RAZOR: Pruning Replaceable Experts in LLMs
Paper • 2609.30465 • Published
Datasets:
domain stringclasses 7
values | sub_source stringclasses 15
values | coding_subclass stringclasses 6
values | messages listlengths 2 24 | tools listlengths 1 94 ⌀ |
|---|---|---|---|---|
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Study the concavity and find the inflection points of the function \\( f(x) = \\frac{x^4}{4} - 2x^3 + \\frac{9x^2}{2} \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step 1 – Compute the second derivative**\n\n\\[\nf(x)=\\frac{x^{4}}{4}-2x^{3}+... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let \\( a \\) be a fixed positive number (\\( a > 0 \\)) and \\( z \\) be a complex number such that \\( \\left| z + \\frac{1}{z} \\right| = a \\). Find the maximum and minimum values of \\( |z| \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Determine all positive integers $n$ for which there exists a polynomial $P(x)$ with integer coefficients such that for each integer $m$, the number $P(m)$ is divisible by $n$ if and only if $m$ is not divisible by $n$.",
"tool_calls": null
},
{
"role": "assistant",
... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "The numbers from $1$ to $100$ are placed in a circle. A number is underlined if it divides its left neighboring number. What is the highest possible quantity of underlined numbers?",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\na_{1},a_... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the equation $f(x) = \\sin(F(x))$ where $F(x) = \\int f(x) \\, dx$ and $f: \\mathbb{R} \\to \\mathbb{R}$, $F: \\mathbb{R} \\to \\mathbb{R}$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "We are looking for real‑valued functions \\(f\\) and the... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all \\( t \\) such that for all \\( x, y, z \\in \\mathbb{R}^* \\):\n\\[ 2(x^3 + y^3 + z^3) + 3(1 + 3t)xyz \\geq (1 + t)(x + y + z)(xy + yz + zx) \\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n2(x^{3}+y^{3}+z^{3})+3(1+3t)xyz\\ge (1+t)(x... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all integers \\( x \\) such that \\( 2^{182} + 4^x + 8^{700} \\) is a perfect square.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nS(x)=2^{182}+4^{x}+8^{700}=2^{182}+2^{2x}+2^{2100}\n\\]\n\nAll three summands are powers of \\(2\\). \nIf ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Evaluate the integral $\\int\\frac{1}{(a \\sin^2 x + b \\cos^2 x)^2} \\, dx$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Solution**\n\n\\[\nI=\\int\\frac{dx}{\\bigl(a\\sin ^2x+b\\cos ^2x\\bigr)^{2}}\\qquad \n(a\\neq0,\\;b\\neq0)\n\\]\n\n---\n\n... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "A checkerboard with size \\( 109 \\times 21 \\) will be tiled with some tiles with size \\( 3 \\times 1 \\). What is the maximum number of tiles which can be placed on the board so that no two tiles overlap, or touch (touching on each tile's vertices are also not allowed)?",
... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find positive distinct integers \\( x_1, x_2, \\ldots, x_{2002} \\) such that \\( x_1^2 + x_2^2 + \\cdots + x_{2002}^2 = 1335(x_1 + x_2 + \\cdots + x_{2002}) \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\nS=\\sum_{i=1}^{2002}x_i ,\... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Simplify the expression $$\\dfrac{a^5+(a-1)^4}{(a-1)^5-a^4}.$$",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\frac{a^5+(a-1)^4}{(a-1)^5-a^4}\n\\]\n\n---\n\n### 1. Expand the powers \n\n\\[\n\\begin{aligned}\n(a-1)^4 &= a^4-4a^3+6a^2-4a+1,\\\... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Simplify the expression\n$$\\cos^7{\\frac{\\pi}{9}}+\\cos^7{\\frac{5\\pi}{9}}+\\cos^7{\\frac{7\\pi}{9}}.$$",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nS=\\cos ^7\\frac{\\pi}{9}+\\cos ^7\\frac{5\\pi}{9}+\\cos ^7\\frac{7\\pi}{9}\n\\]\n\n---\n\n... