Description
Return linearAsymptote=x/2-0.5 and offset=-0.5 for bent identity x+(sqrt(x²+1)-1)/2 toward negative infinity.
Bent identity is x+(sqrt(x²+1)-1)/2. Toward negative infinity it approaches a line with slope one half and offset minus one half. An asymptotic line describes leading behavior rather than the exact activation value at finite input.
Return linearAsymptote=x/2-0.5 and offset=-0.5 for bent identity x+(sqrt(x²+1)-1)/2 toward negative infinity.
When to use this tool
Use Bent Identity Negative Asymptote when checking the stated bent-identity negative asymptote 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 linearAsymptote, offset. Use the output convention below.
Require x<0. Return linearAsymptote=x/2-0.5 and offset=-0.5 for bent identity x+(sqrt(x²+1)-1)/2 toward negative infinity.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number; strictly below 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| linearAsymptote | Negative-tail line x/2-1/2; not the exact finite-input activation value. | Required. Finite number. |
| offset | Offset | Required. Finite number. |
{
"input": {
"x": -10
},
"output": {
"linearAsymptote": -5.5,
"offset": -0.5
}
}Limitations and assumptions
- The returned line is asymptotic, not the activation's exact value at finite x or the limiting value of the activation itself.
- 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
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