[
    {
        "id": "osp-20315",
        "type": "article-journal",
        "title": "Learning Under Forgetting: Statistical Support-Selective Retention in Stochastic Training Dynamics",
        "author": [
            {
                "family": "Gao",
                "given": "Fujie"
            },
            {
                "family": "Zhang",
                "given": "Zuyue"
            },
            {
                "family": "Sun",
                "given": "Gang"
            }
        ],
        "URL": "https://omanscience.com/en/articles/learning-under-forgetting-statistical-support-selective-retention-in-stochastic-training-dynamics",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "Prior work has shown that neural networks exhibit implicit biases toward low-complexity structure (e.g., spectral bias), memorization dynamics, and compression-like effects during training, but a unified dynamical account of selective retention remains incomplete. We propose Repeated Reinforcement with Persistent Forgetting (RPF) dynamics, a minimal framework in which repeated exposure reinforces patterns and structures that recur in the data, while persistent forgetting attenuates learned information. This view treats forgetting not merely as a failure mode, but as a selection mechanism. We build the theory in three successive layers. First, in an independent-feature model, we derive an exposure-selective survival law and a support-dependent retention boundary characterizing which patterns persist under forgetting. Second, in a shared-parameter model, we show that forgetting induces spectral filtering over covariance modes, preserving strongly supported shared components while suppressing weak ones. Third, under small-step and norm/coding approximations, we show how RPF dynamics induce an implicit trade-off between data fitting and the cost of stored information, yielding Minimum Description Length (MDL)-like compression. Controlled experiments provide evidence for this reinforcement--forgetting selection mechanism in scalar memories and a nonlinear shared network. Joint reinforcement and attenuation interventions shift conditional retention, while matched exposure counts reveal forgetting-dependent effects of reinforcement timing and changes in the composition of the retained set. Together, these results show that repeated reinforcement and persistent forgetting jointly provide a controllable source of inductive bias beyond neural architecture and scale."
    }
]