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Three people sold their chickens at the market. The first person had 10 chickens, the second had 16, and the third had 26. They sold some chickens at a higher price in the morning and the rest at a lower price in the afternoon. Each person collected a total of 35 monies by the ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "How can we study the changes of the function $f(x) = x^2 - \\sqrt{x}$ without using the derivative?",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step‑by‑step study of** \n\n\\[\nf(x)=x^{2}-\\sqrt{x},\\qquad x\\ge 0\n\\]\n\n---\n\n### 1. Domain ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Given a plane $P$, find the shape of the orthogonal projection $T'$ of a regular tetrahedron $T$ with side length 1 onto $P$, and determine the maximum area of $T'$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\nT=\\{V_{1},V_{2},V_{3},... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find the $2$-adic valuation $v_2$ of the sum $1 + \\frac{1}{3} + \\frac{1}{5} + \\cdots + \\frac{1}{2k-1}$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nS_k:=1+\\frac13+\\frac15+\\cdots+\\frac1{2k-1}\\qquad(k\\ge 1)\n\\]\n\nLet \n\n\\[\nD:=\\... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let \\( p \\) and \\( q \\) be real numbers. Define a sequence \\( \\{a_n\\} \\) by \\( a_1 = p \\), \\( a_2 = q \\), and \\( a_{n+2} = 2a_{n+1} + a_n \\) for \\( n = 1, 2, \\ldots \\). Find the necessary and sufficient condition on \\( p \\) and \\( q \\) for which the series ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Given a tree $T$, starting with the complete graph on $n$ vertices, subgraphs isomorphic to $T$ are erased at random until no such subgraph remains. For what trees does there exist a positive constant $c$ such that the expected number of edges remaining is at least $cn^2$ for a... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "A frog sitting at the point (1, 2) begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length 1, and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Given a twentieth degree polynomial with integer coefficients, what is the largest number of marked points with integer coordinates and ordinates between 0 and 10 (inclusive) that can lie on the graph of this polynomial?",
"tool_calls": null
},
{
"role": "assistant"... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "How many ways are there to color an $n \\times n$ board with red and black such that every $2 \\times 2$ subsquare contains exactly two red and two black squares, for $n \\geq 2$?",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\na_{i,j}= ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve for \\( x \\) in the equation \\((1-\\tan{x})(1+\\tan{x})(\\tan^2{x}+1)+2^{\\tan^2{x}}=0\\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n(1-\\tan x)(1+\\tan x)(\\tan ^2x+1)+2^{\\tan ^2x}=0\n\\Longrightarrow (1-\\tan ^2x)(\\tan ^2x+1)+2^... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find the real numbers \\( a \\) that satisfy the equation\n\\[ \\lfloor nx \\rfloor = \\sum_{k=1}^{n} \\lfloor x + (k-1)a \\rfloor, \\]\nfor any real numbers \\( x \\) and for a natural number \\( n \\ge 2. \\)",
"tool_calls": null
},
{
"role": "assistant",
"con... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let \\( D \\) be a point on side \\( [AB] \\) of triangle \\( ABC \\) with \\( |AB| = |AC| \\) such that \\( [CD] \\) is an angle bisector and \\( m(\\widehat{ABC}) = 40^\\circ \\). Let \\( F \\) be a point on the extension of \\( [AB] \\) after \\( B \\) such that \\( |BC| = |... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the system of equations:\n\\[\n\\begin{cases}\nx^2(y+3) = 4(2-y) \\\\\ny^2(z+3) = 4(2-z) \\\\\nz^2(x+3) = 4(2-x)\n\\end{cases}\n\\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\begin{cases}\nx^2(y+3)=4(2-y)\\\\[2mm]\ny^2(z+3)=4(2-z)\\\... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Two ants start at points $(-1,1)$ and $(1,1)$ and walk to the right along the parabola $y=x^2$. Their midpoint moves along the line $y=1$ with constant speed $1$. What is the speed of the left ant when it first hits the line $y=1/2$?",
