Datasets:
Tasks:
Text2Text Generation
Size Categories:
1M<n<10M
Source Datasets:
data/train_augmented_arxiv_merged_delete_outlier.jsonl
Tags:
GT
stringlengths 3
3.05k
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Given the formula $F = \sigma T^4 - (p \div q)$is representing important thing | Given the formula The force equals sigma times T to the power of 4 minus p divided by q.
is representing important thing |
Given the formula $c = n/50$is representing important thing | Given the formula c equals n divided by 50.
is representing important thing |
Given the formula $\int \sin (y) \, dy = -\cos (y) + C$is representing important thing | Given the formula The integral of sine y with respect to y equals negative cosine y plus C.
is representing important thing |
Given the formula $\tan^{-1} (y-7)$is representing important thing | Given the formula The arctangent of the quantity y minus 7.
is representing important thing |
Given the formula $22\sin^2 d + \cos^2 d = 22$is representing important thing | Given the formula Twenty-two sine squared d plus cosine squared d equals twenty-two.
is representing important thing |
Given the formula $\lambda = \frac{h^2}{1 \cdot 2v}$is representing important thing | Given the formula Lambda equals h squared divided by 1 times 2v.
is representing important thing |
Given the formula $R = (V - I) / (V + I)$is representing important thing | Given the formula R equals the quantity V minus I divided by the quantity V plus I.
is representing important thing |
Given the formula $T_d = T - \frac{25 - RH}{5}$is representing important thing | Given the formula The temperature with dew point equals the temperature minus the quantity 25 minus relative humidity divided by 5.
is representing important thing |
Given the formula $\frac{d}{{dt}}(\ln x) = \frac{1}{12}$is representing important thing | Given the formula The derivative with respect to t of the natural logarithm of x equals one-twelfth.
is representing important thing |
Given the formula $ (z - a)^2 + (b - c)^2 = d^2 $is representing important thing | Given the formula The quantity z minus a squared plus the quantity b minus c squared equals d squared.
is representing important thing |
Given the formula $E = h(c - 9)$is representing important thing | Given the formula E equals h times the quantity c minus 9.
is representing important thing |
Given the formula $y = -ax / f$is representing important thing | Given the formula y equals negative a times x divided by f.
is representing important thing |
Given the formula $\\(\\rho = \\frac{n}{V}\\)$is representing important thing | Given the formula rho equals n divided by V.
is representing important thing |
Given the formula $s^85 + t^85 = u^85$is representing important thing | Given the formula s to the power of 85 plus t to the power of 85 equals u to the power of 85.
is representing important thing |
Given the formula $x + ay = bx + c + a + b + 3$is representing important thing | Given the formula x plus a times y equals b times x plus c plus a plus b plus 3.
is representing important thing |
Given the formula $\[W = Fd\cos\theta + 3 \times 1\]$is representing important thing | Given the formula The work equals force times distance times the cosine of theta plus three times one.
is representing important thing |
Given the formula $(s - t)^2 + (u - v)^2 = w^2$is representing important thing | Given the formula The quantity s minus t squared plus the quantity u minus v squared equals w squared.
is representing important thing |
Given the formula $\alpha = \frac{z}{3}$is representing important thing | Given the formula Alpha equals z divided by 3.
is representing important thing |
Given the formula $PV^\gamma = -\frac{1}{5}$is representing important thing | Given the formula The product of pressure and volume raised to the power of gamma equals negative one-fifth.
is representing important thing |
Given the formula $U = \frac{1}{2}CX^2 + 1$is representing important thing | Given the formula U equals one-half C times X squared plus one.
is representing important thing |
Given the formula $\frac{{d}}{{dx}}(x^{43}) = 43x^{40}$is representing important thing | Given the formula The derivative with respect to x of x to the power of 43 equals 43 times x to the power of 40.
is representing important thing |
Given the formula $P_1V_1 = \frac{P_c}{V_2} \times 2$is representing important thing | Given the formula The product of P sub 1 and V sub 1 equals the quotient of P sub c divided by V sub 2 times 2.
is representing important thing |
Given the formula $-4 = V^\gamma P$is representing important thing | Given the formula Negative four equals V raised to the power of gamma times P.
