backpropagation.The section presents this as the neural-network foundation before introducing convolutional architectures.Source: §2.1 · p. 3
- Deep networks can represent increasingly complex mappings, but vanishing gradients made them difficult to train until improved activations, larger datasets, regularisation, and GPU computing enabled deeper models.ReLU avoids saturation and supports stronger gradients during backpropagation.Source: §2.1 · pp. 3–4
2.2 Convolutional Neural Networks
- Convolutional neural networks apply learned local filters to images, then combine convolution and pooling layers to build feature maps at progressively coarser resolutions.The illustrated layer maps an RGB image to eight feature maps using distinct 3x3 filters.Source: §2.2 · p. 4, Figure 2 · p. 4
2.3 Deep Residual Networks
- Residual units learn the difference between input and output mappings through shortcut connections, and pre-activated bottleneck units use 1x1, 3x3, and 1x1 convolutions with fewer parameters than two 3x3 convolutions.Pre-activation applies the activation before convolution; the downsampling variant uses a strided convolution and can increase output depth.Source: §2.3 · pp. 4–5
3 CMU DEEPLENS
This section describes CMU DeepLens, a residual-network classifier for strong-lens detection, and its training and implementation. The model outputs a lens probability and uses image preprocessing and augmentation during training.
3.1 Architecture
- The 46-layer DeepLens model processes single- or multi-band images through a convolutional layer and progressively coarser pre-activated bottleneck residual units, then outputs a lens probability.Its final fully connected layer uses a sigmoid activation; ELU is used elsewhere.Source: §3.1 · p. 5, Figure 4 · p. 6
3.2 Classification cost function
- The classifier is trained with binary cross-entropy, interpreted as the cross entropy between the true label distribution and the model's estimated probabilities.The objective is the negative log-likelihood over the training instances.Source: §3.2 · pp. 5–6
3.3 Preprocessing and data augmentation
- Preprocessing subtracts the training-set mean, normalizes by per-band noise standard deviation, clips extreme values, and sets masked pixels to zero; augmentation randomizes rotations, mirroring, and zoom.The authors report no significant performance impact when the preprocessing steps are omitted.Source: §3.3 · p. 6
3.4 Training procedure
- Training uses random-normal initialization, 120 epochs of mini-batches of 128 images, and ADAM with a learning rate starting at 0.001 and divided by 10 every 40 epochs.All layers are trained from scratch.Source: §3.4 · p. 6
3.5 Implementation
- On a Titan X (Pascal) GPU, training on 16,000 45 × 45 images takes about one hour, while classification takes approximately 350 µs per image.The authors report no evidence of overfitting on this dataset and hardware.Source: §3.5 · p. 6
4 STRONG LENSING SIMULATIONS
The simulations combine mock LSST observations with realistic lens and source populations. They model elliptical lenses, add line-of-sight galaxies, and create single-exposure and stacked images under varying observing conditions.
4 STRONG LENSING SIMULATIONS
- The pipeline uses PICS for lens ray-tracing and LensPop for mock observing, with half of the simulated images containing a strongly lensed background galaxy.All images include a central early-type galaxy and additional field galaxies.Source: §4 · p. 7
4.1 Lens galaxy model
- Lens galaxies use a Singular Isothermal Ellipsoid mass profile, with sampled velocity dispersions of 150–350 km/s, axis ratios of 0.5–1.0, lens redshifts of 0.2–0.7, and sources fixed at redshift 2.0.Lens light uses an elliptical Sérsic profile matched to COSMOS galaxy properties.Source: §4.1 · p. 7
4.2 Background sources and additional line-of-sight galaxies
- Detailed CANDELS galaxies are rescaled to source redshift 2.0 and ray-traced near lens caustics, while Hubble Ultra Deep Field galaxies add line-of-sight complexity without being lensed.The fields contain one deflector on one lens plane, without perturbative weak lensing or compound lensing.Source: §4.2 · p. 7
4.3 Mock LSST observations
- Mock LSST images include pixel resampling, Gaussian PSF convolution, Poisson sky-plus-signal noise, and Gaussian read-out noise; exposures vary stochastically in seeing and sky brightness.The study compares the best-seeing single exposure with a stack degraded to the worst seeing; arc S/N is defined using total arc flux, image noise, and source-pixel count.Source: §4.3 · pp. 7–8
5 RESULTS
DeepLens is evaluated on held-out simulated images, with completeness measured against false-positive rate across cuts in Einstein radius and source S/N. At a 1% false-positive rate, performance is high for sufficiently large or bright arcs, and stacked images can recover some poorly resolved lenses.
