Skip to content

Accuracy drops in dflash #23

@shahizat

Description

@shahizat

Hello Dflash team,

I was testing DFlash on a Blackwell 6000 Pro to evaluate how speculative decoding affects output generation. I observed that it performs worse on MMLU math questions than the vanilla meta-llama/Llama-3.1-8B-Instruct when using SGLang.

Question: Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8.

Answer using dflash draft decoding: To meta-llama/Llama-3.1-8B-Instruct - Not correct answer



To find the product of the given polynomials in Z_8[x], we need to multiply them as we would in a regular polynomial ring, but we need to perform the operations modulo 8.

f(x) = 4x - 5

g(x) = 2x^2 - 4x + 2

First, we multiply each term of f(x) by each term of g(x):

(4x)(2x^2) = 8x^3 (mod 8) = 0x^3

(4x)(-4x) = -16x^2 (mod 8) = 0x^2

(4x)(2) = 8x (mod 8) = 0x

(-5)(2x^2) = -10x^2 (mod 8) = 6x^2

(-5)(-4x) = 20x (mod 8) = 4x

(-5)(2) = -10 (mod 8) = 6

Now, we combine like terms:

0x^3 + 0x^2 + 0x + 6x^2 + 4x + 6

Combine like terms:

-6x^2 + 4x + 6

So, the product of f(x) and g(x) in Z_8[x] is -6x^2 + 4x + 6.


Answer without dflash (meta-llama/Llama-3.1-8B-Instruct) - Correct

To find the product of the given polynomials in the polynomial ring Z_8[x], we'll follow the standard multiplication process for polynomials, but we'll perform the arithmetic operations in Z_8.

f(x) = 4x - 5

g(x) = 2x^2 - 4x + 2

First, multiply each term of f(x) by each term of g(x):

(4x * 2x^2) + (4x * (-4x)) + (4x * 2) + ((-5) * 2x^2) + ((-5) * (-4x)) + ((-5) * 2)

Now, simplify the expressions using Z_8 arithmetic:

(8x^3) mod 8 = 0 (since 8 mod 8 = 0)

(-16x^2) mod 8 = 0 (since 16 mod 8 = 0)

(8x) mod 8 = 0 (since 8 mod 8 = 0)

(-10x^2) mod 8 = -2x^2 (since 10 mod 8 = 2)

(20x) mod 8 = 4x (since 20 mod 8 = 4)

(-10) mod 8 = 6 (since 10 mod 8 = 2)

Now, combine like terms:

0 + 0 + 0 - 2x^2 + 4x + 6

The resulting polynomial is:

-2x^2 + 4x + 6

However, this polynomial is in Z[x] (the ring of polynomials with integer coefficients). Since we're working in Z_8[x], we need to express the coefficients in Z_8.

In Z_8, the coefficients -2 and 6 can be expressed as 6 and 6, respectively.

So, the product of the given polynomials in Z_8[x] is:

6x^2 + 4x + 6

Metadata

Metadata

Assignees

No one assigned

    Labels

    No labels
    No labels

    Type

    No type

    Projects

    No projects

    Milestone

    No milestone

    Relationships

    None yet

    Development

    No branches or pull requests

    Issue actions