Rubric-Calibrated Preferences: Cross-Query Calibration of LLM Judgments via Item Response Theory
Paper • 2609.35739 • Published
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TheoremQA_xinyi/concavity.json | Consider a source X with a distortion measure $d(x, \hat{x})$ that satisfies the following property: all columns of the distortion matrix are permutations of the set $\{d_1, d_2, \ldots, d_m\}$. The function $\phi(D) = \max_{b:\sum_{i=1}^m p_i d_i \leq D} H(p)$ is concave. True or False?
True. | |
TheoremQA_maxku/fourier6-FT.json | If x(n) and X(k) are an N-point DFT pair, then x(n+N)=x(n). Is it true?
Yes, it is true.
This property is known as the periodicity property of the Discrete Fourier Transform (DFT). It states that if x(n) and X(k) are an N-point DFT pair, then x(n+N) = x(n) for all values of n. Therefore, the answer is True. | |
TheoremQA_maxku/ipnetwork20-ip.json | Given a network in the figure, From Interface m1 of router R2 it can reach how many destinations?
From Interface m1 of router R2, it can reach a total of 4 destinations. Therefore, the answer is 4. | |
TheoremQA_mingyin/convexity1.json | For a\geq 0, we define $S_a={x | dist(x, S) \leq a}$, where $dist(x,S)=inf_{y\in S}||x-y||$. Suppose S is convex. Is S_a convex? Return 1 for yes and 0 for no.
Let's consider two points x and y in $S_a$. We need to show that for any t in the range [0, 1], the point z = tx + (1-t)y also belongs to $S_a$ to prove that $S... | |
TheoremQA_elainewan/math_calculus_5.json | What is \int_{-3}^1 (7x^2 + x +1)dx?
To solve this integral, we first need to find the antiderivative of the given function, which is:
F(x) = \int (7x^2 + x + 1)dx = (7/3)x^3 + (1/2)x^2 + x + C
Now, we need to evaluate the definite integral from -3 to 1:
\int_{-3}^1 (7x^2 + x + 1)dx = F(1) - F(-3)
F(1) = (7/3)(1)^3... | |
TheoremQA_wenhuchen/definite_matrix1.json | Consider the matrix of A=[[1, 4], [4, 1]], is this a positive definite matrix?
No, the matrix A is not positive definite. Therefore, the answer is False. | |
TheoremQA_maxku/signalprocessing11-nyquist.json | Consider $x(t)$ to be given as, $$ x(t)=\cos (1000 \pi t) $$ . Let the sampling frequency be $2000 \mathrm{~Hz}$. Does aliasing occur?
To determine if aliasing occurs, we need to compare the signal frequency with the Nyquist frequency. The Nyquist frequency is half of the sampling frequency. In this case, the sampling ... | |
TheoremQA_elainewan/math_calculus_2_7.json | \lim_{x \to c} |f(x)| = 0. What is \lim_{x \to c} f(x)?
Since the limit of the absolute value of f(x) as x approaches c is 0, we know that f(x) approaches 0 as x approaches c from both the left and the right. Therefore, the answer is:
\lim_{x \to c} f(x) = 0. | |
TheoremQA_maxku/ipnetwork13-hammingdist.json | Calculate the Hamming pairwise distances and determine the minimum Hamming distance among the following codewords: 00000,10101,01010
The Hamming pairwise distances between the given codewords are:
- Distance between 00000 and 10101 = 3
- Distance between 00000 and 01010 = 2
- Distance between 10101 and 01010 = 5
Ther... | |
TheoremQA_elainewan/math_calculus_2.json | What is \lim_{x o 9} ((x - 9)/(\sqrt{x} - 3))?
To find the limit of the given expression as x approaches 9, we can use the conjugate method. Multiply the numerator and denominator by the conjugate of the denominator, which is (√x + 3):
((x - 9) / (√x - 3)) * ((√x + 3) / (√x + 3))
Now, multiply the numerators and den... | |
TheoremQA_mingyin/Fundamental-Theorem-of-Calculus3.json | what is the value of \int_a^b \frac{dx}{\sqrt{(x-a)(b-x)}}? Round the answer to the thousands decimal.
To solve the integral \int_a^b \frac{dx}{\sqrt{(x-a)(b-x)}}, we can use the substitution method. Let x = a + (b-a)sin^2(t), then dx = 2(b-a)sin(t)cos(t)dt. The integral becomes:
\int_0^{\pi/2} \frac{2(b-a)sin(t)cos(t... | |
TheoremQA_maxku/fourier4-FT.json | Is the Fourier transform of the signal x(t)=(1-e^{-|t|})[u(t+1)-u(t-1)] even?
Yes, the Fourier transform of the given signal x(t) is even.
We can use the properties of Fourier transform to prove this. Let X(f) be the Fourier transform of x(t). Then, we have:
X(f) = ∫[1-e^{-|t|}][u(t+1)-u(t-1)]e^{-j2πft} dt
Using th... | |
TheoremQA_elainewan/math_abstact_algebra_7_8.json | Are groups Z_4 * Z_2 and D_4 isomorphic?
No, groups Z_4 * Z_2 and D_4 are not isomorphic. Therefore, the answer is False. | |
TheoremQA_wenhuchen/ODE2.json | Use Euler's Method to calculate the approximation of y(0.2) where y(x) is the solution of the initial-value problem that is as follows. y''+xy'+y=0 and y(0)=2 and y'(0) = 3.
To use Euler's method, we need to convert the given second-order differential equation into a system of first-order differential equations. Let's ... | |
TheoremQA_elainewan/math_calculus_11.json | What is the limit of the sequence a_n = n/(\sqrt{n^2 + 1})?
To find the limit of the sequence a_n, we can use the fact that for any positive constant c, we have:
lim (n → ∞) (c/n) = 0
Using this fact, we can rewrite the sequence a_n as:
a_n = n/(\sqrt{n^2 + 1}) * (\sqrt{n^2 + 1}/n)
Simplifying the second factor, we... | |
TheoremQA_xinyi/kernel_2.json | A positive-definite kernel function satisfies the Cauchy-Schwartz inequality. True or false?
Therefore, the answer is True. | |
TheoremQA_elainewan/math_algebra_3.json | Is W = {[x, y] in R^2: x >= 0 and y >= 0} a subspace of R^2?
To determine if W is a subspace of R^2, we need to check if it satisfies the three subspace properties:
1. The zero vector (0, 0) is in W.
2. W is closed under vector addition.
3. W is closed under scalar multiplication.
1. The zero vector (0, 0) is in W si... | |
TheoremQA_wenhuchen/stoke's_theorem1.json | Use Stoke's Theorem to evaluate $\iint_S curl \vec{F} \cdot d \vec{r}$ where $\vec{F} = z^2 \vec{i} - 3xy \vec{j} + x^3y^3 \vec{k}$ and $S$ is the part of $z = 5 - x^2 - y^2$ above the plane $z$=1. Assume that S is oriented upwards.
Stoke's Theorem states that $\iint_S curl \vec{F} \cdot d \vec{S} = \oint_C \vec{F} \cd... | |
TheoremQA_xueguangma/options_theory.json | An investor who is bullish about a stock may wish to construct a bull spread for that stock. One way to construct such a spread is to buy a call with strke price $K_1$ and sell a call with the same expiration date but with a strike price of $K_2 > K_1$. If we draw the payoff curve for that a spread, the initial cost of... | |
TheoremQA_mingyin/Arzela-Ascoli-theorem1.json | Let M be the set of bounded functions (i.e. \sup_{x\in[a,b]}|f(x)|<\infty) in C[0,1]. Is the set ${F(x)=\int_0^x f(t) dt | f \in M }$ a sequentially compact set? Answer 1 for yes and 0 for no. Furthermore, it can be proved using 1. Arzelà-Ascoli theorem, 2. Riesz representation theorem, 3. Banach fixed point theorem, 4... | |
TheoremQA_mingyin/liouville-theorem1.json | For the following functions, which are bounded entire functions? 1. f(x)=0; 2. f(x)= 1+i; 3. f(x)=sin(x); 4. f(x)=min{|cos(x)|,1}. Here i=\sqrt{-1} and $|\cdot|$ is the norm of a complex number. Return the numbers of the answers as a list.