5 RESULTS
- The test trains each single-exposure and stack model on 16,000 images and evaluates it on 4,000, measuring completeness and contamination as threshold-dependent TPR and FPR.The 1% FPR threshold is selected to represent an admissible survey contamination level, with the threshold derived from simulations.Source: §5 · p. 8
- 90% completeness is reached at 1% FPR for single exposures with arcs larger than 1.4″, and for stacks with arcs that size when S/N exceeds 80.The two image strategies show very similar behavior; the reported single-exposure result uses the fiducial 1% FPR threshold.Source: §5 · p. 8, Figure 6 · p. 9
- DeepLens recovers some stacked-image lenses with Einstein radii below the median seeing at the fiducial 1% FPR threshold.Figure 7 compares the simulated and recovered populations by S/N and Einstein radius.Source: §5 · p. 8, Figure 7 · p. 9
- False positives are dominated by multiple nearby objects, which the authors expect multi-band colour information to help distinguish from real lenses.The highest-probability examples include true and false positives from both simulation sets.Source: §5 · p. 9
6 DISCUSSION
On the supplied simulations, DeepLens and a classical CNN perform equally despite DeepLens’s greater depth, underscoring the need for more realistic simulations to reveal model differences. The discussion also considers model capacity, image color, and extending detection to rarer lens types.
6 DISCUSSION
- The simulations are too simple to distinguish model complexity, while more realistic simulations could expose simpler models’ limits and help deeper models find robust features.The authors say this shifts much of supervised-learning effort toward producing realistic training simulations.Source: §6 · pp. 9–10
- On our simulations, DeepLens and a CNN following Petrillo et al. (2017) exhibit exactly the same ROC performance on the same training and testing sets of single-epoch images, using the full lens sample without S/N or Einstein-radius cuts.Source: §6 · p. 10, Figure 9 · p. 10
- The fiducial model has 46 layers but could be made substantially deeper to handle more realistic simulations and data.Similar architectures have been trained up to a thousand layers.Source: §6 · p. 10
- Single-band morphology demonstrates lens identification without color, while the model can handle multi-band images and the authors expect color to improve performance.The single-band setting is particularly relevant to Euclid’s VIS images.Source: §6 · p. 10
- The method could target rare exotic lenses by replacing binary classification with multi-class classification and using a weighted cost function to promote their sample purity.Examples include double source plane lenses, lensing catastrophes, and lensed supernovae.Source: §6 · p. 11
7 CONCLUSIONS
CMU DeepLens is a fully automated deep-learning lens finder evaluated on LSST-like simulations. It reaches 90% completeness at 99% non-lens rejection for specified lenses, but the authors caution that simple simulations make real-data performance optimistic and do not reveal model-complexity differences.
7 CONCLUSIONS
- CMU DeepLens is a fully automated strong-lens finder based on deep learning that requires no manual tuning or human intervention beyond training.The authors describe its selection function as easier to quantify given realistic simulations.Source: §7 · p. 11
- At 99% non-lens rejection, completeness reaches 90% for simulated single-exposure lenses with Einstein radii above 1.43″ and lensed-image S/N above 20.The evaluation uses simple but non-trivial LSST g-band strong-lensing simulations.Source: §7 · p. 11
- The reported completeness is optimistic for real data because the simulations omit likely contaminants, and these simulations cannot distinguish the deeper residual network from a conventional CNN.On more realistic challenge simulations, the residual network benefited from its added complexity and outperformed conventional CNNs.Source: §7 · p. 11
- The results point to shifting part of the effort from model development to producing realistic simulations for supervised learning.The authors emphasize realism for both developing and applying these methods.Source: §7 · p. 11
- The code is publicly available, and the simulations used in the work are slated for release with an upcoming paper.The simulations are attributed to Avestruz et al. (2017, in prep).Source: §7 · p. 11