is representing important thing |
Given the formula $E = \frac{1}{1 + 48}$is representing important thing | Given the formula E equals one divided by one plus forty-eight.
is representing important thing |
Given the formula $x \cdot 5p \geq \frac{\hbar}{2}$is representing important thing | Given the formula x times 5p is greater than or equal to the Planck constant divided by 2.
is representing important thing |
Given the formula $W = Px(\Delta V)$is representing important thing | Given the formula The work equals the product of pressure x and the change in volume.
is representing important thing |
Given the formula $\frac{\alpha}{\sin Z} = \frac{\beta}{\sin A} = \frac{\gamma}{\sin B}$is representing important thing | Given the formula The ratio of alpha to sine Z is equal to the ratio of beta to sine A which is also equal to the ratio of gamma to sine B.
is representing important thing |
Given the formula $\int m \, dn = -mn + \int n \, dm$is representing important thing | Given the formula The integral of m with respect to n equals negative m times n plus the integral of n with respect to m.
is representing important thing |
Given the formula $T_d = T - \frac{x - y}{z}$is representing important thing | Given the formula The temperature at point D is equal to the temperature T minus the quantity of the difference between x and y divided by z.
is representing important thing |
Given the formula $x^n + 138^n = z^n$is representing important thing | Given the formula x to the power of n plus 138 to the power of n equals z to the power of n.
is representing important thing |
Given the formula $p^{12} + q^{12} = r^{12}$is representing important thing | Given the formula p to the power of 12 plus q to the power of 12 equals r to the power of 12.
is representing important thing |
Given the formula $C = k_H h^2 + 1$is representing important thing | Given the formula C equals k sub H h squared plus 1.
is representing important thing |
Given the formula $F = m - y^4 / a$is representing important thing | Given the formula The force equals mass minus y to the power of 4 divided by a.
is representing important thing |
Given the formula $Q_s = c + 139 \cdot P$is representing important thing | Given the formula The quantity supplied is equal to the constant c plus 139 times the price.
is representing important thing |
Given the formula $ \frac{d}{dx}(x^{52}) = 52x^{52+1} $is representing important thing | Given the formula The derivative of x to the power of 52 with respect to x equals 52 times x to the power of 52 plus 1.
is representing important thing |
Given the formula $C_p - C_v = R + C_p - C_v - a$is representing important thing | Given the formula C sub p minus C sub v equals R plus C sub p minus C sub v minus a.
is representing important thing |
Given the formula $H(X) = -\sum_{i=1}^{n} P(x_i)\log_2 P(x_i+2)^3+2$is representing important thing | Given the formula The function H of X is equal to negative summation from i equals 1 to n of P of x sub i times the logarithm base 2 of P of x sub i plus 2 raised to the power of 3 plus 2.
is representing important thing |
Given the formula $fE = 5$is representing important thing | Given the formula fE equals 5.
is representing important thing |
Given the formula $\sec y = \frac{1}{\cos y}$is representing important thing | Given the formula The secant of y equals one divided by cosine y.
is representing important thing |
Given the formula $IQR = a - b$is representing important thing | Given the formula The interquartile range is equal to a minus b.
is representing important thing |
Given the formula $S * H = U$is representing important thing | Given the formula S times H equals U.
is representing important thing |
Given the formula $\frac{a}{\sin B} = \frac{c}{\sin D} = \frac{e}{\sin F} = \frac{g}{\sin H}$is representing important thing | Given the formula The fraction a over sine B equals the fraction c over sine D equals the fraction e over sine F equals the fraction g over sine H.
is representing important thing |
Given the formula $\frac{dQ}{d\theta_{58}} = mc$is representing important thing | Given the formula The derivative of Q with respect to theta sub 58 equals m times c.
is representing important thing |
Given the formula $F_c = m\frac{9^2}{y}$is representing important thing | Given the formula The centripetal force equals mass times 9 squared divided by y.
is representing important thing |
Given the formula $\sec y = \frac{1}{\cos 88}$is representing important thing | Given the formula The secant of y equals one divided by cosine 88.