A bounded entire function is a function that is both entire (analytic on the who... | |
TheoremQA_wenhuchen/Lagrange's_theorem.json | Is there a y bewteen x and x+h such that $sin(x+h) - sinx = h * cos(y)$?
Yes, there exists a y between x and x+h such that $sin(x+h) - sinx = h * cos(y)$.
This is known as the Mean Value Theorem for sine function. According to this theorem, for any function that is continuous on a closed interval [a, b] and different... | |
TheoremQA_wenhuchen/morera's_theorem2.json | Is function f defined by $f(z) = \int_0^{\infy} |e^{zt}| / (t+1) dt$ analytical on the left plane D: Re(z) < 0
Yes, the function f is analytical on the left plane D: Re(z) < 0.
To show this, we need to use the theorem of complex analysis which states that if a function is continuous and has a continuous derivative wit... | |
TheoremQA_wenhuchen/differential_equation5.json | Is the differential equation $2tyy' + 2t + ty^2 = 0$ the total derivative of the potential function $\phi(t, y) = t^2 + ty^2$?
To determine if the given differential equation is the total derivative of the potential function, we need to compute the partial derivatives of the potential function with respect to t and y, ... | |
TheoremQA_mingyin/Vitali-cover-theorem1.json | the monotone function f on [0,1] is differentiable almost everywhere. This can be proved by: (a) Fubini Theorem; (b) Tonelli Theorem; (c) Vitali Cover Theorem; (d) None of the above. Which option is correct?
The correct option is (c) Vitali Cover Theorem. | |
TheoremQA_elainewan/math_algebra_2.json | Is the transformation [[-1, 0], [0, -1]] invertible?
The given transformation is a linear transformation that represents a reflection about the origin in a two-dimensional plane. Since the determinant of this transformation is (-1)*(-1) - 0*0 = 1, which is not equal to zero, the transformation is invertible. Therefore,... | |
TheoremQA_wenhuchen/L'Hôpital_rule1.json | What is (sin(2x) / x)^(1+x) when x is approaching 0?
We can use L'Hopital's rule to evaluate the limit. Taking the natural logarithm of the expression, we get:
ln[(sin(2x) / x)^(1+x)] = (1+x)ln(sin(2x)/x)
Taking the derivative of both sides with respect to x, we get:
[ln(sin(2x)/x)]' = 2cot(2x) - 1/x
Plugging in x=... | |
TheoremQA_xinyi/markov_inequality.json | Let $X$ be uniformly distributed over $\{1, 2, \ldots, m\}$. Assume $m=2^n$ . We ask random questions: Is $X\in S_1$? Is $X\in S_2$? ... until only one integer remains. All $2^m$ subsets of $\{1, 2, \ldots, m\}$ are equally likely. Suppose we ask $n+\sqrt{n}$ random questions. Use Markov's inequality to find the probab... | |
TheoremQA_tonyxia/semiconductor3.json | Assume a temperature of 300 K and find the wavelength of the photon necessary to cause an electron to jump from the valence to the conduction band in silicon in nm.
To find the wavelength of the photon necessary to cause an electron to jump from the valence to the conduction band in silicon, we can use the formula:
E ... | |
TheoremQA_tonyxia/quantum3.json | Calculate the momentum uncertainty of an electron within the smallest diameter of a hydrogen atom in kg m/s.
To calculate the momentum uncertainty of an electron within the smallest diameter of a hydrogen atom, we can use the Heisenberg Uncertainty Principle. The principle states that the product of the uncertainties i... | |
TheoremQA_wenhuchen/wiener_process2.json | Let W(t) be the standard Brownian motion, and 0 < s < t. Find the conditional PDF of W(s = 1/2) given that W(t = 1) = 2. What are the mean and variance? Return the list of [mean, variance].
To find the conditional probability density function (PDF) of W(s = 1/2) given that W(t = 1) = 2, we can use the properties of the... | |
TheoremQA_wenhuchen/infinite_series_sum2.json | Find the sum of $\sum_{n=1}^{\infty} (1/e^n + 1/(n*(n+1)))$
We can simplify the given expression as follows:
$$\sum_{n=1}^{\infty} \left(\frac{1}{e^n} + \frac{1}{n(n+1)}\right) = \sum_{n=1}^{\infty} \frac{1}{e^n} + \sum_{n=1}^{\infty} \frac{1}{n(n+1)}$$
The first sum is a geometric series with first term $1/e$ and comm... | |
TheoremQA_elainewan/econ_micro_11.json | John's Lawn Mowing Service is a small business that acts as a price-taker (i.e., MR = P). The prevailing market price of lawn mowing is $20 per acre. John's costs are given by total cost = 0.1q^2 + 10q + 50, where q = the number of acres John chooses to cut a day. Calculate John's maximum daily profit.
To find John's m... | |
TheoremQA_maxku/basic-electronics-2-1.json | Given $V_s = 5V$, $R_1 = 480 \Omega$, $R_2 = 320 \Omega$, and $R_3 = 200 \Omega$, find the power dissipated by the 3 resistors $P_1, P_2, P_3$ in the figure. Represent your answer as a list [$P_1, P_2, P_3$] in the unit of mW.
To find the power dissipated by the resistors, we first need to find the current flowing thro... | |
TheoremQA_jianyu_xu/Graph_2.json | How many labeled trees are there on 6 vertices?
Cayley's formula states that the number of labeled trees on n vertices is n^(n-2). In this case, n = 6, so the number of labeled trees on 6 vertices is 6^(6-2) = 6^4 = 1296. Therefore, the answer is 1296. | |
TheoremQA_elainewan/math_algebra_6.json | For a matrix A, is the function F(A) = det A from the linear space R^{3*3} to R a linear transformation?
To determine if F(A) = det A is a linear transformation, we need to check if it satisfies the two properties of linearity:
1. F(A + B) = F(A) + F(B)
2. F(cA) = cF(A), where c is a scalar.
Let A and B be two 3x3 ma... | |
TheoremQA_panlu/uniform_circular_motion1.json | An Aston Martin V8 Vantage sports car has a lateral acceleration of $0.96g = (0.96)(9.8 m / s^2) = 9.4 m / s^2$. This is the maximum centripetal acceleration the car can sustain without skidding out of a curved path. If the car is traveling at a constant 40m/s on level ground, what is the radius R of the tightest unban... | |
TheoremQA_wenhuchen/definite_matrix2.json | Consider the matrix of A=[[1, -1], [-1, 4]], is this a positive definite matrix?
To determine if the matrix A is positive definite, we need to check if all its eigenvalues are positive. Let's find the eigenvalues of A:
The characteristic equation of A is given by the determinant of (A - λI), where λ is an eigenvalue a... | |
TheoremQA_xueguangma/capital_asset_pricing_model.json | Suppose a stock has the following information. It is listed on the London stock exchange and operates throughout Europe. The yield on a UK 10 year treasury is 2.8%. The stock in question will earn 8.6% as per historical data. The Beta for the stock is 1.4, i.e., it is 140% volatile to the changes in the general stock m... | |
TheoremQA_xinyi/shannon_lower_bound.json | Consider a source X uniform on $\{1,2,\ldots,m\}$ with a distortion measure $d(x, \hat{x})$ that satisfies the following property: all rows and columns of the distortion matrix are permutations of the set $\{d_1, d_2, \ldots, d_m\}$. Then the Shannon lower bound is tight. i.e. $R(D)=H(X)-\phi(D)$. True or False?
Theref... | |
TheoremQA_elainewan/math_algebra_6_2.json | Let V be the space spanned by functions cos(2x) and sin(2x). Find the determinant of the linear transformation D(f) = f' from V to V.
We can represent the linear transformation D(f) = f' as a matrix with respect to the basis {cos(2x), sin(2x)}. The matrix will be:
| 0 2 |
|-2 0 |
To find the determinant of this mat... | |
TheoremQA_elainewan/math_calculus_2_5.json | What is \lim_{x \to (\pi)/2} (cos(x)cos(tan(x)))?
We can solve this limit by using the trigonometric identity cos(a)cos(b) = (1/2)[cos(a+b) + cos(a-b)]. Substituting a = x and b = tan(x), we get cos(x)cos(tan(x)) = (1/2)[cos(x + tan(x)) + cos(x - tan(x))]. Now, we can evaluate the limit as x approaches pi/2.
