Evaluating LLM Reasoning Capabilities and Managing Quotas: From Mathematical Inference to Long-Running Task Scheduling

1. Introduction: Why Mathematical Reasoning Remains a Hard Metric

In various model capability evaluations, mathematical reasoning remains one of the most difficult dimensions to obscure with mere rhetoric. Writing can pass with fluency, and chitchat can win favor through natural tone, but mathematical problems have clear binary outcomes of right or wrong. Whether a model can handle open-ended mathematical problems—those without ready-made answers that require multi-step construction and validation—often best reflects the robustness of its underlying reasoning architecture.

Therefore, when horizontally comparing reasoning models of different generations and specifications, using mathematical tasks as the primary benchmark is both logical and efficient. It helps developers quickly determine whether a model is merely “recalling training data” or genuinely possesses the ability to “deduce unknown paths.”

2. A Tiered Evaluation Framework

Based on extensive usage experience, the performance of current mainstream reasoning models in mathematics can be roughly divided into several tiers. Note that this categorization is not based on precise performance metrics, but rather on an engineering intuition of capability layering, intended to guide task allocation.

Tier 1: Capable of Solving Open-Ended Mathematical Problems

Currently, only a very select few models can stably handle open-ended mathematical problems. “Open-ended” here means the problem itself lacks a standard answer, or requires the model to autonomously define intermediate lemmas, explore multiple paths, and verify results. This capability typically requires the model to have the following characteristics:

• The ability to identify implicit assumptions within a problem;
• The ability to actively construct counterexamples or edge cases during the reasoning process;
• The ability to maintain an unbroken logical chain during prolonged reasoning.

In practice, models reaching this level show noticeable differences between conversational and working environments, but generally belong to the same technological generation.

Tier 2: Strong Reasoning but Divergent Styles

The second tier includes two types of models with distinctly different characteristics. One features a highly concise Chain of Thought (CoT) with compact reasoning steps, mimicking the “jumping deductions” of human experts—it assumes the reader can follow omitted steps. The other exhibits the opposite: extremely long and complex CoTs, detailing every minute step. This is suitable for scenarios requiring “auditable processes,” but at the cost of verbose output and high quota consumption.

While these two types are on par in terms of mathematical capability, their applicable scenarios differ entirely. The former is ideal for interactive exploration, while the latter suits result archiving and instructional demonstrations.

Tier 3: Transitional States Between Historical Versions

If one arranges the historical versions of a specific model series chronologically, it becomes evident that newer versions do not always show monotonic improvement. Sometimes a new version performs better on general tasks but falls short of its predecessor on specific deep-reasoning tasks. Taking a mid-sized reasoning model as an example, its capability sits somewhere between the previous generation’s standard and pro editions—stronger than the standard, but lacking the depth of the pro version.

This “non-monotonic evolution” serves as a reminder to developers: do not judge capabilities solely by version numbers. You must re-verify performance against your specific task types.

3. Trade-offs Between CoT Length and Efficiency

The length of the CoT is an easily overlooked dimension when evaluating reasoning models. A long CoT means more exploration space, but it brings two direct issues:

1. Increased output latency: For interactive scenarios, prolonged user wait times significantly degrade the experience.
2. Accelerated quota consumption: Under time-based or token-based billing plans, long CoTs can rapidly deplete resources.

A phenomenon worth noting is that certain models tend to generate a large amount of “intermediate commentary.” These notes contribute little to the final answer but occupy substantial output space. In contrast, models with concise CoTs are more efficient at conveying the core reasoning path, though they demand a higher comprehension threshold from the reader.

In practical development, the following strategies can be employed to strike a balance:

• Simple validation tasks: Choose models with concise CoTs to quickly obtain readable results;
• Complex proof tasks: Accept the cost of long CoTs in exchange for a more comprehensive derivation process;
• Code review and debugging: Prioritize models that output “conclusions + key evidence” to reduce verbose elaboration.

4. Quota Management for Long-Running Tasks

Long-running tasks present another engineering challenge worth discussing. Handing a task over to a model to run autonomously for several hours is increasingly common in “AI Agent” applications. However, the subsequent rate of quota consumption often exceeds expectations.

Common Quota Structures

A typical plan usually contains two levels of limits:

• Per-session limits: For example, a forced interruption after running continuously for several hours;
• Periodic limits: For example, total available hours per week.

The issue lies in the severe imbalance that can exist between these two limits. If a plan allows 15 hours per week but has a single-session cap of 5 hours, a user can effectively only initiate three maximum-length sessions per week. If a task runs overnight, hits the single-session limit, and automatically resumes, it may quickly trigger the periodic limit.

Hidden Sources of Quota Consumption

Beyond tasks actively submitted by users, there are several hidden sources of consumption:

1. Sub-agent calls: If the model routing layer calls other models to execute sub-tasks, these calls are also billed against the main session’s quota.
2. CoT expansion: The verbose CoTs mentioned earlier persist during code execution tasks and are often amplified.
3. Error retries: If an autonomously running task encounters an exception, the model may repeatedly attempt different error-handling paths, leading to exponential growth in consumption.

Engineering Optimization Recommendations

To address these issues, optimization can be approached from the following angles:

1. Set "checkpoints" for long-running tasks to periodically save intermediate states;
2. Explicitly constrain the model's output length and retry limits in the instruction file;
3. Split tasks into multiple short sessions to avoid hitting single-session time limits;
4. Prioritize sub-tasks and delegate low-value work to lightweight models;
5. Monitor the quota consumption curve to identify abnormal peaks and locate their sources.

Point 4 deserves elaboration: if the primary model possesses task distribution capabilities, it is advisable to explicitly state in the instructions which work can be delegated and which must be executed by the primary model itself. Low cognitive burden tasks like “code formatting checks” or “variable naming convention validations” can be entirely handled by lightweight models, rather than consuming the reasoning budget of high-end reasoning models.

5. Practical Principles for Model Selection

Synthesizing the discussions above, several general selection principles for developers can be distilled:

• Select models by task depth: Do not use the “most powerful model” for every task. Use lightweight models for light tasks, and reserve high-end specifications for deep reasoning.
• Select models by output style: Opt for concise CoTs when quick interaction is needed; choose detailed CoTs when process documentation is required.
• Select models by quota structure: Understand the time limit structure of your plan before deciding on task orchestration. If the per-session limit is very low, the plan is not suitable for long-running autonomous tasks.
• Maintain version rollback awareness: Newer versions do not universally outperform older ones across all dimensions. Establish your own benchmark test suites for critical tasks.

6. Conclusion

The pace of evolution in large model capabilities is rapid, but “fast” does not mean “stable.” For developers, rather than chasing the latest version numbers, it is better to establish a personalized evaluation system: clarify task types, standardize test cases, log quota consumption, and observe CoT characteristics. Only by integrating these engineering details into daily practice can developers maintain stable output quality in an environment of rapid model iteration. When a new round of models is released, this approach allows you to speak with data and experience, rather than passively following the marketing rhythm.