On the Importance of Multistability for Horizon Generalization in Reinforcement Learning

In reinforcement learning (RL), agents acting in partially observable Markov decision processes (POMDPs) must rely on memory, typically encoded in a recurrent neural network (RNN), to integrate information from past observations. Long-horizon POMDPs, in which the relevant observation and the optimal action are separated by many time steps (called the horizon), are particularly challenging: training suffers from poor generalization, severe sample inefficiency, and prohibitive exploration costs. Ideally, an agent trained on short horizons would retain optimal behavior at arbitrarily longer ones, but no formal framework currently characterizes when this is achievable. To fill this gap, we formalized temporal horizon generalization, the property that a policy remains optimal for all horizons, derived a necessary and sufficient condition for it, and experimentally evaluated the ability of nonlinear and parallelizable RNN variants to achieve it. This paper presents the resulting theoretical framework, the empirical evaluation, and the dynamical interpretation linking RNN behavior to temporal horizon generalization. Our analyses reveal that multistability is necessary for temporal horizon generalization and, in simple tasks, sufficient; more complex tasks further require transient dynamics. In contrast, modern parallelizable architectures, namely state space models and gated linear RNNs, are monostable by construction and consequently fail to generalize across temporal horizons. We conclude that multistability and transient dynamics are two essential and complementary dynamical regimes for horizon generalization, and that no current parallelizable RNN exhibits both. Designing parallelizable architectures that combine these regimes thus emerges as a key direction for scalable long-horizon RL.

Improving the Performance and Learning Stability of Parallelizable RNNs Designed for Ultra-Low Power Applications

Sequence learning is dominated by Transformers and parallelizable recurrent neural networks (RNNs) such as state-space models, yet learning long-term dependencies remains challenging, and state-of-the-art designs trade power consumption for performance. The Bistable Memory Recurrent Unit (BMRU) was introduced to enable hardware-software co-design of ultra-low power RNNs: quantized states with hysteresis provide persistent memory while mapping directly to analog primitives. However, BMRU performance lags behind parallelizable RNNs on complex sequential tasks. In this paper, we identify gradient blocking during state updates as a key limitation and propose a cumulative update formulation that restores gradient flow while preserving persistent memory, creating skip-connections through time. This leads to the Cumulative Memory Recurrent Unit (CMRU) and its relaxed variant, the $α$CMRU. Experiments show that the cumulative formulation dramatically improves convergence stability and reduces initialization sensitivity. The CMRU and $α$CMRU match or outperform Linear Recurrent Units (LRUs) and minimal Gated Recurrent Units (minGRUs) across diverse benchmarks at small model sizes, with particular advantages on tasks requiring discrete long-range retention, while the CMRU retains quantized states, persistent memory, and noise-resilient dynamics essential for analog implementation.

Fast reconstruction of degenerate populations of conductance-based neuron models from spike times

Neurons communicate through spikes, and spike timing is a crucial part of neuronal processing. Spike times can be recorded experimentally both intracellularly and extracellularly, and are the main output of state-of-the-art neural probes. On the other hand, neuronal activity is controlled at the molecular level by the currents generated by many different transmembrane proteins called ion channels. Connecting spike timing to ion channel composition remains an arduous task to date. To address this challenge, we developed a method that combines deep learning with a theoretical tool called Dynamic Input Conductances (DICs), which reduce the complexity of ion channel interactions into three interpretable components describing how neurons spike. Our approach uses deep learning to infer DICs directly from spike times and then generates populations of "twin" neuron models that replicate the observed activity while capturing natural variability in membrane channel composition. The method is fast, accurate, and works using only spike recordings. We also provide open-source software with a graphical interface, making it accessible to researchers without programming expertise.