Using th... | |
TheoremQA_xueguangma/forward_price_3.json | The current price of gold is $412 per ounce. The storage cost is $2 per ounce per year, payable quaterly in advance. Assuming a constant intrest rate of 9% compounded quarterly, what is the theoretial forward price of gold for delivery in 9 months?
We can use the formula for the theoretical forward price of a commodity... | |
TheoremQA_tonyxia/maxplanar3.json | True of false: one can draw a simple connected planar graph with 200 vertices and 400 faces
False.
According to Euler's formula, for a simple connected planar graph with V vertices, E edges, and F faces, we have V - E + F = 2.
Substituting V = 200 and F = 400, we get E = 602.
However, for a simple connected plana... | |
TheoremQA_jianyu_xu/Catalan_2.json | How many paths are there from the origin (0,0) to the point (10,10) on a grid such that the path only moves up or right and does not cross the diagonal line y = x?
To find the number of paths from the origin (0,0) to the point (10,10) on a grid without crossing the diagonal line y = x, we can use the concept of Catalan... | |
TheoremQA_maxku/cv-imageprocessing9-digital-image.json | Calculate the required memory size in Mebibytes (MiB) (in 3 sig.fig.) for storing a frame in 1080p if the sampling scheme R'G'B' 4:4:4 is used. Note that there are 1920 × 1080 pixels in one 1080p frame. Each pixel contains three primary-colour components. Each primary-colour component requires 1 byte of memory for sto... | |
TheoremQA_xueguangma/sharpe_ratio.json | Let’s assume that the 10-year annual return for the S&P 500 (market portfolio) is 10%, while the average annual return on Treasury bills (a good proxy for the risk-free rate) is 5%. The standard deviation is 15% over a 10-year period. Whats the market Sharpe Ratio?
The market Sharpe Ratio can be calculated as the exces... | |
TheoremQA_tonyxia/statisticalphysics5.json | Calculate the Fermi energy for copper in eV.
The Fermi energy for copper can be calculated using the formula:
E_F = (h^2 / 2m) * (3π^2 * n)^2/3
where h is the Planck constant, m is the mass of an electron, and n is the number density of electrons in copper.
Using the values h = 6.626 x 10^-34 J s, m = 9.109 x 10^-31... | |
TheoremQA_wenhuchen/jensen1.json | For any triangle ABC, we have sin(A) + sin(B) + sin(C) $\le$ 3\sqrt(3)/2, is this true or false?
This inequality is true for any triangle ABC. Therefore, the answer is True. | |
TheoremQA_maxku/cv-cnn4.json | Consider Convolutional Neural Network D2 which takes input images of size 32x32 with 1 colour channels. The first layer of D2 uses 4 filters of size 5x5, a stride of 2, and zero-padding of width 1. The dimensions of the resulting activation map for each filter in this first layer will be k x k. What is the value of k?
... | |
TheoremQA_elainewan/math_algebra_4.json | Is the set of 3 * 3 matrices in reduced row-echelon form a subspace of R^{3 * 3}?
To determine if the set of 3 * 3 matrices in reduced row-echelon form is a subspace of R^{3 * 3}, we need to check if it satisfies the following three conditions:
1. The zero matrix is in the set.
2. The set is closed under addition.
3. ... | |
TheoremQA_wenhuchen/t_test1.json | Based on field experiments, a new variety green gram is expected to given an yield of 12.0 quintals per hectare. The variety was tested on 10 randomly selected farmers fields. The yield ( quintals/hectare) were recorded as 14.3,12.6,13.7,10.9,13.7,12.0,11.4,12.0,12.6,13.1. Do the results conform the expectation with Le... | |
TheoremQA_wenhuchen/binomial.json | What is the coefficient of $x^2y^5$ for the formula $(x + 2y)^7$?
To find the coefficient of $x^2y^5$ in the expansion of $(x + 2y)^7$, we can use the binomial theorem. The general term of the binomial expansion is given by:
${n \choose k} a^{n-k} b^k$
In our case, $n = 7$, $a = x$, and $b = 2y$. We want to find the ... | |
TheoremQA_wenhuchen/eigen_value1.json | For matrix A = [[5, 4], [1, 2]], what are its eigen values?
To find the eigenvalues of matrix A, we need to solve the characteristic equation, which is given by the determinant of (A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
Matrix A - λI = [[5 - λ, 4], [1, 2 - λ]]
The determinant of this mat... | |
TheoremQA_xueguangma/future_value_1.json | For a $1,000 investment, what is the future value of the investment if the interest rate is 8% compounded annually for 3 years?
We can use the formula for compound interest to find the future value of the investment. The formula is:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value (or princip... | |
TheoremQA_mingyin/Banach-Steinhaus-theorem1.json | Suppose H is a Banach space, and {x_n}\in H, x\in H. Then x_n weakly converges to x is equivalent to: ||x_n|| is bounded; for a dense set M* in H*, it holds \lim_{n\rightarrow\infty} f(x_n)=f(x) for all f\in M*. Is this correct? Answer 1 for yes and 0 for no.
The statement is correct. Therefore, the answer is 1. | |
TheoremQA_xinyi/chi_square_test.json | The Chi-square statistic $\chi^2=\sum_c\frac{(P(x)-Q(x))^2}{Q(x)}$ is (twice) the first term in the Taylor series expansion of $D(P||Q)$ about $Q$. True or False?
True.
The Kullback-Leibler divergence between two probability distributions $P$ and $Q$ is defined as $D(P||Q)=\sum_x P(x)\log\frac{P(x)}{Q(x)}$.
Expandi... | |
TheoremQA_xueguangma/present_value_2.json | For the 3 payments of $1000 each end-of-year, with 7% rate of return, what is the present value if the first payment is made at the end of fifth year?
To find the present value of the 3 payments of $1000 each at the end of the fifth, sixth, and seventh years, we will use the present value formula:
PV = CF / (1 + r)^n
... | |
TheoremQA_elainewan/math_abstact_algebra_7_3.json | What is the order of the group S_3 * Z_2?
The group S_3 is the symmetric group of degree 3 and has order 6. The group Z_2 is the cyclic group of order 2. The direct product of two groups G and H, denoted by G * H, is a group whose elements are ordered pairs (g, h) where g is an element of G and h is an element of H, an... | |
TheoremQA_elainewan/math_abstact_algebra_7_7.json | The function f: U_5 o U_5 given by f(x) = x^2 is a homomorphism. What is K_f?
Since f is a homomorphism, we know that K_f is a subgroup of U_5.
To find K_f, we need to find all the elements x in U_5 such that f(x) = x^2 is the identity element in U_5, which is 1.
The elements of U_5 are {1, 2, 3, 4}, so we can sim... | |
TheoremQA_wenhuchen/cramer's_rule1.json | For the two linear equations $2 * x + 3 * y = 10$ and $4 * x + 4 * y = 12$ iwth variables x and y. Use cramer's rule to solve these two variables.
To solve the given system of linear equations using Cramer's rule, we first need to find the determinants of the coefficient matrix, and the matrices obtained by replacing t... | |
TheoremQA_maxku/cv-cnn1.json | Given a color image of size 28 x 28 x 3 pixels, how many convolutional filters in the first layer of a Convolutional Neural Network if the first layer's output tensor has size 26 x 26 x 64?
To find the number of convolutional filters in the first layer, we need to consider the output tensor size and the input tensor si... | |
TheoremQA_jianyu_xu/Ramsey_5.json | Coloring the edges of a complete graph with n vertices in 2 colors (red and blue), what is the smallest n that guarantees there is either a 4-clique in red or a 5-clique in blue?
To find the smallest n that guarantees either a 4-clique in red or a 5-clique in blue, we can use the Ramsey's theorem. The Ramsey number R(m... | |
TheoremQA_tonyxia/particle4.json | The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory collides gold ions onto other gold ions head on. The energy of the gold ions is 100 GeV per nucleon. What is the center-of-mass energy of the collision in TeV?
