InfMem: Learning System-2 Memory Control for Long-Context Agent

Reasoning over ultra-long documents requires synthesizing sparse evidence scattered across distant segments under strict memory constraints. While streaming agents enable scalable processing, their passive memory update strategy often fails to preserve low-salience bridging evidence required for multi-hop reasoning. We propose InfMem, a control-centric agent that instantiates System-2-style control via a PreThink-Retrieve-Write protocol. InfMem actively monitors evidence sufficiency, performs targeted in-document retrieval, and applies evidence-aware joint compression to update a bounded memory. To ensure reliable control, we introduce a practical SFT-to-RL training recipe that aligns retrieval, writing, and stopping decisions with end-task correctness. On ultra-long QA benchmarks from 32k to 1M tokens, InfMem consistently outperforms MemAgent across backbones. Specifically, InfMem improves average absolute accuracy by +10.17, +11.84, and +8.23 points on Qwen3-1.7B, Qwen3-4B, and Qwen2.5-7B, respectively, while reducing inference time by $3.9\times$ on average (up to $5.1\times$) via adaptive early stopping.

Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumps

We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion process are derived by a Brownian motion and an independent compensated Poisson random measure. In this novel algorithm, a pair of deep neural networks for the approximations of the gradient and the integral kernel is introduced in a crucial way based on deep FBSDE method. To derive the error estimates for this deep learning algorithm, the convergence of Markovian iteration, the error bound of Euler time discretization, and the simulation error of deep learning algorithm are investigated. Two numerical examples are provided to show the efficiency of this proposed algorithm.