"tool_calls": null
},
{
"role"... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find a positive integer \\( n \\) for which\n\\[ \\bigg\\lfloor 1 + \\frac{1}{\\sqrt{2}} + \\frac{1}{\\sqrt{3}} + \\frac{1}{\\sqrt{4}} + \\cdots + \\frac{1}{\\sqrt{n}} \\bigg\\rfloor = 12. \\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "First note... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "What is the maximum value of \n\\[\n\\sqrt{|x_1 - x_2|} + \\sqrt{|x_2 - x_3|} + \\sqrt{|x_3 - x_4|} + \\cdots + \\sqrt{|x_{n-1} - x_n|} + \\sqrt{|x_n - x_1|}\n\\]\nwhere \\(0 \\leq x_i \\leq 1\\) for \\(i = 1, 2, 3, \\ldots, n\\) and \\(n\\) is an odd integer greater than or eq... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let \\( f, g : \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f \\) is Lebesgue measurable on \\( \\mathbb{R} \\) and \\( g \\) is continuous on \\( \\mathbb{R} \\). Determine whether \\( f \\circ g \\) is measurable. Provide a counterexample if it is not always measurable.",
... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "A sequence of numbers is generated as follows: Let \\( a_1 = 1 \\) and for \\( n \\ge 1 \\), choose \\( a_{n+1} \\) at random from the positive integers from 1 to \\( 10 - a_n \\), inclusive. On average, what fraction of the terms in the sequence will be equal to 1?",
"tool... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the equation \\( x^2 + 7x = (2x + 1) \\sqrt{x^2 + x + 6} \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nx^{2}+7x=(2x+1)\\sqrt{x^{2}+x+6}\\qquad (1)\n\\]\n\n---\n\n### 1. Isolate the square‑root \n\n\\(2x+1\\neq0\\) because for \\(x=... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let \\(\\beta \\in (0,1]\\) be fixed. Let \\(x, y \\in \\left[0, \\frac{\\pi}{2}\\right)\\) such that \\(\\tan x + \\tan y = \\sqrt{2\\beta}\\). Find the minimum and the maximum possible values of \\(\\cos x + \\cos y\\).",
"tool_calls": null
},
{
"role": "assistant... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Evaluate the integral \\(\\int \\frac{x^4-1}{x^2\\sqrt{x^4+x^2+1}} \\, dx\\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nI=\\int\\frac{x^{4}-1}{x^{2}\\sqrt{x^{4}+x^{2}+1}}\\;dx\n\\]\n\n---\n\n### 1. Simplify the integrand \n\n\\[\n\\frac{x... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Determine the smallest number of squares that need to be colored on a \\( 1001 \\times 1001 \\) board such that:\n(i) If two squares share a side, then at least one of them must be colored;\n(ii) Among any six successive squares in a row or in a column, some two adjacent ones m... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find the least positive integer $n$ such that $\\cos\\frac{\\pi}{n}$ cannot be written in the form $p+\\sqrt{q}+\\sqrt[3]{r}$ with $p,q,r\\in\\mathbb{Q}$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\text{Find the smallest }n\\text{ such tha... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let \\(a\\), \\(b\\), \\(c\\), and \\(d\\) be nonnegative numbers. Determine the least positive \\(\\alpha\\) and the best positive \\(k\\) for which the following inequality holds:\n\\[\n\\sqrt{1+\\alpha \\sum (a-b)^2} + k \\left(\\frac{abc + abd + acd + bcd}{4}\\right) \\ge (... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the equation: $\\tan\\left(\\frac{3\\pi}{4} \\cdot \\frac{x+6}{x+3}\\right) \\cdot \\tan\\left(\\frac{3\\pi}{4} \\cdot \\frac{x-1}{x+1}\\right) = 1$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\tan\\Bigl(\\frac{3\\pi }4\\,\\frac{x+6}{... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Evaluate the integral $\\int \\frac{\\arcsin\\frac{x}{2}}{\\sqrt{2-x}} \\, dx$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nI=\\int \\frac{\\arcsin\\frac{x}{2}}{\\sqrt{2-x}}\\;dx\n\\]\n\n---\n\n### 1. Integration by parts \n\nTake \n\n\\[\... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all \\( x, y \\in \\mathbb{N} \\) satisfying \\( \\frac{x^2 + y}{xy + 1} \\in \\mathbb{Z} \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\begin{aligned}\n&\\text{Let }d=xy+1.