To find the center-of-mass energy of the collision, we need to consider that go... | |
TheoremQA_maxku/ipnetwork21-ip-2.json | Consider the following graph, with links costs listed, and assume we are using shortest-path (or lowest-cost) routing, and that routing has equilibrated to a constant set of routing tables. The routing algorithm uses poisoned reverse, advertising an infinite weight for the poisoned paths. is the distance that B adverti... | |
TheoremQA_panlu/linear_expansion1.json | A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20°C. The markings on the tape are calibrated for this temperature. When it is 35°C, the surveyor uses the tape to measure a distance. The value that she reads off the tape is 35.794 m. What is the actual distance? (Unit: m)
We can... | |
TheoremQA_maxku/signalprocessing7-phaseshift.json | Consider that the following two signals: $x(t)$ and $v(t)$ $$ x(t)=\left\{\begin{array}{cc} 1 & 0 \leq t \leq 3 \\ 0 & \text { otherwise } \end{array} \quad v(t)=\left\{\begin{array}{cc} 1 & 0 \leq t \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\right. $$ Let $y(\tau)=\int_{-\infty}^{\infty} x(\tau-t) v(t) d t$.... | |
TheoremQA_tonyxia/particle5.json | The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory collides gold ions onto other gold ions head on. The energy of the gold ions is 100 GeV per nucleon. What is the speed of the gold ions as a fraction of the speed of light?
We can use the formula for relativistic kinetic energy:
K = (γ -... | |
TheoremQA_elainewan/math_real_analysis_additional_1.json | Let (x_n) be a sequence defined by x_1 = 2 and x_{n+1} = 1 + 1/(1 + x_n). If (x_n) converges, what must its limit be in decimals?
Let's assume that the sequence (x_n) converges to a limit L. Then, as n goes to infinity, x_n approaches L, and x_{n+1} also approaches L. We can use this fact to find the limit L.
Since x_... | |
TheoremQA_mingyin/log-concave1.json | Is the cumulative distribution function of the standard gaussian distribution $F(x)=1/\sqrt{2 \pi} \int_{-\infty}^x e^{-t^2/2} dt$ is log-concave? Return 1 for yes and 0 for no.
The cumulative distribution function of the standard Gaussian distribution is log-concave. Therefore, the answer is 1. | |
TheoremQA_mingyin/Bounded-variation1.json | Let f be a real function on [0,1]. If the bounded variation of f on [0,1] equals f(1)-f(0), then: (a) f is increasing on [0,1]; (b) f is decreasing on [0,1]; (c) None of the above. Which one is correct?
The correct option is (c) None of the above.
The fact that the bounded variation of f on [0,1] equals f(1)-f(0) doe... | |
TheoremQA_xueguangma/dividend_discount_model_1.json | Lore Ltd. estimates that its dividend growth will be 13% per year for the next five years. It will then settle to a sustainable, constant, and continuing rate of 5%. Let’s say that the current year’s dividend is $14 and the required rate of return (or discount rate) is 12%. What is the current fair value of Lore Ltd. s... | |
TheoremQA_maxku/graphtheory4-vertexcover.json | Let a undirected graph G with edges E = {<0,3>, <1,3>, <2,3>}, which <A,B> represent Node A is connected to Node B. What is the minimum vertex cover of G? Represent the vertex cover in a list of ascending order.
A minimum vertex cover is a set of vertices such that each edge in the graph is incident to at least one ver... | |
TheoremQA_mingyin/double-integral4.json | compute the line integral of \int_K xy dx, \int_L xy dx, where K is a straight line from (0,0) to (1,1) and L is the Parabola y=x^2 from (0,0) to (1,1). return the answer as a list
We can parameterize the line K as r(t) = <t, t>, 0 <= t <= 1, and the parabola L as r(t) = <t, t^2>, 0 <= t <= 1. Then, we can compute the ... | |
TheoremQA_xinyi/kraft_inequality.json | Let $C$ be a variable length code that satisfies the Kraft inequality with equality but does not satisfy the prefix condition. Then $C$ has finite decoding delay. True or False?
False. A variable length code that satisfies the Kraft inequality with equality but does not satisfy the prefix condition may have infinite de... | |
TheoremQA_elainewan/math_calculus_2_10.json | Suppose g(x) is the horizontal asymptote of function f(x) = (3^x)/(1+3^{-x}). What are possible values of g(2023)?
To find the horizontal asymptote of the given function f(x), we need to take the limit of f(x) as x approaches positive or negative infinity.
As x approaches infinity, 3^{-x} approaches 0, so the denomin... | |
TheoremQA_elainewan/math_calculus_3_8.json | Julian is jogging around a circular track of radius 50 m. In a coordinate system with its origin at the center of the track, Julian's x-coordinate is changing at a rate of -1.25 m/s when his coordinates are (40, 30). Find dy/dt at this moment.
We know that the track is circular and has a radius of 50 m. Therefore, the ... | |
TheoremQA_tonyxia/statisticalphysics2.json | Compute the mean translational kinetic energy of a mole of ideal gas in J, both at room temperature 293 K.
To compute the mean translational kinetic energy of a mole of ideal gas, we can use the following formula:
Mean translational kinetic energy = (3/2) * R * T
where R is the ideal gas constant (8.314 J/mol·K) and ... | |
TheoremQA_wenhuchen/derivative2.json | Does the function $y=xe^{-x^2/2}$, does it satisfy the equation $xy' = (1 - x^2)y$
To determine if the function $y = xe^{-x^2/2}$ satisfies the equation $xy' = (1 - x^2)y$, we first need to find the derivative of the function with respect to $x$.
Using the product rule, we have:
$y' = (1)e^{-x^2/2} + x(-x)e^{-x^2/2}... | |
TheoremQA_tonyxia/relativity3.json | The atomic mass of the 4He atom is 4.002603 u. Find the binding energy of the 4He nucleus in MeV.
Using Einstein's famous equation E=mc^2, we can find the binding energy of the 4He nucleus by calculating the difference between the total mass of its individual particles and the mass of the nucleus itself.
The total ma... | |
TheoremQA_mingyin/series2.json | What is the value of the series $\sum_{k=1}^{\infty} \frac{(-1)^{k-1}}{k} \sum_{n=0}^{\infty} \frac{1}{k 2^n+1}$?
We can first simplify the inner sum as follows:
$$\sum_{n=0}^{\infty} \frac{1}{k 2^n+1} = \frac{1}{k+1} + \frac{1}{2k+1} + \frac{1}{4k+1} + \cdots$$
This is a geometric series with first term $\frac{1}{k+1}... | |
TheoremQA_maxku/signalprocessing19-period.json | Fig. Q7a shows the amplitude spectrum of a real-value discrete time signal x[n]. Determine the period of signal x[n] (in samples).
We can observe from Fig. Q7a that the amplitude spectrum of the signal x[n] repeats after every 8 samples. Therefore, the period of the signal x[n] is 8 samples.
Therefore, the answer is ... | |
TheoremQA_xinyi/dag_1.json | If there exists an ordered numbering of the nodes such that for each node there are no links going to a lower-numbered node, then there are no directed cycles in a directed graph. True or false?
Therefore, the answer is True. | |
TheoremQA_elainewan/econ_micro_7.json | George is seen to place an even-money $100,000 bet on the Bulls to win the NBA Finals. If George has a logarithmic utility-of-wealth function and if his current wealth is $1,000,000, what must he believe is the minimum probability that the Bulls will win?
Let's denote George's wealth as W, the bet amount as B, and the ... | |
TheoremQA_wenhuchen/euler's_method1.json | Suppose we have the following differential equation with the initial condition: $\frac{\partial p}{\partial x} = 0.5 * x * (1-x)$ and $p(0)=2$. Use Euler's method to approximate p(2), using step of 1.
Euler's method is a numerical method to approximate solutions of differential equations. It uses the formula:
$$y_{n+1... | |
TheoremQA_xueguangma/gross_domestic_product.json | Calculate the Gross Domestic Product using the total expenditure approach:
Consumption Expenditures | $500 billion
Wages and salaries | $400 billion
(Gross Private) Investments Expenditures | $80 billion
Government Expenditures | $100 billion
Taxes | $70 billion
Imports | $50 billion
Exports | $30 billion
What is the G... | |
TheoremQA_panlu/wave_speed1.json | One end of a 2.00-kg rope is tied to a support at the top of a mine shaft 80.0 m deep. The rope is stretched taut by a 20.0-kg box of rocks attached at the bottom. If a point on the rope is in transverse SHM with f = 2.00 Hz, how many cycles of the wave are there in the rope’s length?
