LoRA Update One Weight Entry Term Tool

Description

Return one rank-scaled low-rank update entry.

A low-rank update represents a weight change as the product of two smaller matrices, with a scaling convention applied to that product. Counting their entries and evaluating one updated weight are distinct operations; neither trains an adapter or checks the quality of an adapted model.

Return one rank-scaled low-rank update entry.

When to use this tool

Use LoRA Update One Weight Entry Term when checking a low-rank update entry or its stated matrix-parameter count.

How to use the tool and how it works

Enter aRow, bColumn, alpha, rank, baseWeight. Follow any array-alignment requirements below. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read update, adaptedWeight. Use the output convention below.

Return one rank-scaled low-rank update entry. Require aligned factor vectors of length rank with positive whole rank; update = alpha*dot(aRow,bColumn)/rank, adaptedWeight = baseWeight+update.^[1]

LoRA represents a weight update using low-rank factors. These helpers cover one factor-product entry or its parameter count, rather than training an adapter or selecting an effective rank.^[2]

Input field	Meaning and units	Accepted input
aRow	One rank-length factor row aligned with bColumn.	Required. Array of finite number; maximum items 256.
bColumn	B Column	Required. Array of finite number; maximum items 256.
alpha	Signed update-scaling numerator; update scales by alpha/rank.	Required. Finite number.
rank	Rank	Required. Safe integer; minimum 1.
baseWeight	Base Weight	Required. Finite number.

Output field	Interpretation	Returned shape
update	Update	Required. Finite number.
adaptedWeight	Adapted Weight	Required. Finite number.

json

{
  "input": {
    "aRow": [
      1,
      2
    ],
    "bColumn": [
      3,
      4
    ],
    "alpha": 4,
    "rank": 2,
    "baseWeight": 10
  },
  "output": {
    "update": 22,
    "adaptedWeight": 32
  }
}

Limitations and assumptions

Alpha may be signed and matrix roles are supplied; no full adapter, optimization or trained model is produced.
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

Inspect the full adapter configuration, matrix orientation, rank and scaling convention for implementation-specific training or inference.

References

Calculation and input contract: artificial-intelligence/lora-update-one-weight-entry-term — tool.io
LoRA: Low-Rank Adaptation of Large Language Models — Edward J. Hu and coauthors

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