\\quad d\\mid x^{2}+y\\Longrightarrow \n\\frac{x^{2}+y}{xy+1... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Let $\\ell$ be a line in the plane and let $90^\\circ < \\theta < 180^\\circ$. Consider distinct points $P, Q, R$ such that:\n- $P$ lies on $\\ell$ and $PQ$ is perpendicular to $\\ell$.\n- $R$ lies on the same side of $\\ell$ as $Q$, and $R$ does not lie on $\\ell$.\n- For any ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all primes \\( p \\) and \\( q \\) such that \\( q \\mid p^q + 1 \\) and \\( q + p \\mid q^{q+p} - p^p \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\text{Find all prime pairs }(p,q)\\text{ such that } \n\\begin{cases}\nq\\mid p^{\\,... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all convex polygons for which the following property holds: for any interior point of the given polygon and for any side, the foot of the perpendicular drawn from this point on the selected side lies inside that side.",
"tool_calls": null
},
{
"role": "assistan... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Evaluate the integral \\(\\int_0^1 \\frac{\\tanh^{-1} x \\cdot \\ln x}{x(1-x)(1+x)} \\, dx\\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Solution**\n\n\\[\nI=\\int_{0}^{1}\\frac{\\operatorname{artanh}x\\,\\ln x}{x\\,(1-x)(1+x)}dx\n =\\int_... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the system of equations:\n\\[\n\\left\\{\\begin{matrix}\n(x+y)\\sqrt{x^2-4x+5}+(x-2)\\sqrt{(x+y)^2+1}=0\n\\\\\nx-y(x^2-y^2)=2(1-x^2+y^2)\n\\end{matrix}\\right.\n\\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\begin{cases}\n(x+y)\\sqrt... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Evaluate the sum $\\sum_{n=1}^{\\infty} \\frac{1}{2^n (1+\\sqrt[2^n]{2})}$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nS=\\sum_{n=1}^{\\infty}\\frac{1}{2^{n}\\bigl(1+\\sqrt[2^{n}]{2}\\bigr)}\n\\]\n\n---\n\n**1. Rewrite each term**\n\n\\[\n\... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all values of positive integers $a$ and $b$ such that it is possible to place $a$ ones and $b$ zeros at the vertices of a polygon with $a+b$ sides. After rotating the numbers at the vertices, exactly one pair of neighboring $0$ and $1$ should switch places, while all other... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "How many integer tuples $(x, y, z)$ satisfy $0 \\leq x, y, z < 2011$, $xy + yz + zx \\equiv 0 \\pmod{2011}$, and $x + y + z \\equiv 0 \\pmod{2011}$?",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\np=2011\\qquad(\\text{prime}).\n\\]\n\nAl... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Evaluate the sum $\\tan(1) + \\tan(5) + \\tan(9) + \\cdots + \\tan(173) + \\tan(177)$. Note: $\\tan$ is the tangent function.",
"tool_calls": null
},
{
"role": "assistant",
"content": "The angles are equally spaced by \\(4^{\\circ}\\).\nSince \n\n\\[\n4^{\\circ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all real numbers \\( a \\) such that the equation \\( x(x+1)^3 = (2x + a + 1)(x + a) \\) has exactly four real roots.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\nx(x+1)^{3}=(2x+a+1)(x+a)\n\\qquad (x\\in\\mathbb R)\n\\]\n\n---\n\n### 1. ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all harmonic functions \\( u: \\mathbb{R}^n \\to \\mathbb{R} \\) such that \\( |u(x)| \\le C|x|^m \\) for all \\( |x| \\ge 1 \\), where \\( C \\) is a constant and \\( m \\in (0,2) \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Answer.** ... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the following system of equations:\n\\[\n\\left\\{\n\\begin{matrix}\nx^5 = 2x + 7y + 27 \\\\\ny^5 = 5x + 4y + 27\n\\end{matrix}\n\\right.\n\\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "First observe that the two equations give a simple rel... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "A piece of paper in the shape of a right triangle is folded such that the smaller leg rests on the hypotenuse. If the segment $a = 9$ and segment $b = \\frac{24}{5}$, calculate the lengths of the sides of the paper.",
"tool_calls": null
},
{