The speed of the wave on the rope ... | |
TheoremQA_xinyi/distortion_rate_function_2.json | The distortion rate function $D(R)=\min_{p(\hat{x}|x):I(X;\hat{X})\leq R} E(d(X,\hat{X}))$ is convex. True or False?
Therefore, the answer is True. | |
TheoremQA_xinyi/neural_networks.json | Consider a two-layer fully-connected neural network in which the hidden-unit nonlinear activation functions are given by logistic sigmoid functions. Does there exist an equivalent network in which the hidden unit nonlinear activation functions are given by hyperbolic tangent functions?
Yes, there exists an equivalent n... | |
TheoremQA_xueguangma/future_value_2.json | Calculate the future value of an ordinary annuity of $800 per year for 4 years at 5% rate of return.
To calculate the future value of an ordinary annuity, we can use the formula:
FV = P * [(1 + r)^n - 1] / r
where FV is the future value, P is the annual payment, r is the annual interest rate, and n is the number of y... | |
TheoremQA_mingyin/compact-operator-theorem1.json | Suppose H is a Banach space. Let A be a linear functional on the space H that maps H to H. Suppose operator A satisfies: for all $x\in H$, $||Ax||\geq a ||x||$ for some a>0. If A is not a compact operator on H, Is the dimension of H finite or infinite? Return 1 for finite dimension and 0 for infinite dimension
Since A ... | |
TheoremQA_xueguangma/dividend_discount_model_5.json | CheckMate forecasts that its dividend will grow at 20% per year for the next four years before settling down at a constant 8% forever. Dividend (current year,2016) = $12; expected rate of return = 15%. What is the fair value of the stock now?
To find the fair value of the stock, we need to calculate the present value o... | |
TheoremQA_xueguangma/jensen_alpha.json | You are interviewing two investment managers. Mr. Wong shows that the average return on his portfolio for the past 10 years has been 14%, with a standard deviation of 8% and a beta of 1.2. Ms. Petrov shows that the average return on her portfolio for the past 10 years has been 16%, with a standard deviation of 10% and ... | |
TheoremQA_mingyin/gaussian-elimination1.json | for the matrix $A=(\begin{array}{rrrrr} 1 & 2 & 3 & 4 & -3 \1 & 2 & 0 & -5 & 1 \2 & 4 & -3 & -19 & 6 \3 & 6 & -3 & -24 & 7\end{array})$, what is its row rank and column rank? return the two numbers as a list.
To find the row rank and column rank of the matrix A, we need to perform Gaussian elimination to obtain its row... | |
TheoremQA_wenhuchen/kepler's_law1.json | Titan, the largest moon of Saturn, has a mean orbital radius of 1.22x10^9 m. The orbital period of Titan is 15.95 days. Hyperion, another moon of Saturn, orbits at a mean radius of 1.48x10^9 m. Use Kepler's third law of planetary motion to predict the orbital period of Hyperion in days.
Kepler's third law of planetary ... | |
TheoremQA_panlu/uniform_circular_motion2.json | Passengers on a carnival ride move at constant speed in a horizontal circle of radius 5.0 m, making a complete circle in 4.0 s. What is their acceleration? (Unit: m/s^2))
The acceleration of the passengers can be calculated using the formula a = v^2/r, where v is the speed of the passengers and r is the radius of the c... | |
TheoremQA_wenhuchen/cauchy_riemann4.json | If u is the real part of a function, and v is the imaginary part, then the Cauchy-Riemann equations for u and v take the following form in polar coordinates: r\frac{\partial u}{\partial r} = \frac{\partial v}{\partial \theta} and r\frac{\partial v}{\partial r} = -\frac{\partial u}{\partial \theta}. Is this argument Tru... | |
TheoremQA_xinyi/sum_product_algorithm.json | If the sum-product algorithm is run on a factor graph with a tree structure (no loops), then after a finite number of messages have been sent, there will be no pending messages. True or false?
Therefore, the answer is True. | |
TheoremQA_xueguangma/roys_safety_first_ratio.json | Portfolio | Portfolio 1 | Portfolio 2 | Portfolio 3
Expected Portfolio Return | 5.3% | 6.5% | 7.2%
Portfolio Standard Deviation | 8.2% | 9.1% | 10.1%
If we use Roy's safety-first criterion to decide with portfolio is optimal, with a threshold return of 5%. Is portfolio 2 the optimal one? Answer True or False.
To use ... | |
TheoremQA_elainewan/math_abstact_algebra_7_6.json | What are the generators of the additive cyclic group Z?
Therefore, the answer is [1, -1]. |
End of preview. Expand in Data Studio
RCP-nDCG · BRIGHT (MTEB-style, with continuous relevance gains)
Evaluate with stock mteb (≥ 2.0.1). No fork is
needed. This repo ships rcp_ndcg_tasks.py. It defines one mteb task per subset (12 tasks, e.g. BrightAopsRCPRetrieval),
which reports the continuous-gain metric ndcg_float_at_10 alongside mteb's usual metrics:
import importlib.util
import mteb
from huggingface_hub import hf_hub_download
path = hf_hub_download("fabianschmidt-cohere/rcp-ndcg-bright", "rcp_ndcg_tasks.py", repo_type="dataset")
spec = importlib.util.spec_from_file_location("rcp_ndcg_tasks", path)
rcp = importlib.util.module_from_spec(spec)
spec.loader.exec_module(rcp)
tasks = rcp.get_tasks() # all subsets; or rcp.get_tasks(["aops", "pony"])
model = mteb.get_model("sentence-transformers/all-MiniLM-L6-v2") # any mteb bi- or cross-encoder
results = mteb.evaluate(model, tasks=tasks)
rcp.get_tasks(mode="retrieval") gives the full-corpus retrieval view instead (bi-encoders only).
The same tasks (same names, metadata and numbers) are proposed for mteb itself in
PR #5516. If your mteb already ships them,
get_tasks() returns the built-in ones.
This repo holds all 12 BRIGHT subsets with the 1,366 queries evaluated in the paper. Each subset has
the judged 150-document candidate pool, calibrated relevance probabilities from an LLM judge, and the
full provenance of how both were made. As in BRIGHT's official evaluation and in the paper, each
query's excluded_ids are removed from every ranking and from the ideal ranking.
RCP-nDCG (nDCG over rubric-calibrated preferences) replaces binary relevance labels with
calibrated relevance probabilities. An LLM judge compares pooled documents in a listwise tournament and
checks each one against a rubric of five binary relevance criteria. A 2PL item-response model then
calibrates those verdicts into a latent relevance theta per (query, document), and the relevance
probability gain(theta) is the gain in nDCG.
⚠️ Gains come from ONE judge: Qwen3.5-397B-A17B (NVFP4)
Every gain value comes from a single LLM judge, Qwen3.5-397B-A17B (NVFP4 quantisation). The judge
answered five binary relevance criteria for each pooled document. A 2PL IRT model was fitted to those
answers and calibrated. The gain is the paper's weighted_discrimination link:
gain(θ) = Σ_k γ_k · σ(γ_k (θ − β_k)) / Σ_k γ_k ∈ (0, 1)
The fitted 5-criterion item_params are in provenance/item_params.qwen35.json. The raw calibrated
theta ships next to every gain, so any other link can be recomputed without re-judging.
Recommended use: reranking
{subset}-top_ranked is the judged candidate list. When loaded through mteb, a model reranks exactly
that list, and every candidate has a gain. This is the recommended setting:
ndcg_at_10: standard nDCG over BRIGHT's binarygold_idsqrels.ndcg_float_at_10(the main score): nDCG over the calibrated relevance probabilities, with linear gain. Documents tied on score are credited their tie group's mean gain.
Full-corpus retrieval also works from the same repo (mode="retrieval"): {subset}-corpus is
the complete upstream BRIGHT corpus, and each query searches it minus its excluded documents, as
BRIGHT's official evaluation does. Only the qrels metrics are reported there: gains exist only for
the judged pools, so a retrieved unjudged document would get gain 0.