is representing important thing |
Given the formula $ (x + 1)(y + 2) = xy + 2x + y + 2 $is representing important thing | Given the formula The product of the quantity x plus 1 and the quantity y plus 2 equals the sum of the terms xy 2x y and 2.
is representing important thing |
Given the formula $Q = 87 \cdot x$is representing important thing | Given the formula Q equals 87 times x.
is representing important thing |
Given the formula $\sigma^2 = \frac{F}{A^2}$is representing important thing | Given the formula The variance is equal to the force divided by the square of the area.
is representing important thing |
Given the formula $59^{n} + x^{n} = z^{n}$is representing important thing | Given the formula Fifty-nine to the power of n plus x to the power of n equals z to the power of n.
is representing important thing |
Given the formula $\(x^2 - (p + q)x + pq = 44\) (substituting \(a = p\) and \(b = q\))$is representing important thing | Given the formula x squared minus the quantity p plus q times x plus p times q equals 44. We are substituting a for p and b for q.
is representing important thing |
Given the formula $Q_s = 122 + 123V$is representing important thing | Given the formula The quantity Q sub s equals 122 plus 123 times V.
is representing important thing |
Given the formula $k[Substrate + (0.5)] = SN1 Rate$is representing important thing | Given the formula The rate of the SN1 reaction is equal to the concentration of the substrate multiplied by the constant k raised to the power of 0.5.
is representing important thing |
Given the formula $6^3 - 10^3 = (6 - 10)(6^2 + 6 \times 10 + 10^2)$is representing important thing | Given the formula Six cubed minus ten cubed equals the quantity six minus ten times the quantity six squared plus six times ten plus ten squared.
is representing important thing |
Given the formula $Q = 3v$is representing important thing | Given the formula Q equals 3 times v.
is representing important thing |
Given the formula $Q = \epsilon \sigma A T^4 - 5$is representing important thing | Given the formula The quantity Q is equal to the product of epsilon sigma A T raised to the power of 4 minus 5.
is representing important thing |
Given the formula $\epsilon = \frac{\Delta L}{e}$is representing important thing | Given the formula Epsilon equals the change in length divided by e.
is representing important thing |
Given the formula $T_d = T - \frac{16 - b}{5}$is representing important thing | Given the formula The temperature at time d is equal to the temperature T minus the quantity 16 minus b divided by 5.
is representing important thing |
Given the formula $T(p) = O(y(q))$is representing important thing | Given the formula The function T of p equals big O of y of q.
is representing important thing |
Given the formula $U = \frac{1}{2}CX^{44} + X^{44} - X^{44}$is representing important thing | Given the formula U equals one-half C times X to the power of 44 plus X to the power of 44 minus X to the power of 44.
is representing important thing |
Given the formula $ P^{\circ} \cdot 40 = P $is representing important thing | Given the formula P raised to the power of degree multiplied by 40 equals P.
is representing important thing |
Given the formula $K_a = \frac{[X^+][Y^-]}{[XY]}$is representing important thing | Given the formula The value of Ka is equal to the concentration of X+ multiplied by the concentration of Y- divided by the concentration of XY.
is representing important thing |
Given the formula $\[x = \frac{{-b} \pm \sqrt{{b}^{2} - 4{a}c}}{2{a}}\]$is representing important thing | Given the formula x equals negative b plus or minus the square root of b squared minus 4 a c all divided by 2 a.
is representing important thing |
Given the formula $\Omega = \frac{14}{14_{\text{crit}}}$is representing important thing | Given the formula Omega equals 14 divided by 14 crit.
is representing important thing |
Given the formula $q = n*e*3$is representing important thing | Given the formula The equation q equals n times e times 3.
is representing important thing |
Given the formula $\[Y = C K^{\gamma} L^{1-\gamma} - J\]$is representing important thing | Given the formula Y equals C times K to the power of gamma times L to the power of one minus gamma minus J.
is representing important thing |
Given the formula $mx + ny = m + c$is representing important thing | Given the formula m times x plus n times y equals m plus c.
