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1. Computing transition path theory quantities with trajectory stratification

   https://doi.org/10.1063/5.0087058  

   Vani, Bodhi P.; Weare, Jonathan; Dinner, Aaron R. (July 2022, The Journal of Chemical Physics)

   Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low probability segments. However, it can be challenging to apply transition path theory to data from such methods because determining whether configurations and trajectory segments are part of reactive trajectories requires looking backward and forward in time. Here, we show how this issue can be overcome efficiently by introducing simple data structures. We illustrate the approach in the context of nonequilibrium umbrella sampling, but the strategy is general and can be used to obtain transition path theory statistics from other methods that sample segments of unbiased trajectories. 

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2. Identifying and bounding the probability of necessity for causes of effects with ordinal outcomes

   https://doi.org/10.1093/biomet/asaf049  

   Zhang, Chao; Geng, Zhi; Li, Wei; Ding, Peng (July 2025, Biometrika)

   Abstract Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity. 

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3. Scalable Learning for Spatiotemporal Mean Field Games Using Physics-Informed Neural Operator

   https://doi.org/10.3390/math12060803  

   Liu, Shuo; Chen, Xu; Di, Xuan (March 2024, Mathematics)

   This paper proposes a scalable learning framework to solve a system of coupled forward–backward partial differential equations (PDEs) arising from mean field games (MFGs). The MFG system incorporates a forward PDE to model the propagation of population dynamics and a backward PDE for a representative agent’s optimal control. Existing work mainly focus on solving the mean field game equilibrium (MFE) of the MFG system when given fixed boundary conditions, including the initial population state and terminal cost. To obtain MFE efficiently, particularly when the initial population density and terminal cost vary, we utilize a physics-informed neural operator (PINO) to tackle the forward–backward PDEs. A learning algorithm is devised and its performance is evaluated on one application domain, which is the autonomous driving velocity control. Numerical experiments show that our method can obtain the MFE accurately when given different initial distributions of vehicles. The PINO exhibits both memory efficiency and generalization capabilities compared to physics-informed neural networks (PINNs). 

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4. Exploiting Update Leakage in Searchable Symmetric Encryption

   https://doi.org/10.1145/3626232.3653260  

   Haltiwanger, Jacob; Hoang, Thang (June 2024, ACM)

   Dynamic Searchable Symmetric Encryption (DSSE) provides efficient techniques for securely searching and updating an encrypted database. However, efficient DSSE schemes leak some sensitive information to the server. Recent works have implemented forward and backward privacy as security properties to reduce the amount of information leaked during update operations. Many attacks have shown that leakage from search operations can be abused to compromise the privacy of client queries. However, the attack literature has not rigorously investigated techniques to abuse update leakage. In this work, we investigate update leakage under DSSE schemes with forward and backward privacy from the perspective of a passive adversary. We propose two attacks based on a maximum likelihood estimation approach, the UFID Attack and the UF Attack, which target forward-private DSSE schemes with no backward privacy and Level 2 backward privacy, respectively. These are the first attacks to show that it is possible to leverage the frequency and contents of updates to recover client queries. We propose a variant of each attack which allows the update leakage to be combined with search pattern leakage to achieve higher accuracy. We evaluate our attacks against a real-world dataset and show that using update leakage can improve the accuracy of attacks against DSSE schemes, especially those without backward privacy. 

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5. Learning Modulo Theories

   Fredrikson, Amtt; Lu, Kaiji; Vijayakumar, Saranya; Jha, Somesh; Ganesh, Vijay; Wang, Zifan (January 2023, arXiv.org)

   Recent techniques that integrate solver layers into Deep Neural Networks (DNNs) have shown promise in bridging a long-standing gap between inductive learning and symbolic reasoning techniques. In this paper we present a set of techniques for integrating Satisfiability Modulo Theories (SMT) solvers into the forward and backward passes of a deep network layer, called SMTLayer. Using this approach, one can encode rich domain knowledge into the network in the form of mathematical formulas. In the forward pass, the solver uses symbols produced by prior layers, along with these formulas, to construct inferences; in the backward pass, the solver informs updates to the network, driving it towards representations that are compatible with the solver’s theory. Notably, the solver need not be differentiable. We implement SMTLayer as a Pytorch module, and our empirical results show that it leads to models that 1) require fewer training samples than conventional models, 2) that are robust to certain types of covariate shift, and 3) that ultimately learn representations that are consistent with symbolic knowledge, and thus naturally interpretable. 

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