"role": "assistant",
... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "There are a number of towns on a circular road. They are served by five buses. Each bus travels the entire road but only stops at five towns. For every pair of towns, there is a bus that stops at both. Find the largest possible number of towns.",
"tool_calls": null
},
{... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Solve the system of equations:\n\\[ \\begin{cases} x^3 + y^3 = 68 \\\\ x^2 - y^2 = 7 \\sqrt{5} \\end{cases} \\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\begin{cases}\nx^3+y^3=68\\\\[2mm]\nx^2-y^2=7\\sqrt5\n\\end{cases}\n\\]\n\n---\n\n**1... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Bob and Tom each have a cube and some red and blue paint. They paint each side of their cubes either red or blue. What is the probability that the two painted cubes are indistinguishable?",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step 1 – Coun... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all triples \\((k, m, n)\\) of positive integers such that \\(m\\) is a prime and the following conditions are satisfied:\n1. \\(kn\\) is a perfect square.\n2. \\(\\frac{k(k-1)}{2} + n\\) is a fourth power of a prime.\n3. \\(k - m^2 = p\\) where \\(p\\) is a prime.\n4. \\(... | null |
Math | nemotron-cascade2-math | null | [
{
"role": "user",
"content": "Find all polynomials \\( P(x) \\) with odd degree such that \\( P(x^2 - 2) = P^2(x) - 2 \\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\n\\boxed{P(x)=2\\,T_{2k+1}\\!\\Bigl(\\frac{x}{2}\\Bigr)\\qquad(k=0,1,2,\\dots)}\n\\]\n\nwhere \\(T_n\\) de... | null |
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RazorCal
RazorCal is a general-purpose calibration corpus released with RAZOR. It contains 2,048 samples across seven domains (about 8 MB). Each record includes input messages and source attribution. The records carry no architecture-specific fields, so the corpus also suits FFN or layer pruning, perplexity measurement and other calibration-based compression; RAZOR uses it to estimate per-expert statistics. Reasoning traces are omitted because the calibration loader does not consume them. Potential contact identifiers, home-directory usernames, private-network examples and literal password examples are replaced with placeholders.
This repository re-publishes the corpus in a row-oriented format: each of the 2,048 samples is one dataset row. It is converted from the original single-file release at Nickyang/RazorCal, which is also included unchanged at source/RazorCal.json so that the conversion can be verified against the original artifact.
Composition
| Domain | Samples |
|---|---|
| Coding | 512 |
| Math | 256 |
| Science (STEM) | 256 |
| Chinese-STEM | 256 |
| Instruction Following | 256 |
| Tool Calling | 256 |
| World Knowledge | 256 |
| Total | 2,048 |
Format
Each row is one sample with the following columns:
| Column | Type | Description |
|---|---|---|
domain |
string | one of the seven domains above |
sub_source |
string | recorded upstream source attribution |
coding_subclass |
string, nullable | subclass label, present on Coding samples |
messages |
list of structs | chat messages with role, content and optional tool_calls (id, type, index, function.name, function.arguments) |
tools |
list of structs, nullable | tool definitions with type and function (name, description, parameters) |
The corpus defines a single train split holding all 2,048 samples; no train/validation/test semantics are implied.
Conversions applied to the original file, needed to keep a single valid arrow schema:
tool_calls[].function.argumentsandtools[].function.parametersare free-form JSON objects whose value types conflict across records (for example a string and a number under the same key path of different records). They are recorded as JSON strings; parse them withjson.loadsbefore use.- The optional message fields
tool_call_idandnameare null for every record in the original file and are omitted here. - Empty
tool_callsandtoolslists are recorded as null.