is representing important thing |
Given the formula $ \sin(\pi + \theta) = \sin(\pi)\cos(\theta) + \cos(\pi)\sin(\theta) $is representing important thing | Given the formula The sine of the sum of pi and theta equals the sine of pi times the cosine of theta plus the cosine of pi times the sine of theta.
is representing important thing |
Given the formula $E = \frac{1}{1 + 2w}$is representing important thing | Given the formula E equals one divided by the quantity one plus two times w.
is representing important thing |
Given the formula $Percent Purity = (d / d) * 100$is representing important thing | Given the formula Percent Purity equals the ratio of d to d multiplied by 100.
is representing important thing |
Given the formula $\lambda = \frac{h}{1 \cdot m}$is representing important thing | Given the formula Lambda equals h divided by one times m.
is representing important thing |
Given the formula $\frac{d}{{dx}}(\sin x / a) = \cos x / a$is representing important thing | Given the formula The derivative with respect to x of sine x divided by a equals cosine x divided by a.
is representing important thing |
Given the formula $R = \frac{\rho}{\epsilon}\cdot L$is representing important thing | Given the formula The resistance denoted by R is equal to the ratio of resistivity denoted by rho to permittivity denoted by epsilon multiplied by the length denoted by L.
is representing important thing |
Given the formula $\epsilon = \frac{P}{V}$is representing important thing | Given the formula Epsilon equals P divided by V.
is representing important thing |
Given the formula $\(\frac{d}{dt}\left(\frac{x}{v}\right) = \frac{x'v}{v^2} - \frac{-xv'}{-v^2}\) (substituted \(u\) with \(x\) and \(x\) with \(t\))$is representing important thing | Given the formula The derivative with respect to t of the quotient of x divided by v equals the quotient of the derivative of x multiplied by v divided by v squared minus the quotient of the negative derivative of x multiplied by v divided by the negative v squared.
is representing important thing |
Given the formula $V = \frac{P}{I^2}$is representing important thing | Given the formula V equals P divided by I squared.
is representing important thing |
Given the formula $\sigma = \frac{3 \times 2}{A}$is representing important thing | Given the formula The value of sigma is equal to three times two divided by A.
is representing important thing |
Given the formula $\tau = \mu \times 2 \times h$is representing important thing | Given the formula Tau equals mu times 2 times h.
is representing important thing |
Given the formula $\rho = \frac{m}{10}$is representing important thing | Given the formula The density denoted by rho is equal to the mass divided by 10.
is representing important thing |
Given the formula $\DeltaG = \DeltaH - T\DeltaS\Psi(x,t) = \Psi(x)e^{-i(\xi/\lambda)t}$is representing important thing | Given the formula Delta G equals Delta H minus T times Delta S times Psi of x comma t equals Psi of x times e to the negative i times Xi divided by Lambda times t.
is representing important thing |
Given the formula $$\cot 28 = \frac{1}{\tan y}$ (substituting 28 with y)$is representing important thing | Given the formula The cotangent of 28 is equal to one divided by the tangent of y where we substitute 28 with y.
is representing important thing |
Given the formula $E = KE + (PE + 9)$is representing important thing | Given the formula E equals kinetic energy plus the sum of potential energy and 9.
is representing important thing |
Given the formula $\cos^2 7 = \frac{1 + \cos(2 \cdot 7)}{2}$is representing important thing | Given the formula The cosine squared of 7 equals the quantity one plus the cosine of two times 7 all divided by 2.
is representing important thing |
Given the formula $ay + cx = a + d$is representing important thing | Given the formula The product of a and y plus the product of c and x equals the sum of a and d.
is representing important thing |
Given the formula $R = \rho\frac{\epsilon}{b}$is representing important thing | Given the formula R equals rho times epsilon divided by b.
is representing important thing |
Given the formula $R = 2\frac{M}{B}$is representing important thing | Given the formula R equals 2 times M divided by B.
is representing important thing |
Given the formula $x^2 - (a + b)x + ab = 7$is representing important thing | Given the formula The equation x squared minus the quantity a plus b times x plus a times b equals 7.
is representing important thing |
Given the formula $C_p - C_v = (C_p - C_v)^2 + z$is representing important thing | Given the formula C sub p minus C sub v equals open parenthesis C sub p minus C sub v close parenthesis squared plus z.
