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IBM

MCP Math Server

by IBM

gradient_descent_momentum

Optimize functions using gradient descent with momentum to accelerate convergence in numerical optimization problems.

Instructions

Perform gradient descent with momentum for faster convergence (Domain: numerical, Category: optimization)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
fYes
grad_fYes
x0Yes
learning_rateNo
momentumNo
max_iterationsNo
toleranceNo
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It mentions 'faster convergence', which hints at performance, but fails to disclose critical behavioral traits such as what the tool returns (e.g., optimized parameters, convergence status), error handling, computational requirements, or side effects. For a complex optimization tool with 7 parameters, this is a significant gap in transparency.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted text, and the structure efficiently conveys the core information without unnecessary elaboration.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity (optimization algorithm with 7 parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits essential details such as return values, error conditions, performance characteristics, and parameter explanations. For a tool of this nature, the description should provide more context to guide effective use.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, meaning none of the 7 parameters have descriptions in the schema. The tool description adds no information about parameters like 'f', 'grad_f', or 'x0', leaving their semantics (e.g., function definitions, initial point format) completely undocumented. This fails to compensate for the lack of schema coverage, making parameter understanding difficult.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Perform gradient descent with momentum for faster convergence'. It specifies the verb ('perform'), resource ('gradient descent'), and a key feature ('with momentum'), distinguishing it from basic gradient descent. However, it doesn't explicitly differentiate from sibling tools like 'gradient_descent' or 'adam_optimizer' beyond the mention of momentum.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage in optimization contexts ('Domain: numerical, Category: optimization') and suggests momentum aids 'faster convergence', but it lacks explicit guidance on when to use this tool versus alternatives like 'gradient_descent' or 'adam_optimizer'. No prerequisites, exclusions, or specific scenarios are mentioned, leaving usage somewhat vague.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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