Extreme Length Generalization in a Compact Recurrent Architecture for One-Shot Exploration

• One-shot missions need controllers that remain reliable far beyond rehearsed conditions, where slow degradation may go undetected in time.Source: §I · p. 1
• Attention faces positional extrapolation failures and O(L^2) cost, while recurrent baselines can drift on extreme-length sequences.An ALiBi probe reaches chance by 100×; GRU baselines fall to 10–30% at 100,000×, and Mamba is at chance by 100× on every seed.Source: §I · p. 1
• This work adds a ten-seed FRANK re-run with swept learning rates, statistical testing, and hardware deployment to prior FRANK results and a single-seed lesion analysis.Source: §I · p. 1

• The onboard FRANK policy consumes 13 lidar rays and a body-frame waypoint offset, then emits wheel velocities at 50 Hz.A watchdog zeroes the command if lidar scans stop.Source: Figure 1 · p. 1
• FRANK combines four recurrent modules with learned time constants, content-addressable key-value memory, a feedforward reflex path, and a 507K-parameter budget.A sigmoid inhibit signal blends recurrent and reflex outputs; the tau-gated update clamps each module’s learned τ to [1, 100] steps.Source: §II · p. 1, Figure 2 · p. 2
• All components run every timestep without routing, and the recurrent and reflex output paths are blended by the inhibit signal.The components differ in computational structure, and the paper contrasts this design with prior routed modular architectures and homogeneous modules that did not specialize in another setup.Source: §II · p. 1, Figure 2 · p. 2
• Six FRANK seeds remain at 100% accuracy out to two million tokens on the state-transition task.The figure also compares seeds reaching perfect accuracy at 105× per architecture; the best baseline seed, GRU, reaches 30.3%.Source: Figure 3 · p. 2

Experimental setup

• The state-transition task predicts the cumulative sum of uniformly random digits modulo 10 at every position; extreme-length cells use ten independent two-million-token streams.Evaluation sequences differ from training sequences only in length.Source: §III · p. 2

Results

• 6 of 10 FRANK seeds retained exactly 100.0% accuracy at 100,000× training length; none of 50 baseline cells generalized, and the best baseline reached 30.3%.Baselines included GRU, RIMs, Mamba, and two reduced FRANK variants.Source: §III · p. 2

Targeted lesions

• At 10% damage, the four tasks showed distinct component-reliance profiles despite using the same architecture without routing, task labels, or component-specific loss.Source: Figure 4 · p. 2

Navigation

• The simulation figure depicts the training obstacle field, a commanded waypoint and executed path, and the policy’s 13 lidar rays.Source: Figure 5 · p. 2

Results

• At 10×, GRU matched FRANK at 96.8% against 96.6%, but strong standard-scale performance did not reliably predict extreme-length success.Of 13 cells at or above 90% at 10×, seven reached 1.0000 at 100,000× and two fell to chance.Source: §III · p. 2
• The lateral-connection ablation found 6 of 10 seeds generalized versus 3 of 10 without laterals, a nonsignificant difference (Fisher p = 0.37).The successful seeds shared one member, suggesting laterals changed which training basins were reached, not the generalization rate.Source: §III · p. 2

IV. COMPONENT LESION STUDIES

• Lesions zero random fractions of one trained component’s weights and measure accuracy at training lengths; every cell was at least 97.5% accurate undamaged.The study uses n = 10 seeds per task and n = 8 for recall.Source: §IV · p. 2
• No two tasks share a lesion profile: copy is brain-critical, recall leans on recurrent modules, chain grades components, and sum eventually needs all three.At 70% damage, sum’s reflex falls to 10.3%, while copy’s reflex still holds 97.1%.Source: §IV · p. 3
• The lesion study does not test what the reflex contributes to length generalization; the reduced modules-plus-memory model also fails at 10×, not only at long horizons.Lesions damage a component within trained FRANK at training length, whereas the reduced model trains without a reflex or veto gate.Source: §IV · p. 3
• Copy and recall reproduce the single-seed analysis, but chain memory is supporting rather than essential and sum’s reflex is load-bearing late, not critical early.The sum collapse occurs across the full damage curve.Source: §IV · p. 3
• At 10% global weight zeroing, the GRU holds 99.6% against FRANK’s 65.6%, favoring the GRU for graceful degradation.FRANK’s outcome variation under 20% chain damage is nevertheless higher than every baseline’s.Source: §IV · p. 3

V. PHYSICAL ROBOT DEMONSTRATION

• In simulation and on hardware, the policy reaches commanded waypoints while avoiding obstacles without teleoperation, qualitatively at this stage.The larger deployed policy has 1.01M parameters.Source: §V · p. 3
• The policy uses 13 lidar rays, waypoint offset, and four timesteps of prior action to emit left and right wheel velocities at 50 Hz.It carries no map between timesteps and uses wheel odometry for waypoint offset; there is no planner or stop gate.Source: §V · p. 3
• The authors frame learned control as a fixed-compute, no-map alternative for one-shot settings, while retaining classical planners as the default when maps and reliable pose estimates exist.The demonstration vehicle represents the constraint, not planetary or subsea terrain.Source: §V · p. 3

VI. LIMITATIONS AND FUTURE WORK

• Generalization varies by seed, and all four sequence tasks are synthetic.Source: §VI · p. 3
• Odometry drift is the deployment’s binding long-horizon limit: accumulated mecanum wheel error degrades the waypoint offset, which the network cannot detect or correct.The same policy input can accept a pose from scan matching or another external fix.Source: §VI · p. 3
• The specialization claim lacks a homogeneous-component control, and the contrast with [3] is based on their setup rather than a test here.A circular hidden-state representation of the kind transformers learn for modular arithmetic was tested and failed.Source: §VI · p. 3
• Future work will quantify obstacle-layout success, path efficiency, failure modes, sim-to-hardware differences, drifting-pose degradation, latency, and power.Source: §VI · p. 3

• 6 of 10 FRANK seeds hold exact accuracy at 105× their training length, while none of the 50 baseline configurations does.Source: §VII · p. 3
• Targeted lesions show that capability sits in task-dependent places inside one undifferentiated network.Source: §VII · p. 3