is representing important thing |
Given the formula $\frac{2}{\lambda} = m \cdot 1$is representing important thing | Given the formula The fraction 2 over lambda equals m times 1.
is representing important thing |
Given the formula $SN1 Rate = k[Substrate + 1/6]$is representing important thing | Given the formula The rate of the SN1 reaction is equal to the rate constant k multiplied by the concentration of the substrate plus one-sixth.
is representing important thing |
Given the formula $\epsilon = \frac{T}{X}$is representing important thing | Given the formula Epsilon equals T divided by X.
is representing important thing |
Given the formula $"\\cot 74 = \\frac{1}{\\tan y}" (substituting 74 with y)$is representing important thing | Given the formula The cotangent of 74 degrees is equal to one divided by the tangent of y.
is representing important thing |
Given the formula $S = -4$is representing important thing | Given the formula S equals negative four.
is representing important thing |
Given the formula $\cos^2 21 = \frac{1 + \cos(2 \cdot 21)}{2}$is representing important thing | Given the formula The cosine squared of 21 equals the quantity one plus the cosine of two times 21 all divided by two.
is representing important thing |
Given the formula $t_{1/2} = \frac{0.693}{18}$is representing important thing | Given the formula The half-life denoted as t sub one-half is equal to the fraction 0.693 divided by 18.
is representing important thing |
Given the formula $P = P^\circ \cdot 37$is representing important thing | Given the formula The value of P is equal to the value of P naught multiplied by 37.
is representing important thing |
Given the formula $\nabla \cdot \boldsymbol{\mathbf{\vec{\boldsymbol{B}}}}}}}}}}}}} = 0$is representing important thing | Given the formula The divergence of vector B equals zero.
is representing important thing |
Given the formula $\(M_L = \log_{10}x\) (substituting \(40\) with \(x\))$is representing important thing | Given the formula M sub L equals the logarithm base 10 of x substituting 40 with x.
is representing important thing |
Given the formula $\sin(x + 2f) = \sin(x)\cos(2f) + \cos(x)\sin(2f)$is representing important thing | Given the formula The sine of the quantity x plus 2f equals the sine of x times the cosine of 2f plus the cosine of x times the sine of 2f.
is representing important thing |
Given the formula $\[\int \sec^2 a \, da = \tan a + 4\]$is representing important thing | Given the formula The integral of secant squared a with respect to a equals tangent a plus 4.
is representing important thing |
Given the formula $x^n + y^n = 76^n$is representing important thing | Given the formula x to the power of n plus y to the power of n equals 76 to the power of n.
is representing important thing |
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MathBridge : Enhancing ASR and TTS Models with LLM for Accessible Mathematical Learning in Students with Disabilities
Abstract
MathBridge is a Automatic Speech Recognition (ASR) and Text to Speech (TTS) pipeline designed for converting mathematical equations to aid students with disabilities. Unlike conventional ASR/TTS systems which cannot translate spoken math into LaTeX or make formula images into spoken math word, MathBridge addresses this gap, enhancing math education for students with hearing/visual impairments. MathBridge utilizes a LLM to transform both spoken and written mathematical content into formats accessible for students with hearing and visual impairments. Previously unattainable, the newly proposed metric, Cosine Character Error Rate (CCER), showcases high accuracy, recorded at 0.114 for ASR pipeline. This signifies that roughly 80% of the equations are accurately communicated. Also, the Real Time Factor (RTF) for the ASR pipeline stands at 11.09, and for the TTS pipeline stands at 17.87. This demonstrates the real-time feasibility of both pipelines.
This page is for anonymous submission for INTERSPEECH 2024 and it shows dataset used in MathBridge
- Figure 1: Generating Train/Evaluation Dataset.
Statistics
Table 1: Various sources for obtaining LaGT dataset.
Source Type Size LLM Synthetic Data 76K Arxiv 252.2K pix2tex Raw Data 235K New Raw Data 17.2K Total 0.49M Augmented Total 8.25M Figure 2: Token histogram of LaGT, SpNT using T5 tokenizer.
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