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---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:21000
- loss:ContrastiveTensionLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget:
- source_sentence: ' "The lemma follows by invoking Lemma 4.1 and Lemma A.1.\n\u220e",'
sentences:
- ' "To better address non-stationarity with changing uncertainty, we introduce
Location-Scale Noise Model (LSNM) into DDPMs, which relaxes the traditional Additive
Noise Model (ANM) by incorporating a contextually changing variance: \ud835\udc18=f\u2062(\ud835\udc17)+g\u2062(\ud835\udc17)\u2062\u03f5\ud835\udc18\ud835\udc53\ud835\udc17\ud835\udc54\ud835\udc17bold-italic-\u03f5\\mathbf{Y}=f(\\mathbf{X})+\\sqrt{g(\\mathbf{X})}\\boldsymbol{\\epsilon}bold_Y
= italic_f ( bold_X ) + square-root start_ARG italic_g ( bold_X ) end_ARG bold_italic_\u03f5,
where g\u2062(\ud835\udc17)\ud835\udc54\ud835\udc17g(\\mathbf{X})italic_g ( bold_X
) is an \ud835\udc17\ud835\udc17\\mathbf{X}bold_X-dependent variance model. LSNM
is capable of modeling both the contextual mean through f\u2062(\ud835\udc17)\ud835\udc53\ud835\udc17f(\\mathbf{X})italic_f
( bold_X ) and the contextual uncertainty through g\u2062(\ud835\udc17)\ud835\udc54\ud835\udc17\\sqrt{g(\\mathbf{X})}square-root
start_ARG italic_g ( bold_X ) end_ARG. In the special case where g\u2062(\ud835\udc17)\u22611\ud835\udc54\ud835\udc171g(\\mathbf{X})\\equiv
1italic_g ( bold_X ) \u2261 1, this simplifies to the standard ANM. Building upon
this more flexible and expressive assumption, we propose the Non-stationary Diffusion
Model (NsDiff) framework, which provides an uncertainty-aware noise schedule for
both forward and reverse diffusion processes. In summary, our contributions are
as:\n\n\n\u2022\n\nWe observe that the ANM is inadequate for capturing the varying
uncertainty and propose a novel framework that integrates LSNM to allow for explict
uncertainty modeling. This work is the first attempt to introduce LSNM into probabilistic
time series forecasting.\n\n\n\n\u2022\n\nTo fundamentally elevate the noise modeling
capabilities of DDPM, we seamlessly integrate time-varying variances into the
core diffusion process through an uncertainty-aware noise schedule that dynamically
adapts the noise variance at each step.\n\n\n\n\n\u2022\n\nExperimental results
indicate that NsDiff achieves superior performance in capturing uncertainty. Specifically,
in comparison to the second-best recent baseline TMDM, NsDiff improves up to 66.3%
on real-world datasets and 88.3% on synthetic datasets.",'
- ' "The deep neural network representation of the Bifrost simulations is
highly compressed compared to the original Bifrost data: the deep neural network
has 44,261 floating point values whereas the Bifrost simulation cube has 96\u22c596\u22c564\u22c520=11,796,480\u22c5969664201179648096\\cdot
96\\cdot 64\\cdot 20=11,796,48096 \u22c5 96 \u22c5 64 \u22c5 20 = 11 , 796 , 480
floating point values. This corresponds to a compression by a factor of 267; this
compression factor may be different for other numerical simulations and depends
on their smoothness. In addition, the deep neural network can be evaluated at
any point in space and time covered by the simulations, therefore enabling a trivial
way to interpolate between grid points; furthermore, gradients are calculate with
high efficiency with automatic differentiation. As such, it might be worth considering
releasing deep-neural-network representations of (magneto)hydrodynamic simulations.",'