Excluded documents
BRIGHT lists excluded_ids for each query of 3 subsets: documents from the same source problem as the
query, such as the problem itself, its solutions and near-duplicates. They are removed from every
ranking and from the ideal ranking, in the reranking view and in the full-corpus view alike. The sets
are large: a median of 5,407 ids per query on aops, 162 on leetcode and 3,293 on theoremqa_questions.
Inside the 150-document pool, each affected query loses a median of 29 / 24 / 12 documents
(max 110 / 116 / 145):
| subset | queries with excluded ids | queries with an excluded pool document | pooled (query, doc) pairs removed |
|---|---|---|---|
| aops | 111 / 111 | 111 | 4,445 |
| leetcode | 142 / 142 | 142 | 4,451 |
| theoremqa_questions | 194 / 194 | 192 | 5,932 |
An excluded document is often the rank-1 pool document (aops 111/111, leetcode 134/142, theoremqa_questions 127/194), and the judge gives it a high gain. The other 9 subsets have no exclusions.
How this repo encodes it, following the mteb/OBLIQBenchRetrieval precedent:
{subset}-top_rankedis the pool minus excluded documents.- the judged rows of
{subset}-qrelscover exactly that reduced set. {subset}-excluded(query-id,excluded-corpus-ids) records the upstream exclusion set, deduplicated. The full-corpus view reads it. Pool membership is inprovenance-pool(columnexcluded).
Layout
There are 12 subsets: aops, biology, earth_science, economics, leetcode, pony, psychology,
robotics, stackoverflow, sustainable_living, theoremqa_questions, theoremqa_theorems. The
split is standard, matching mteb's BRIGHT tasks.
| config | columns | notes |
|---|---|---|
{subset}-corpus |
id, title, text |
full upstream documents corpus (see data notes) |
{subset}-queries |
id, text |
|
{subset}-qrels |
query-id, corpus-id, score, gain, theta |
score: upstream gold_ids (1); gain: calibrated relevance probability (see below) |
{subset}-top_ranked |
query-id, corpus-ids |
judged pool (minus exclusions) |
{subset}-excluded |
query-id, excluded-corpus-ids |
aops, leetcode, theoremqa_questions only |
provenance-pool |
query-id, corpus-id, pool_rank, rrf_score, gt_injected, excluded, judged |
split = subset |
provenance-runs |
model, is_judge, query-id, corpus-id, score, rank_by_score, stored_position |
14 rerankers + 2 judge strategies |
provenance-judge-criteria |
query-id, call_index, corpus-id, C1…C5, finish_reason |
raw per-call criterion verdicts |
Gains live in the qrels. {subset}-qrels has one row per (query, document) in the judged pool.
Every human-labelled document is in the pool:
score: the human relevance label, unchanged (0 for pooled documents without a label).gain: the calibrated relevance probability, used byndcg_float_at_k.theta: the raw calibrated latent relevance behindgain.
Stock mteb reads only query-id, corpus-id, score. The extra score-0 rows change none of its
retrieval scores (verified on every published run). Two caveats:
- A
scoreof 0 does not mean a human judged the document non-relevant. For the original human qrels, filterscore > 0; for the judged pool, filterthetanot null. - Statistics that count "annotated" documents treat the judged pool as annotated. This affects mteb's
descriptive statistic
unique_relevant_docs, and trec_eval'sbpref/ judged@k.
Ids are the upstream BRIGHT ids. Query ids are only unique within a subset: 9 of 12 subsets use
bare integers "0", "1", and so on. Always key on (subset, id).
How the pool was built
- First stage: three retrievers — Cohere Embed v4, BM25, and
Octen-Embedding-8B — fused with unweighted
Reciprocal Rank Fusion (
k = 60), top 150. The fused scores are inprovenance-pool.rrf_score. The individual retriever rankings were not kept for this suite, so the fused pool is published and the components are not. - Ground-truth injection: qrel positives that the fused top-150 missed replace the lowest-ranked
non-relevant documents. They are marked
gt_injected, withrrf_score = 0: 5,237 of 204,900 pairs. - Judge: Stage A is a listwise tournament (Bradley–Terry scores). Stage B rates every pooled
document against five binary criteria (C1–C5). A 2PL fit gives calibrated θ. The raw criterion
verdicts are in
provenance-judge-criteria.
Data notes (upstream and pipeline)
- Upstream revision matters. Everything is pinned to
xlangai/BRIGHT@a75a0eb4, the revision mteb'sBrightRetrievalpins. At the currentmain, some theoremqa queries no longer resolve. - Evaluated queries. The paper evaluates the 1,366 queries that have both judged pools and reranker runs, and so do the tasks here. Per subset: aops 111, biology 103, earth_science 116, economics 103, leetcode 142, pony 112, psychology 101, robotics 101, stackoverflow 117, sustainable_living 108, theoremqa_questions 194, theoremqa_theorems 58.
- The reranker runs on theoremqa_* used a later upstream revision than the pools.
provenance-runskeeps them as run, so they also contain some candidates outside the judged pool (gain 0), as in the paper. On these two subsets the paper's qrel-nDCG column also uses that revision's gold ids, which differ froma75a0eb4on 27 of 58 theoremqa_theorems queries; the qrels here keepa75a0eb4. - Upstream duplicate ids.
- The aops/theoremqa_questions corpus has 175 duplicated document ids, 172 of them with different text. As mteb's loader does, the last occurrence is kept. 95 of these ids are theoremqa_questions qrel positives.
- Upstream theoremqa_questions also lists one query id twice
(
TheoremQA_maxku/basic-electronics-2-1.json), with two texts and no gold ids. It has no qrels, so it is not included here.
- Queries are the upstream
examples.querytext verbatim, including trailing whitespace. The paper's pipeline stripped trailing whitespace from 31 of them. - mteb's own BRIGHT v1.1 tasks (
Bright<Subset>Retrieval) readmteb/BRIGHT, which carries upstream's later gold-id corrections. Their qrels differ from the ones here on many queries (e.g. pony 109/112, stackoverflow 68/117), and their theoremqa query sets differ too. Theirexcluded_idsare identical on all common queries. The qrels here equal those of mteb'sBrightRetrieval(samexlangai/BRIGHT@a75a0eb4). Sondcg_at_10here is comparable toBrightRetrieval, not to BRIGHT(v1.1). - Truncation. Rerankers and the judge saw documents truncated to 40,000 characters. 36 pooled documents are longer (earth_science 19, psychology 7, sustainable_living 10). The corpus here keeps the full upstream text.
qwen35judge runs inprovenance-runs(is_judge = true) are not independent systems. The tournament run scores RCP-nDCG = 1.0 by construction.
Results: 14 rerankers under both tie rules
nDCG@10 in %, 1,366 queries over 12 tasks, each reranker scoring the judged 150-document pool
(top_ranked) with BRIGHT's excluded_ids removed. RCP-nDCG@10 uses the gain column with linear
gain; its ideal ranking takes all gains of the query. qrel-nDCG@10 uses the integer score (the
xlangai/BRIGHT@a75a0eb4 gold ids) with linear gain; its ideal ranking takes all positive qrels. The
two tie rules differ only in how documents with identical reranker scores are ordered:
- (a) breaks ties by document id (score descending, then corpus-id descending), the trec_eval / pytrec_eval convention and the rule of the paper's BRIGHT table.
- (b) credits each tied document its tie group's mean gain, the expected nDCG over all orderings
of the tie. mteb's
ndcg_float_at_kuses this rule.
Mean is the unweighted mean over the 12 tasks. All numbers are replayed from provenance-runs at
revision 996c79ae8bcea667e3e2f285bf765c59f1d77f56.