Everything else is preserved verbatim. The corpus metadata recorded in the original file's meta object:
{
"name": "RazorCal",
"total_samples": 2048,
"max_length_per_sample": 32000,
"domains": {
"Math": 256,
"Science (STEM)": 256,
"Chinese-STEM": 256,
"Instruction Following": 256,
"Tool Calling": 256,
"World Knowledge": 256,
"Coding": 512
},
"coding_subclass_distribution": {
"swe_issue_fix": 40,
"engineering_oop_api": 111,
"cp_python_stdin": 138,
"cp_cpp_stdin": 99,
"func_signature_completion": 100,
"leetcode_class_solution": 24
},
"homepage": "https://github.com/nick7nlp/RAZOR",
"description": "RazorCal is a multi-domain calibration corpus released with RAZOR. It is a general-purpose calibration mixture: the records carry no architecture-specific fields and can be used for expert, FFN or layer pruning as well as other calibration-based compression. Source labels record attribution; see the datasheet for provenance, privacy processing, and usage limitations.",
"license": "Source-specific terms apply; see LICENSE-DATA.",
"privacy_processing": "Reasoning traces are omitted. Contact identifiers, home-directory usernames, private-network examples, and literal password examples are replaced with placeholders."
}
Loading the rows:
import json
from datasets import load_dataset
dataset = load_dataset("inference-optimization/RazorCal", split="train")
sample = dataset[0]
messages = sample["messages"]
for call in messages[-1]["tool_calls"] or []:
call["function"]["arguments"] = json.loads(call["function"]["arguments"])
For the RAZOR CLI, use the unchanged original file:
curl -L -o RazorCal.json \
https://huggingface.co/datasets/inference-optimization/RazorCal/resolve/main/source/RazorCal.json
razor saliency --model <model-path> --data RazorCal.json --out out/sal
Recorded sources
A source label records attribution information; it is not, by itself, proof of a record-level match to an upstream release.
| Domain | sub_source labels and counts |
Recorded source description |
|---|---|---|
| Math | nemotron-cascade2-math (160); nemotron-math-v2-high-aime-style (96) |
Nemotron-Cascade-2-SFT-Data math slice; Nemotron-Math-V2 |
| Science (STEM) | Nemotron-Science-V1-RQA (176); Nemotron-Science-V1-MCQ (80) |
Nemotron-Science-V1 |
| World Knowledge | OpenHermes-2.5 (256) |
OpenHermes-2.5 via smoltalk2 |
| Coding | Dolci-Python-Algorithms (205); competitive-programming-python (141); competitive-programming-cpp (115); Nemotron-SFT-SWE-V2-agentless (40); Nemotron-OpenCode-general (11) |
Dolci; competitive-programming, SWE and OpenCode corpora |
| Instruction Following | Dolci-Precise-IF (256) |
Dolci instruction-following corpus |
| Tool Calling | Nemotron-Agentic-tool-calling-v2 (256) |
Nemotron agentic/tool-calling corpus |
| Chinese-STEM | multilingual-chinese-math (86); multilingual-chinese-code (85); multilingual-chinese-stem (85) |
Multilingual Chinese categories |
The nemotron-cascade2-math records were taken as a whole domain slice rather
than sampled individually, so the label records the upstream dataset but not a
per-record identifier within it. Source labels alone do not establish
provenance. See FIDELITY_AUDIT.md for provenance
boundaries and LICENSE-DATA for recorded license information.
Usage limitations
RazorCal is calibration data, not an independent evaluation benchmark. Domain coverage does not guarantee preservation of model quality. Review possible overlap with evaluation data for the intended use.
The original record array contains 587 tool messages without populated
tool_call_id links and 11 tool definitions with empty parameters objects;
in this repository the always-null tool_call_id and name fields are
omitted, as documented under Format. Tokenizer chat templates and
schema validators may require additional handling at load time.
Public source material can still contain personal references or unsuitable content; source labels do not establish that records are free of such content. See DATASHEET.md for intended use and limitations.
Citation and licensing
Source-specific terms continue to apply; no single replacement license is asserted for all RazorCal records. Retain applicable upstream attribution. See LICENSE-DATA and NOTICE before use or redistribution.
This repository contains no code; LICENSE-CODE is retained from the upstream release for completeness. See DATASHEET.md for intended use and limitations and FIDELITY_AUDIT.md for the scope of available provenance evidence.
@misc{song2026razorpruningreplaceableexperts,
title={RAZOR: Pruning Replaceable Experts in LLMs},
author={Mingyang Song and Mao Zheng},
year={2026},
eprint={2609.30465},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2609.30465},
}
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