- ' "\u03f5y\u2062(\u03bc)={1nt\u2062\u2211i=nkntey\u2062(ti,\u03bc)=1nt\u2062\u2211i=nknt|y~\u2062(ti,\u03bc)\u2212y\u2062(ti,\u03bc)|if\u00a0\u20621nt\u2062\u2211i=nknt|y\u2062(ti,\u03bc)|\u22641,1nt\u2062\u2211i=nkntey,r\u2062e\u2062l\u2062(ti,\u03bc)=1nt\u2062\u2211i=nknt|y~\u2062(ti,\u03bc)\u2212y\u2062(ti,\u03bc)|/|y\u2062(ti,\u03bc)|if\u00a0\u20621nt\u2062\u2211i=nknt|y\u2062(ti,\u03bc)|>1.subscriptitalic-\u03f5\ud835\udc66\ud835\udf07cases1subscript\ud835\udc5b\ud835\udc61superscriptsubscript\ud835\udc56subscript\ud835\udc5b\ud835\udc58subscript\ud835\udc5b\ud835\udc61subscript\ud835\udc52\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf071subscript\ud835\udc5b\ud835\udc61superscriptsubscript\ud835\udc56subscript\ud835\udc5b\ud835\udc58subscript\ud835\udc5b\ud835\udc61~\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf07\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf07if\u00a01subscript\ud835\udc5b\ud835\udc61superscriptsubscript\ud835\udc56subscript\ud835\udc5b\ud835\udc58subscript\ud835\udc5b\ud835\udc61\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf0711subscript\ud835\udc5b\ud835\udc61superscriptsubscript\ud835\udc56subscript\ud835\udc5b\ud835\udc58subscript\ud835\udc5b\ud835\udc61subscript\ud835\udc52\ud835\udc66\ud835\udc5f\ud835\udc52\ud835\udc59subscript\ud835\udc61\ud835\udc56\ud835\udf071subscript\ud835\udc5b\ud835\udc61superscriptsubscript\ud835\udc56subscript\ud835\udc5b\ud835\udc58subscript\ud835\udc5b\ud835\udc61~\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf07\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf07\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf07if\u00a01subscript\ud835\udc5b\ud835\udc61superscriptsubscript\ud835\udc56subscript\ud835\udc5b\ud835\udc58subscript\ud835\udc5b\ud835\udc61\ud835\udc66subscript\ud835\udc61\ud835\udc56\ud835\udf071\\centering\\epsilon_{y}(\\mu)=\\begin{cases}\\frac{1}{n_{t}}\\sum\\limits_{i=n_{k}}^%\n{n_{t}}e_{y}(t_{i},\\mu)=\\frac{1}{n_{t}}\\sum\\limits_{i=n_{k}}^{n_{t}}|\\tilde{y}%\n(t_{i},\\mu)-y(t_{i},\\mu)|&\\text{if
}\\frac{1}{n_{t}}\\sum\\limits_{i=n_{k}}^{n_{t%\n}}|y(t_{i},\\mu)|\\leq 1,\\\\\n\\frac{1}{n_{t}}\\sum\\limits_{i=n_{k}}^{n_{t}}e_{y,rel}(t_{i},\\mu)=\\frac{1}{n_{t%\n}}\\sum\\limits_{i=n_{k}}^{n_{t}}|\\tilde{y}(t_{i},\\mu)-y(t_{i},\\mu)|/|y(t_{i},%\n\\mu)|&\\text{if
}\\frac{1}{n_{t}}\\sum\\limits_{i=n_{k}}^{n_{t}}|y(t_{i},\\mu)|>1.%\n\\end{cases}\\@add@centeringitalic_\u03f5
start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT ( italic_\u03bc ) = { start_ROW
start_CELL divide start_ARG 1 end_ARG start_ARG italic_n start_POSTSUBSCRIPT italic_t
end_POSTSUBSCRIPT end_ARG \u2211 start_POSTSUBSCRIPT italic_i = italic_n start_POSTSUBSCRIPT
italic_k end_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT
italic_t end_POSTSUBSCRIPT end_POSTSUPERSCRIPT italic_e start_POSTSUBSCRIPT italic_y
end_POSTSUBSCRIPT ( italic_t start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ,
italic_\u03bc ) = divide start_ARG 1 end_ARG start_ARG italic_n start_POSTSUBSCRIPT
italic_t end_POSTSUBSCRIPT end_ARG \u2211 start_POSTSUBSCRIPT italic_i = italic_n
start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT
italic_n start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_POSTSUPERSCRIPT |
over~ start_ARG italic_y end_ARG ( italic_t start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT
, italic_\u03bc ) - italic_y ( italic_t start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT
, italic_\u03bc ) | end_CELL start_CELL if divide start_ARG 1 end_ARG start_ARG
italic_n start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG \u2211 start_POSTSUBSCRIPT
italic_i = italic_n start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT end_POSTSUBSCRIPT
start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT
end_POSTSUPERSCRIPT | italic_y ( italic_t start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT
, italic_\u03bc ) | \u2264 1 , end_CELL end_ROW start_ROW start_CELL divide start_ARG
