B reast density is an important risk factor for breast cancer (1-3). Additionally, areas of higher density can mask findings within mammograms, leading to lower sensitivity (4). Many states have passed breast density notification laws requiring clinics to inform women of their breast density (5). Radiologists typically assess breast density by using the Breast Imaging Reporting and Data System (BI-RADS) lexicon, which divides breast density into four categories: A, almost entirely fatty; B, scattered areas of fibroglandular density; C, heterogeneously dense; and D, extremely dense (examples are presented in Fig E1 [supplement]) (6). Unfortunately, radiologists exhibit intra-and interreader variability in the assessment of BI-RADS breast density, which can result in differences in clinical care and estimated risk (7-9).Deep learning (DL) has previously been used to assess BI-RADS breast density for film (10) and full-field digital mammographic (FFDM) images (11-16), with some models demonstrating closer agreement with consensus estimates than individual radiologists (14). To realize the promise of the use of these DL models in clinical practice, two key challenges must be met. First, because digital breast tomosynthesis (DBT) is increasingly used in breast cancer screening (17) due to improved reader performance (18-20), DL models should be compatible with DBT examinations. To aid in radiologist interpretation of breast cancer and breast density, DBT examinations contain twodimensional images in addition to three-dimensional images. These two-dimensional images may be either FFDM images or synthetic two-dimensional mammographic (SM) images derived from the three-dimensional images. Figure E2 (supplement) shows the differences in image characteristics between FFDM and SM images. The relatively recent adoption of DBT at many institutions means that the datasets available for training DL models are often fairly limited for DBT examinations compared with FFDM examinations. Second, DL models must offer consistent performance across sites, where differences in imaging technology, patient demographics, or assessment practices could impact model performance. To be practical, this

Mammography-based screening has helped reduce the breast cancer mortality rate, but has also been associated with potential harms due to low specificity, leading to unnecessary exams or procedures, and low sensitivity. Digital breast tomosynthesis (DBT) improves on conventional mammography by increasing both sensitivity and specificity and is becoming common in clinical settings. However, deep learning (DL) models have been developed mainly on conventional 2D full-field digital mammography (FFDM) or scanned film images. Due to a lack of large annotated DBT datasets, it is difficult to train a model on DBT from scratch. In this work, we present methods to generalize a model trained on FFDM images to DBT images. In particular, we use average histogram matching (HM) and DL fine-tuning methods to generalize a FFDM model to the 2D maximum intensity projection (MIP) of DBT images. In the proposed approach, the differences between the FFDM and DBT domains are reduced via HM and then the base model, which was trained on abundant FFDM images, is fine-tuned. When evaluating on image patches extracted around identified findings, we are able to achieve similar areas under the receiver operating characteristic curve (ROC AUC) of ∼ 0.9 for FFDM and ∼ 0.85 for MIP images, as compared to a ROC AUC of ∼ 0.75 when tested directly on MIP images.

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State estimation is the task of estimating the state of a partially observable dynamical system given a sequence of executed actions and observations. In logical settings, state estimation can be realized via logical filtering, which is exact but can be intractable. We propose logical smoothing, a form of backwards reasoning that works in concert with approximated logical filtering to refine past beliefs in light of new observations.  We characterize the notion of logical smoothing together with an algorithm for backwards-forwards state estimation.  We also present an approximation of our smoothing algorithm that is space efficient. We prove properties of our algorithms, and experimentally demonstrate their behaviour, contrasting them with state estimation methods for planning. Smoothing and backwards-forwards reasoning are important techniques for reasoning about partially observable dynamical systems, introducing the logical analogue of effective techniques from control theory and dynamic programming.

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