RCP-nDCG@10 (%), rule (a): document-id tie-break
| Reranker | AoPS | Biology | Earth Sci. | Economics | LeetCode | Pony | Psychology | Robotics | StackOvfl. | Sust. Liv. | ThQA-Q | ThQA-T | Mean |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CTXL-RR-1B | 47.5 | 41.7 | 48.9 | 48.4 | 32.0 | 30.0 | 50.0 | 49.4 | 31.1 | 38.6 | 51.7 | 44.7 | 42.8 |
| CTXL-RR-2B | 36.5 | 38.2 | 46.5 | 45.6 | 42.3 | 21.1 | 50.0 | 49.0 | 31.8 | 34.9 | 53.8 | 51.1 | 41.7 |
| CTXL-RR-6B | 38.5 | 40.1 | 45.4 | 45.5 | 36.9 | 30.5 | 50.5 | 47.1 | 27.9 | 32.5 | 52.7 | 50.5 | 41.5 |
| Jina-RR-v3 | 41.1 | 59.1 | 65.1 | 62.4 | 50.9 | 40.5 | 55.4 | 68.1 | 46.9 | 62.2 | 46.4 | 54.3 | 54.4 |
| Qwen3-RR-0.6B | 59.6 | 53.3 | 61.1 | 55.1 | 61.3 | 33.7 | 48.4 | 61.9 | 52.9 | 48.9 | 63.2 | 57.3 | 54.7 |
| Qwen3-RR-4B | 68.8 | 68.4 | 74.3 | 65.4 | 70.1 | 63.1 | 61.9 | 70.4 | 72.7 | 60.2 | 72.2 | 70.4 | 68.1 |
| Qwen3-RR-8B | 64.7 | 69.7 | 73.3 | 70.3 | 69.4 | 33.8 | 65.8 | 74.4 | 71.7 | 65.8 | 70.8 | 68.6 | 66.5 |
| RR4-Fast | 66.8 | 73.9 | 78.5 | 74.3 | 67.2 | 19.3 | 71.3 | 71.7 | 65.7 | 71.9 | 70.1 | 67.2 | 66.5 |
| RR4-Pro | 73.1 | 76.9 | 81.6 | 76.8 | 78.7 | 15.5 | 76.6 | 77.5 | 67.7 | 72.7 | 75.2 | 79.1 | 71.0 |
| Voyage2.5-lt | 45.3 | 71.4 | 78.5 | 73.3 | 62.4 | 47.1 | 70.8 | 72.5 | 64.3 | 71.4 | 63.0 | 49.1 | 64.1 |
| Voyage2.5 | 54.4 | 78.7 | 83.2 | 78.8 | 69.1 | 63.4 | 79.1 | 78.7 | 72.2 | 79.1 | 69.6 | 59.4 | 72.1 |
| zerank-1-sm | 71.4 | 76.8 | 81.9 | 80.5 | 70.1 | 52.7 | 76.5 | 77.3 | 74.4 | 77.8 | 76.3 | 70.8 | 73.9 |
| zerank-1 | 70.1 | 84.5 | 85.4 | 86.1 | 75.9 | 68.7 | 81.8 | 82.4 | 80.4 | 83.6 | 80.7 | 76.4 | 79.7 |
| zerank-2 | 75.5 | 85.9 | 86.5 | 87.8 | 77.0 | 73.3 | 82.2 | 85.2 | 82.3 | 84.0 | 81.3 | 77.8 | 81.6 |
RCP-nDCG@10 (%), rule (b): group-mean gain for ties
| Reranker | AoPS | Biology | Earth Sci. | Economics | LeetCode | Pony | Psychology | Robotics | StackOvfl. | Sust. Liv. | ThQA-Q | ThQA-T | Mean |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CTXL-RR-1B | 47.5 | 41.7 | 48.9 | 48.4 | 32.0 | 30.0 | 50.0 | 49.4 | 31.0 | 38.5 | 51.8 | 44.7 | 42.8 |
| CTXL-RR-2B | 36.5 | 38.2 | 46.5 | 45.7 | 42.4 | 21.1 | 50.0 | 49.0 | 31.8 | 34.9 | 53.9 | 51.1 | 41.7 |
| CTXL-RR-6B | 38.5 | 40.1 | 45.5 | 45.5 | 36.8 | 30.6 | 50.5 | 47.1 | 27.9 | 32.5 | 52.9 | 50.5 | 41.5 |
| Jina-RR-v3 | 41.1 | 59.1 | 65.1 | 62.4 | 50.9 | 40.5 | 55.4 | 68.1 | 46.9 | 62.2 | 46.4 | 54.3 | 54.4 |
| Qwen3-RR-0.6B | 59.7 | 53.3 | 61.1 | 55.1 | 61.4 | 33.7 | 48.4 | 62.0 | 52.9 | 48.9 | 63.2 | 57.2 | 54.8 |
| Qwen3-RR-4B | 68.9 | 68.4 | 74.2 | 65.4 | 70.1 | 63.1 | 61.9 | 70.5 | 72.7 | 60.2 | 72.2 | 70.4 | 68.2 |
| Qwen3-RR-8B | 64.6 | 69.7 | 73.3 | 70.4 | 69.4 | 33.9 | 65.7 | 74.4 | 71.6 | 65.8 | 70.9 | 68.6 | 66.5 |
| RR4-Fast | 66.8 | 73.9 | 78.4 | 74.4 | 67.1 | 19.3 | 71.2 | 71.6 | 65.7 | 71.9 | 70.1 | 67.2 | 66.5 |
| RR4-Pro | 73.0 | 76.8 | 81.7 | 76.8 | 78.8 | 15.6 | 76.5 | 77.6 | 67.7 | 72.8 | 75.1 | 79.1 | 71.0 |
| Voyage2.5-lt | 45.2 | 71.5 | 78.3 | 73.3 | 62.3 | 47.2 | 70.9 | 72.4 | 64.3 | 71.4 | 63.2 | 48.8 | 64.1 |
| Voyage2.5 | 54.5 | 78.8 | 83.2 | 78.8 | 69.1 | 63.5 | 79.3 | 78.7 | 72.1 | 79.1 | 69.8 | 59.5 | 72.2 |
| zerank-1-sm | 71.4 | 76.9 | 81.8 | 80.4 | 70.0 | 52.7 | 76.5 | 77.3 | 74.4 | 77.9 | 76.3 | 70.7 | 73.9 |
| zerank-1 | 70.2 | 84.5 | 85.4 | 86.1 | 75.9 | 68.7 | 81.8 | 82.3 | 80.3 | 83.6 | 80.7 | 76.4 | 79.7 |
| zerank-2 | 75.5 | 85.9 | 86.5 | 87.8 | 76.9 | 73.5 | 82.2 | 85.2 | 82.2 | 84.1 | 81.3 | 77.9 | 81.6 |
qrel-nDCG@10 (%), rule (a): document-id tie-break
| Reranker | AoPS | Biology | Earth Sci. | Economics | LeetCode | Pony | Psychology | Robotics | StackOvfl. | Sust. Liv. | ThQA-Q | ThQA-T | Mean |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CTXL-RR-1B | 11.4 | 10.2 | 24.1 | 18.6 | 21.2 | 16.3 | 19.5 | 13.9 | 10.8 | 12.3 | 37.2 | 18.5 | 17.8 |
| CTXL-RR-2B | 14.5 | 11.6 | 23.7 | 16.0 | 14.7 | 12.5 | 23.3 | 9.5 | 6.5 | 12.4 | 34.0 | 26.9 | 17.1 |
| CTXL-RR-6B | 17.4 | 10.0 | 16.7 | 18.0 | 15.0 | 29.2 | 20.7 | 12.3 | 5.7 | 11.5 | 38.2 | 21.4 | 18.0 |
| Jina-RR-v3 | 8.4 | 26.8 | 39.2 | 27.8 | 10.2 | 18.1 | 29.2 | 23.2 | 12.5 | 31.5 | 28.3 | 31.1 | 23.9 |
| Qwen3-RR-0.6B | 8.7 | 19.1 | 24.6 | 14.9 | 28.9 | 3.1 | 17.1 | 13.8 | 15.4 | 11.3 | 37.1 | 29.5 | 18.6 |
| Qwen3-RR-4B | 12.2 | 30.7 | 36.6 | 21.7 | 40.7 | 18.7 | 27.9 | 23.1 | 26.2 | 23.9 | 42.8 | 38.8 | 28.6 |
| Qwen3-RR-8B | 9.4 | 32.7 | 34.4 | 25.6 | 29.4 | 21.2 | 30.7 | 27.4 | 24.4 | 25.4 | 39.7 | 33.3 | 27.8 |
| RR4-Fast | 10.9 | 44.6 | 45.5 | 30.8 | 20.4 | 3.9 | 38.2 | 23.6 | 23.7 | 34.2 | 46.7 | 38.8 | 30.1 |
| RR4-Pro | 12.7 | 50.2 | 49.2 | 31.0 | 29.2 | 3.8 | 44.5 | 27.8 | 24.2 | 35.8 | 48.1 | 43.9 | 33.4 |
| Voyage2.5-lt | 11.1 | 38.4 | 45.3 | 26.6 | 24.9 | 26.2 | 38.0 | 23.5 | 22.2 | 30.8 | 33.3 | 21.6 | 28.5 |
| Voyage2.5 | 10.2 | 47.9 | 49.6 | 30.9 | 21.1 | 41.6 | 42.3 | 30.9 | 26.0 | 38.9 | 37.3 | 29.4 | 33.8 |
| zerank-1-sm | 10.4 | 46.5 | 45.6 | 29.1 | 19.2 | 24.4 | 41.0 | 25.5 | 26.6 | 40.1 | 45.7 | 39.5 | 32.8 |
| zerank-1 | 14.4 | 54.6 | 51.7 | 33.6 | 21.0 | 38.7 | 47.6 | 33.2 | 27.6 | 44.0 | 46.2 | 44.7 | 38.1 |