1 end_ARG start_ARG italic_n start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG
\u2211 start_POSTSUBSCRIPT italic_i = italic_n start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT
end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_t
end_POSTSUBSCRIPT end_POSTSUPERSCRIPT italic_e start_POSTSUBSCRIPT italic_y ,
italic_r italic_e italic_l end_POSTSUBSCRIPT ( italic_t start_POSTSUBSCRIPT italic_i
end_POSTSUBSCRIPT , italic_\u03bc ) = divide start_ARG 1 end_ARG start_ARG italic_n
start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG \u2211 start_POSTSUBSCRIPT
italic_i = italic_n start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT end_POSTSUBSCRIPT
start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT
end_POSTSUPERSCRIPT | over~ start_ARG italic_y end_ARG ( italic_t start_POSTSUBSCRIPT
italic_i end_POSTSUBSCRIPT , italic_\u03bc ) - italic_y ( italic_t start_POSTSUBSCRIPT
italic_i end_POSTSUBSCRIPT , italic_\u03bc ) | / | italic_y ( italic_t start_POSTSUBSCRIPT
italic_i end_POSTSUBSCRIPT , italic_\u03bc ) | end_CELL start_CELL if divide start_ARG
1 end_ARG start_ARG italic_n start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG
\u2211 start_POSTSUBSCRIPT italic_i = italic_n start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT
end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_t
end_POSTSUBSCRIPT end_POSTSUPERSCRIPT | italic_y ( italic_t start_POSTSUBSCRIPT
italic_i end_POSTSUBSCRIPT , italic_\u03bc ) | > 1 . end_CELL end_ROW\n\n(12)",'
- source_sentence: ' "While significant research addresses design tolerance
optimisation in manufacturing, there is very little focus on production inspection
machines such as AOIs for manufactured products. For AOIs inspecting PCBs, each
component may demand a distinct tolerance for each type of inspection, leading
to thousands of possible scenarios. Consequently, a general paradigm is needed
that accommodates inspection of all components, including new introductions that
the system has not previously encountered.",'
sentences:
- ' "Indeed, for any e\u2208D0\ud835\udc52subscript\ud835\udc370e\\in D_{0}italic_e
\u2208 italic_D start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, there exists a \u03b4\ud835\udeff\\deltaitalic_\u03b4-tube
Te\u03b4\u2062(ae)subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52T^{\\delta}_{e}(a_{e})italic_T
start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_e
end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT )
centred at some ae\u2208Asubscript\ud835\udc4e\ud835\udc52\ud835\udc34a_{e}\\in
Aitalic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT \u2208 italic_A such
that\n\n\n\n1|Te\u03b4\u2062(ae)|n\u2062|E\u2229Te\u03b4\u2062(ae)|n>\u03bb.1subscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52\ud835\udc5bsubscript\ud835\udc38subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52\ud835\udc5b\ud835\udf06\\frac{1}{\\left|T^{\\delta}_{e}(a_{e})\\right|_{n}}\\left|E\\cap
T^{\\delta}_{e}(a_{%\ne})\\right|_{n}>\\lambda.divide start_ARG 1 end_ARG start_ARG
| italic_T start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT
italic_e end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG | italic_E \u2229 italic_T
start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_e
end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT )
| start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT > italic_\u03bb .\n\n\n\nSince
Emsubscript\ud835\udc38\ud835\udc5aE_{m}italic_E start_POSTSUBSCRIPT italic_m
end_POSTSUBSCRIPT and E\u00af\u00af\ud835\udc38\\overline{E}over\u00af start_ARG
