GLOBE: Geometry-Guided Early Stopping for Reasoning — Halving Output Without Losing Accuracy

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GLOBE: Geometry-Guided Early Stopping for Reasoning — Halving Output Without Losing Accuracy

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GLOBE is a training-free online early-stopping algorithm that identifies when reasoning can stop via unit-sphere semantic trajectories, cutting output tokens by 49.7% and latency by 51.0% across five benchmarks while matching full CoT accuracy.

Article Content

Chain-of-Thought (CoT) improves large models' problem-solving ability, but models often continue "overthinking" after the answer is already reachable — increasing inference costs and potentially corrupting correct intermediate results. To address this, researchers propose GLOBE — a training-free online early-stopping algorithm that decides when to stop generation by analyzing the geometric shape of semantic trajectories.

Overthinking: The Hidden Cost of CoT

CoT improves performance on complex tasks by having the model generate intermediate steps, but more steps isn't always better. The paper points out that models often keep generating even after the correct answer is reachable, and these extra steps directly inflate serving costs; more subtly, subsequent steps may overwrite originally correct intermediate results, actually lowering accuracy.

Existing early-stopping methods mostly rely on answer confidence or fixed heuristic rules, lacking a characterization of the overall direction of the reasoning process. GLOBE takes a different angle: rather than looking only at single-step confidence, it maps reasoning segments onto a unit sphere and observes the "shape" of the entire semantic trajectory.

Chain-of-Thought (CoT) is a prompting and reasoning paradigm: the model explicitly generates a series of intermediate reasoning steps before giving the final answer, decomposing complex problems into manageable subproblems. Proposed by Wei et al. in 2022, this method significantly improved accuracy on math word problems, symbolic reasoning, and multi-hop QA, and spawned variants such as zero-shot CoT and Self-Consistency voting. The cost of CoT is that the number of tokens generated at inference time grows multiplicatively, making "when to stop" one of the core problems in inference efficiency optimization.

Unit-sphere embedding is the foundation of GLOBE's trajectory analysis: each reasoning text segment is mapped to a high-dimensional vector by an embedding model, then L2-normalized so that it lies on a unit sphere of radius 1. Normalization eliminates the influence of vector magnitude, allowing similarity to be measured directly by inner product or cosine distance; the direction change (angle) between adjacent points on the trajectory thus becomes an intuitive indicator of whether "semantics are advancing."

Two-Stage Mechanism: Probe First, Then Watch the Trajectory

GLOBE's core is a two-stage online control flow that requires no additional training.

Probe Stage: Branch Generates a Short Answer

The algorithm first generates a brief tentative answer in an independent branch, in parallel with the main generation stream. If the tentative answer's confidence exceeds a set threshold, the main flow stops immediately and adopts that answer. This step cheaply probes "is this already enough to solve the problem?"

If the probe fails, generation continues and enters the trajectory stage.

Trajectory Stage: Detecting Direction Reversals

GLOBE embeds each completed reasoning segment as a point on the unit sphere, forming a semantic trajectory as segments accumulate. When this path repeatedly changes direction with little net progress, the algorithm judges that reasoning has entered a "spinning in place" state and terminates generation. This geometric signal is closer to the actual behavior pattern of reasoning than confidence alone.

Combining the two stages lets GLOBE both capture the moment "the answer has appeared" and recognize the deadlock where "thinking further is useless."

Direction reversal of semantic trajectories refers to the angle between embedding vectors of adjacent reasoning segments on the sphere approaching or exceeding 90 degrees, i.e., the next segment no longer advances along the previous direction. If, over several consecutive segments, cumulative direction change is large while net displacement is small, reasoning is circling rather than advancing in high-dimensional semantic space. Combined with "net progress," this criterion can distinguish "reasonable backtracking and verification" from "ineffective repetition": the former is usually accompanied by continuous accumulation of net displacement, while the latter manifests as stalled displacement.

Experimental Results: Half the Tokens, Same Accuracy

The paper evaluates GLOBE on five benchmarks covering math reasoning, tool calling, and agent memory tasks, and validates on two models. Results show:

• Output tokens reduced by 49.7%
• End-to-end actual latency (E2E) reduced by 51.0%
• Five-task average accuracy reaches 80.58%, comparable to full CoT

These numbers show that early stopping does not come at the expense of correctness, but instead cuts away a large number of redundant steps. For service providers deploying CoT reasoning at scale, nearly half the token and latency savings mean significant cost reduction.

End-to-end actual latency (E2E) refers to the wall-clock time from request dispatch to final answer return, including model generation, tool-call round trips, network transmission, and scheduling overhead — closer to real service experience than mere token counts. GLOBE's probe branch runs in parallel with the main flow, so its probing cost can be masked by the generation process; this is one reason its E2E reduction (51.0%) is slightly higher than its token reduction (49.7%).

Why the Geometric Perspective Is Worth Noting

GLOBE's insight is turning "should we stop?" into an observable geometric problem: whether reasoning makes substantive progress in semantic space is reflected in the directionality of the trajectory. Compared with black-box confidence thresholds, this trajectory-shape-based signal is more transparent and easier to compute online.

Of course, the quality of unit-sphere embeddings depends on the choice of embedding model, and threshold settings may vary with task distributions — these are aspects that need tuning in practice. The paper's contribution is providing a training-free, pluggable early-stopping framework that opens a new direction for efficiency optimization of CoT reasoning.

Key Takeaways

GLOBE uses a probe branch to accelerate the determination that "the answer has appeared," and unit-sphere trajectories to identify "spinning in place," achieving half the output tokens and half the latency without accuracy loss across five benchmarks. For CoT deployment scenarios plagued by overthinking, this is a low-cost optimization path worth watching.

One-line Summary

GLOBE uses training-free online early stopping, relying on a probe branch and spherical-trajectory geometry to judge when CoT should stop.

Paragraph Summary

The article introduces GLOBE, a training-free online early-stopping algorithm for mitigating "overthinking" in large-model chain-of-thought. GLOBE uses a two-stage mechanism: first generating a brief tentative answer in an independent branch, stopping the main flow if confidence exceeds a threshold; if not, embedding reasoning segments onto a unit sphere to form a semantic trajectory, and terminating when the trajectory repeatedly changes direction with little net progress. Across five benchmarks covering math reasoning, tool calling, and agent memory, GLOBE achieves 49.7% fewer output tokens and 51.0% lower end-to-end latency, with average accuracy of 80.58% matching full CoT. The article argues that geometric trajectory signals are more transparent and easier to compute online than single-step confidence, offering a low-cost, pluggable path to CoT inference efficiency optimization.