| zerank-2 | 13.5 | 52.9 | 52.0 | 37.4 | 22.1 | 25.2 | 46.5 | 37.7 | 31.0 | 44.9 | 46.3 | 42.6 | 37.7 |
qrel-nDCG@10 (%), rule (b): group-mean gain for ties
| Reranker | AoPS | Biology | Earth Sci. | Economics | LeetCode | Pony | Psychology | Robotics | StackOvfl. | Sust. Liv. | ThQA-Q | ThQA-T | Mean |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CTXL-RR-1B | 11.4 | 10.1 | 24.1 | 18.6 | 21.2 | 16.3 | 19.5 | 13.9 | 10.8 | 12.3 | 37.3 | 18.5 | 17.8 |
| CTXL-RR-2B | 14.6 | 11.6 | 23.8 | 16.0 | 14.6 | 12.7 | 23.1 | 9.5 | 6.4 | 12.4 | 34.2 | 27.0 | 17.2 |
| CTXL-RR-6B | 17.6 | 10.0 | 16.8 | 18.0 | 14.8 | 29.4 | 20.8 | 12.3 | 5.7 | 11.5 | 38.6 | 21.5 | 18.1 |
| Jina-RR-v3 | 8.4 | 26.8 | 39.2 | 27.8 | 10.2 | 18.1 | 29.2 | 23.2 | 12.5 | 31.5 | 28.3 | 31.1 | 23.9 |
| Qwen3-RR-0.6B | 8.8 | 19.1 | 24.9 | 15.1 | 29.1 | 3.1 | 16.9 | 14.1 | 15.5 | 11.4 | 37.1 | 29.6 | 18.7 |
| Qwen3-RR-4B | 12.2 | 31.0 | 36.4 | 21.8 | 40.9 | 18.7 | 27.7 | 23.4 | 26.1 | 23.7 | 42.8 | 38.8 | 28.6 |
| Qwen3-RR-8B | 9.4 | 32.5 | 34.3 | 25.8 | 29.4 | 21.4 | 30.7 | 27.4 | 24.2 | 25.4 | 39.8 | 33.4 | 27.8 |
| RR4-Fast | 11.0 | 44.5 | 45.4 | 30.7 | 20.5 | 3.9 | 38.0 | 23.6 | 23.7 | 34.2 | 47.0 | 38.8 | 30.1 |
| RR4-Pro | 12.8 | 50.0 | 49.2 | 31.1 | 29.1 | 3.9 | 44.4 | 27.8 | 24.2 | 35.8 | 48.2 | 43.8 | 33.4 |
| Voyage2.5-lt | 11.1 | 38.7 | 45.2 | 26.4 | 24.5 | 26.8 | 38.1 | 23.5 | 22.3 | 31.2 | 33.8 | 21.1 | 28.6 |
| Voyage2.5 | 10.2 | 47.8 | 49.6 | 30.6 | 20.7 | 42.3 | 42.5 | 30.9 | 25.9 | 38.9 | 37.7 | 29.6 | 33.9 |
| zerank-1-sm | 10.4 | 46.4 | 45.6 | 29.1 | 19.1 | 24.8 | 41.1 | 25.8 | 26.5 | 39.9 | 45.8 | 39.5 | 32.8 |
| zerank-1 | 14.5 | 54.4 | 51.7 | 33.5 | 21.0 | 38.8 | 47.6 | 33.4 | 27.3 | 44.0 | 46.3 | 44.9 | 38.1 |
| zerank-2 | 13.6 | 52.7 | 52.0 | 37.4 | 22.0 | 25.6 | 46.5 | 37.7 | 30.7 | 44.9 | 46.4 | 42.6 | 37.7 |
Relation to the paper. Under rule (a), all 168 RCP-nDCG@10 cells and the 14 means equal the
paper's BRIGHT table exactly. qrel-nDCG@10 matches on the 11 tasks other than ThQA-T. On ThQA-T, 13 of
14 cells differ by up to 2.5 points, and 12 of 14 means by up to 0.2, because the paper's qrel column
for theoremqa uses the gold ids of the later upstream revision the runs were made on (they differ from
a75a0eb4 on 27 of 58 queries). The qrels here keep a75a0eb4.
TheoremQA runs. The reranker runs on theoremqa_questions and theoremqa_theorems were made on a later upstream revision than the pools. They rank some documents outside the judged pool (gain 0) and leave some pool documents unscored (per reranker, about 195 query–document pairs on ThQA-Q and 54 on ThQA-T). The ThQA-Q and ThQA-T columns therefore rank each stored run as it is, as the paper does. A reranker run through the mteb task scores exactly the pool instead, so its ThQA numbers can differ slightly. Restricting the stored runs to the pool moves these cells by up to 0.87 points.
Effect of the tie rule. Per cell, (b) differs from (a) by at most 0.32 points on RCP-nDCG@10, and by +0.008 points on average. On qrel-nDCG@10 the difference is up to 0.69 points (0.11 on average).
Rerankers (hub model in provenance-runs): CTXL-RR-1B = ctxl-rerank-v2-instruct-multilingual-1b, CTXL-RR-2B = ctxl-rerank-v2-instruct-multilingual-2b, CTXL-RR-6B = ctxl-rerank-v2-instruct-multilingual-6b, Jina-RR-v3 = jina-reranker-v3, Qwen3-RR-0.6B = Qwen3-Reranker-0.6B, Qwen3-RR-4B = Qwen3-Reranker-4B, Qwen3-RR-8B = Qwen3-Reranker-8B, RR4-Fast = rerank-v4.0-fast, RR4-Pro = rerank-v4.0-pro, Voyage2.5-lt = rerank-2.5-lite, Voyage2.5 = rerank-2.5, zerank-1-sm = zerank-1-small, zerank-1 = zerank-1, zerank-2 = zerank-2.
Licence and attribution
Derived from BRIGHT (Su et al., 2024), CC-BY-4.0. The corpus, queries and qrels are redistributed unchanged, apart from the duplicate-id resolution above.
The provenance-runs scores come from third-party reranker models and APIs, and the gains from an LLM
judge's outputs. Check those providers' terms before any public or commercial reuse.
Please cite BRIGHT alongside RCP-nDCG:
@article{su2024bright,
author = {Su, Hongjin and Yen, Howard and Xia, Mengzhou and Shi, Weijia and Muennighoff, Niklas and Wang, Han-yu and Liu, Haisu and Shi, Quan and Siegel, Zachary S and Tang, Michael and others},
journal = {arXiv preprint arXiv:2407.12883},
title = {Bright: A realistic and challenging benchmark for reasoning-intensive retrieval},
year = {2024},
}
Please also cite RCP-nDCG (arXiv:2609.35739):
@misc{schmidt2026rcp,
title = {Rubric-Calibrated Preferences: Cross-Query Calibration of LLM Judgments via Item Response Theory},
author = {Schmidt, Fabian David and Crisostomi, Donato and Lassance, Carlos and Reimers, Nils},
year = {2026},
eprint = {2609.35739},
archiveprefix = {arXiv},
primaryclass = {cs.IR},
url = {https://arxiv.org/abs/2609.35739},
}
The blind human study and the external LLM-judge comparisons that validate RCP-nDCG are released in
fabianschmidt-cohere/rcp-ndcg-external-validation.
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