italic_E end_ARG form a partition of E\ud835\udc38Eitalic_E, we obtain\n\n\n\n1|Te\u03b4\u2062(ae)|n\u2062|Em\u2229Te\u03b4\u2062(ae)|n+1|Te\u03b4\u2062(ae)|n\u2062|E\u00af\u2229Te\u03b4\u2062(ae)|n>\u03bb.1subscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52\ud835\udc5bsubscriptsubscript\ud835\udc38\ud835\udc5asubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52\ud835\udc5b1subscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52\ud835\udc5bsubscript\u00af\ud835\udc38subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udc52subscript\ud835\udc4e\ud835\udc52\ud835\udc5b\ud835\udf06\\frac{1}{\\left|T^{\\delta}_{e}(a_{e})\\right|_{n}}\\left|E_{m}\\cap
T^{\\delta}_{e}%\n(a_{e})\\right|_{n}+\\frac{1}{\\left|T^{\\delta}_{e}(a_{e})\\right|_{n}}\\left|%\n\\overline{E}\\cap
T^{\\delta}_{e}(a_{e})\\right|_{n}>\\lambda.divide start_ARG 1 end_ARG start_ARG
| italic_T start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT
italic_e end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG | italic_E start_POSTSUBSCRIPT
italic_m end_POSTSUBSCRIPT \u2229 italic_T start_POSTSUPERSCRIPT italic_\u03b4
end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT ( italic_a
start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT ) | start_POSTSUBSCRIPT italic_n
end_POSTSUBSCRIPT + divide start_ARG 1 end_ARG start_ARG | italic_T start_POSTSUPERSCRIPT
italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT
( italic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT ) | start_POSTSUBSCRIPT
italic_n end_POSTSUBSCRIPT end_ARG | over\u00af start_ARG italic_E end_ARG \u2229
italic_T start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT
italic_e end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT > italic_\u03bb .\n\n\n\nThus,
at least one of the terms on the left-hand side must be greater than \u03bb2\ud835\udf062\\frac{\\lambda}{2}divide
start_ARG italic_\u03bb end_ARG start_ARG 2 end_ARG, implying e\u2208Dm\u222aD\u00af\ud835\udc52subscript\ud835\udc37\ud835\udc5a\u00af\ud835\udc37e\\in
D_{m}\\cup\\overline{D}italic_e \u2208 italic_D start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT
\u222a over\u00af start_ARG italic_D end_ARG from the definition (3.14) and (3.19).
Since\n\n\n\n|Dm|n\u22121+|D\u00af|n\u22121\u2a7e|D0|n\u22121=\u03b50subscriptsubscript\ud835\udc37\ud835\udc5a\ud835\udc5b1subscript\u00af\ud835\udc37\ud835\udc5b1subscriptsubscript\ud835\udc370\ud835\udc5b1subscript\ud835\udf000\\left|D_{m}\\right|_{n-1}+\\left|\\overline{D}\\right|_{n-1}\\geqslant\\left|D_{0}%\n\\right|_{n-1}=\\varepsilon_{0}|
italic_D start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT | start_POSTSUBSCRIPT
italic_n - 1 end_POSTSUBSCRIPT + | over\u00af start_ARG italic_D end_ARG | start_POSTSUBSCRIPT
italic_n - 1 end_POSTSUBSCRIPT \u2a7e | italic_D start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT
| start_POSTSUBSCRIPT italic_n - 1 end_POSTSUBSCRIPT = italic_\u03b5 start_POSTSUBSCRIPT
0 end_POSTSUBSCRIPT\n\n\n\nand the stopping condition ensures\n\n\n\n|Dm|n\u22121<14\u2062\u03b50,subscriptsubscript\ud835\udc37\ud835\udc5a\ud835\udc5b114subscript\ud835\udf000\\left|D_{m}\\right|_{n-1}<\\frac{1}{4}\\varepsilon_{0},|
italic_D start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT | start_POSTSUBSCRIPT
italic_n - 1 end_POSTSUBSCRIPT < divide start_ARG 1 end_ARG start_ARG 4 end_ARG
italic_\u03b5 start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ,\n\n\n\nit follows that\n\n\n(3.20)\n\n|D\u00af|n\u22121\u2a7e14\u2062\u03b50.subscript\u00af\ud835\udc37\ud835\udc5b114subscript\ud835\udf000\\left|\\overline{D}\\right|_{n-1}\\geqslant\\frac{1}{4}\\varepsilon_{0}.|
over\u00af start_ARG italic_D end_ARG | start_POSTSUBSCRIPT italic_n - 1 end_POSTSUBSCRIPT
\u2a7e divide start_ARG 1 end_ARG start_ARG 4 end_ARG italic_\u03b5 start_POSTSUBSCRIPT
0 end_POSTSUBSCRIPT .\n\n\n\nFor any \u03be\u2208D\u00af\ud835\udf09\u00af\ud835\udc37\\xi\\in\\overline{D}italic_\u03be
