Description
Let p=sigmoid(x), t=tanh(softplus(x)) and a=1-t².
Mish is x*tanh(softplus(x)), combining a smooth gate with the original input. Its first and second input derivatives depend on both the gate and its derivatives. Stable scalar helper evaluation differs from differentiating a complete tensor computation or training a network.
Let p=sigmoid(x), t=tanh(softplus(x)) and a=1-t².
When to use this tool
Use Mish Scalar Second Derivative when checking the stated Mish scalar input derivative convention.
How to use the tool and how it works
- Enter x. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Let p=sigmoid(x), t=tanh(softplus(x)) and a=1-t². Return a*(2*p+x*(p*(1-p)-2*t*p²)), the second input derivative of Mish; return zero directly when a rounds to zero.1
Mish combines the input with tanh of softplus. These scalar calculus helpers do not execute a network or transfer the paper’s empirical performance claims to supplied values.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Scalar derivative with respect to the variable and at the fixed coordinates specified above; not a tensor/model gradient. | Required. Finite number. |
{
"input": {
"x": 0
},
"output": {
"derivative": 0.64
}
}Limitations and assumptions
- This is a scalar formula with numerical saturation, not an exact symbolic tensor Hessian or a model-quality claim.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete explicit function and the intended parameter, branch and numerical conventions for symbolic, tensor or model-level differentiation; assess training behavior independently.
References
Similar or alternative tools
- Activation: Mish Scalar Derivative
Evaluate the existing Softplus tool at x and Tanh at that output.
- Activation: Tanh Scalar Second Derivative Tool
Evaluate the analytic second scalar derivative of tanh using its bounded forward value.