SIGMA: Single Interpolated Generative Model for Anomalies

TL;DR

The paper tackles the computational bottleneck of resonant anomaly detection by proposing SIGMA, which trains a single flow on all data and uses parameter interpolation to the signal region, thereby avoiding per-SR retraining. It builds on conditional flow matching to approximate the background distribution, incorporating a frequency embedding to capture high-frequency components associated with localized signals. The key contributions are the data-driven, all-data background template with fast SR interpolation, a comparative analysis of CR-based and SIGMA interpolation in terms of SIC performance, and substantial training-time gains over prior methods. This approach enables scalable, model-agnostic bump-hunt analyses on large datasets while preserving sensitivity to localized anomalies, with $R_{ m optimal}(x)=\frac{p_{\rm data}(x)}{p_{\rm background}(x)}$ guiding the detection framework.

Abstract

A key step in any resonant anomaly detection search is accurate modeling of the background distribution in each signal region. Data-driven methods like CATHODE accomplish this by training separate generative models on the complement of each signal region, and interpolating them into their corresponding signal regions. Having to re-train the generative model on essentially the entire dataset for each signal region is a major computational cost in a typical sliding window search with many signal regions. Here, we present SIGMA, a new, fully data-driven, computationally-efficient method for estimating background distributions. The idea is to train a single generative model on all of the data and interpolate its parameters in sideband regions in order to obtain a model for the background in the signal region. The SIGMA method significantly reduces the computational cost compared to previous approaches, while retaining a similar high quality of background modeling and sensitivity to anomalous signals.

Figures (9)

• Figure 1: ResNet architecture
• Figure 2: For $N_{sig}=3000$ and $m \in \rm SR$, we show: (Top Panel) The histograms of the samples of the features. The shaded blue histogram is the background present in the data. The shaded yellow is the signal added to the background. (Bottom Panel) The pulls with respect to the background distribution.
• Figure 3: (Left) SIC curves for a signal injection of $1000$ (which corresponds to $S/\sqrt{B} \approx 2.2$). (Right) SIC at $\epsilon_B=0.001$ for different signal injections. While $v^{\rm CR}_{\theta}$ retains the best signal sensitivity, the much more computationally efficient $v^{\rm int}_{\theta}$ (context) is only a little bit worse by comparison. Meanwhile, $v^{\rm int}_{\theta}$ (linear) shows considerably worse performance at lower signal strengths.
• Figure 4: The SIC curve for background template obtained $v^{\rm data}_{\theta}$ (in black, solid) and $\tilde{v}^{\rm data}_{\theta}$ (in black, dotted), trained on data without signal injection are similar to IAD. However, comparing the same models when trained with signal injection, show that the SIC for $v^{\rm data}_{\theta}$ (with frequency embedding), is worse than $\tilde{v}^{\rm data}_{\theta}$ (without frequency embedding). This is because $v^{\rm data}_{\theta}$ learns the small signal component in data, better than $\tilde{v}^{\rm data}_{\theta}$. Hence, the frequency embedding is crucial for the model to best learn the data.
• Figure 5: The weight distributions for classifier trained on samples from $v^{\text{data}}$ (Top Left)/ $v^{\text{CR}}$ (Bottom Left)/ $v^{\text{int}}$ (context) (Top Right)/ $v^{\text{int}}$ (linear) (Bottom Right) vs true background. The AUC of $v^{\rm int}_{\theta}$ (context) is slightly worse than $v^{\rm data}_{\theta}$, which produces a long tail for $\log (\text{weight}) > 0$ corresponding to the signal.