\u2208 over\u00af start_ARG italic_D end_ARG, there exists a \u03b4\ud835\udeff\\deltaitalic_\u03b4-tube
T\u03be\u03b4\u2062(a\u03be)subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09T^{\\delta}_{\\xi}(a_{\\xi})italic_T
start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_\u03be
end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT
) centred at a\u03be\u2208Asubscript\ud835\udc4e\ud835\udf09\ud835\udc34a_{\\xi}\\in
Aitalic_a start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT \u2208 italic_A
such that\n\n\n\n1|T\u03be\u03b4\u2062(a\u03be)|n\u2062|\u22c3i=0m\u22121(E\u2229\u212ci)\u2229T\u03be\u03b4\u2062(a\u03be)|n>\u03bb2.1subscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5bsubscriptsuperscriptsubscript\ud835\udc560\ud835\udc5a1\ud835\udc38subscript\u212c\ud835\udc56subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5b\ud835\udf062\\frac{1}{\\left|T^{\\delta}_{\\xi}(a_{\\xi})\\right|_{n}}\\left|\\bigcup_{i=0}^{m-1}(%\nE\\cap\\mathcal{B}_{i})\\cap
T^{\\delta}_{\\xi}(a_{\\xi})\\right|_{n}>\\frac{\\lambda}{%\n2}.divide start_ARG
1 end_ARG start_ARG | italic_T start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT
start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT
italic_\u03be end_POSTSUBSCRIPT ) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT
end_ARG | \u22c3 start_POSTSUBSCRIPT italic_i = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT
italic_m - 1 end_POSTSUPERSCRIPT ( italic_E \u2229 caligraphic_B start_POSTSUBSCRIPT
italic_i end_POSTSUBSCRIPT ) \u2229 italic_T start_POSTSUPERSCRIPT italic_\u03b4
end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ( italic_a
start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ) | start_POSTSUBSCRIPT italic_n
end_POSTSUBSCRIPT > divide start_ARG italic_\u03bb end_ARG start_ARG 2 end_ARG
.\n\n\n\nThis implies\n\n\n(3.21)\n\n\u2211i=0m\u22121|\u212ci\u2229T\u03be\u03b4\u2062(a\u03be)|n|T\u03be\u03b4\u2062(a\u03be)|n\u2a7e\u2211i=0m\u22121|(E\u2229\u212ci)\u2229T\u03be\u03b4\u2062(a\u03be)|n|T\u03be\u03b4\u2062(a\u03be)|n\u2a7e|\u22c3i=0m\u22121(E\u2229\u212ci)\u2229T\u03be\u03b4\u2062(a\u03be)|n|T\u03be\u03b4\u2062(a\u03be)|n>\u03bb2superscriptsubscript\ud835\udc560\ud835\udc5a1subscriptsubscript\u212c\ud835\udc56subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5bsubscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5bsuperscriptsubscript\ud835\udc560\ud835\udc5a1subscript\ud835\udc38subscript\u212c\ud835\udc56subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5bsubscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5bsubscriptsuperscriptsubscript\ud835\udc560\ud835\udc5a1\ud835\udc38subscript\u212c\ud835\udc56subscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5bsubscriptsubscriptsuperscript\ud835\udc47\ud835\udeff\ud835\udf09subscript\ud835\udc4e\ud835\udf09\ud835\udc5b\ud835\udf062\\begin{split}\\frac{\\sum_{i=0}^{m-1}\\left|\\mathcal{B}_{i}\\cap
T^{\\delta}_{\\xi}(%\na_{\\xi})\\right|_{n}}{\\left|T^{\\delta}_{\\xi}(a_{\\xi})\\right|_{n}}&\\geqslant%\n\\frac{\\sum_{i=0}^{m-1}\\left|(E\\cap\\mathcal{B}_{i})\\cap
T^{\\delta}_{\\xi}(a_{\\xi%\n})\\right|_{n}}{\\left|T^{\\delta}_{\\xi}(a_{\\xi})\\right|_{n}}\\\\\n&\\geqslant\\frac{\\left|\\bigcup_{i=0}^{m-1}(E\\cap\\mathcal{B}_{i})\\cap
T^{\\delta}%\n_{\\xi}(a_{\\xi})\\right|_{n}}{\\left|T^{\\delta}_{\\xi}(a_{\\xi})\\right|_{n}}>\\frac{%\n\\lambda}{2}\\end{split}start_ROW
start_CELL divide start_ARG \u2211 start_POSTSUBSCRIPT italic_i = 0 end_POSTSUBSCRIPT
start_POSTSUPERSCRIPT italic_m - 1 end_POSTSUPERSCRIPT | caligraphic_B start_POSTSUBSCRIPT
italic_i end_POSTSUBSCRIPT \u2229 italic_T start_POSTSUPERSCRIPT italic_\u03b4
end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ( italic_a
