Autonomous robots on one-shot missions run over horizons far longer than the trajectories seen during training, under a fixed onboard compute budget. We present FRANK, a 507K-parameter recurrent architecture that combines tau-gated recurrent modules, content-addressable memory, and a feedforward reflex pathway. We evaluate it against recurrent, state-space, and reduced modular baselines at matched parameter count on four algorithmic sequence tasks, trained at length 5-20 and evaluated out to two million tokens. At 100,000x the maximum training length, 6 of 10 FRANK seeds retain exactly 100.0% accuracy, while none of the 50 baseline configurations does, five architectures at ten seeds each with none left incomplete (Fisher exact, two-sided p = 4.2E-6. Targeted lesions across the four tasks yield four distinct component-reliance profiles, consistent with task-dependent allocation across the recurrent, memory, and reflex pathways. Separately, a FRANK policy trained in simulation drives a physical ground vehicle to commanded waypoints through obstacles without teleoperation.
Figures & tables
Fig. 1: System overview. (a) The deployed vehicle. (b) The FRANK policy runs onboard a Raspberry Pi 5 on a ROSMASTER X3, consuming 13 RPLIDAR A1 rays and the body-frame waypoint offset and emitting wheel velocities at 50 Hz; a watchdog zeroes the command if lidar scans stop.
Fig. 2: The FRANK architecture, after [ 1 ] . All components active every timestep; no routing. The inhibit signal blends the recurrent and reflex output paths.
Fig. 3: (a) Per-seed FRANK accuracy against evaluation scale on the state-transition task; six seeds are exactly flat at 100% out to two million tokens. (b) Seeds reaching perfect accuracy at 105× per architecture; the best baseline seed at that scale reaches 30.3% (GRU).
Fig. 4: Targeted lesion at 10% damage. Four tasks, four distinct reliance profiles from the same architecture, with no routing, no task labels, and no component-specific loss.
Fig. 5: Navigation in simulation. (a) The obstacle field used for training. (b) Commanded waypoint (green) and the executed path. (c) The 13 lidar rays that form the policy’s entire exteroceptive observation.
Modern language models reason within bounded context, an inherent constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in isolated contexts. We prove that any computable problem admits a recursive decomposition of reasoning in which each subtask requires only exponentially smaller active context than standard autoregressive models; this strictly surpasses any context management approach confined to a single sequence, such as summarization. We further generalize our framework to modern agentic systems with arbitrary context processing and control flows, and prove that recursive models can achieve optimal power within this broader class. Experimentally, we test two settings: fine-tuning a pretrained base model for recursive SAT solving, and training a small model from scratch on Go traces generated by exact game-tree search. Both show improved long-horizon accuracy with small active contexts.
In streaming tasks, recurrent models can carry latent computation across time, allowing each update to build on representations produced earlier. This raises a basic question: once temporal recurrence provides sequential computation across steps, how much depth is still needed within each step? Prior work has shown that recurrence can make shallow models competitive. We instead study this question as a compute-allocation problem, varying within-step depth, expert width, and the number of parallel experts per layer across several compute budgets. For each budget, we compare the best observed recurrent and non-recurrent allocations and the performance they achieve under approximately matched per-step computation. Across Sokoban and autoregressive FineWeb language modeling, we find that temporal recurrence shifts the best observed compute allocation toward substantially fewer layers, with comparable or better performance.
Ivan Anokhin, Johan Obando-Ceron, Irina Rish +1
Mila – Qu´ebec AI Institute · Universit´e de Montr´eal · Sakana AI
We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.
Apurva Gandhi, Satyaki Chakraborty, Xiangjun Wang +2