start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ) | start_POSTSUBSCRIPT italic_n
end_POSTSUBSCRIPT end_ARG start_ARG | italic_T start_POSTSUPERSCRIPT italic_\u03b4
end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ( italic_a
start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT ) | start_POSTSUBSCRIPT italic_n
end_POSTSUBSCRIPT end_ARG end_CELL start_CELL \u2a7e divide start_ARG \u2211 start_POSTSUBSCRIPT
italic_i = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m - 1 end_POSTSUPERSCRIPT
| ( italic_E \u2229 caligraphic_B start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT
) \u2229 italic_T start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT
italic_\u03be end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG start_ARG | italic_T
start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_\u03be
end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG end_CELL end_ROW start_ROW
start_CELL end_CELL start_CELL \u2a7e divide start_ARG | \u22c3 start_POSTSUBSCRIPT
italic_i = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m - 1 end_POSTSUPERSCRIPT
( italic_E \u2229 caligraphic_B start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT
) \u2229 italic_T start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT
italic_\u03be end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG start_ARG | italic_T
start_POSTSUPERSCRIPT italic_\u03b4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_\u03be
end_POSTSUBSCRIPT ( italic_a start_POSTSUBSCRIPT italic_\u03be end_POSTSUBSCRIPT
) | start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG > divide start_ARG
italic_\u03bb end_ARG start_ARG 2 end_ARG end_CELL end_ROW",'
- ' "In [kipvar], the authors first add and subtract terms to\nexplicitly
express\nIn\u2062(f,\u22c5)subscript\ud835\udc3c\ud835\udc5b\ud835\udc53\u22c5I_{n}(f,\\cdot)italic_I
start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_f , \u22c5 ) in terms
of\nDynkin martingale and then pass to\nthe limit \u03bb\u21930\u2193\ud835\udf060\\lambda\\downarrow
0italic_\u03bb \u2193 0, before\nanalyzing that result in a second limit as\nn\u2192\u221e\u2192\ud835\udc5bn\\to\\inftyitalic_n
\u2192 \u221e. This is the approach of\n[varadhan95, liggett99, landim] as well.\nThe
essential idea of the present proof is to first note that\nfor f\u2208\ud835\udc9f(\u2212A^)\u221212\u2283\u211bA^\ud835\udc53subscript\ud835\udc9fsuperscript^\ud835\udc3412superset-ofsubscript\u211b^\ud835\udc34f\\in\\mathscr{D}_{(-\\hat{A})^{-\\frac{1}{2}}}\\supset\\mathscr{R}_{\\hat{A}}italic_f
\u2208 script_D start_POSTSUBSCRIPT ( - over^ start_ARG italic_A end_ARG ) start_POSTSUPERSCRIPT
- divide start_ARG 1 end_ARG start_ARG 2 end_ARG end_POSTSUPERSCRIPT end_POSTSUBSCRIPT
\u2283 script_R start_POSTSUBSCRIPT over^ start_ARG italic_A end_ARG end_POSTSUBSCRIPT,
the sequence\n\u039bn\u2062(f,\u03bbn,\u22c5)subscript\u039b\ud835\udc5b\ud835\udc53subscript\ud835\udf06\ud835\udc5b\u22c5\\Lambda_{n}(f,\\lambda_{n},\\cdot)roman_\u039b
start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_f , italic_\u03bb start_POSTSUBSCRIPT
italic_n end_POSTSUBSCRIPT , \u22c5 ) converges to zero\nin probability as n\u2192\u221e\u2192\ud835\udc5bn\\to\\inftyitalic_n
\u2192 \u221e for a choice of the sequence \u03bbnsubscript\ud835\udf06\ud835\udc5b\\lambda_{n}italic_\u03bb
start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT\ntending to zero. From this it
follows that\nIn\u2062(f,\u22c5)subscript\ud835\udc3c\ud835\udc5b\ud835\udc53\u22c5I_{n}(f,\\cdot)italic_I
start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_f , \u22c5 ) and In\u2062(f,\u22c5)\u2212\u039bn\u2062(f,\u03bbn,\u22c5)\u2261An\u2062(f,\u03bbn,\u22c5)subscript\ud835\udc3c\ud835\udc5b\ud835\udc53\u22c5subscript\u039b\ud835\udc5b\ud835\udc53subscript\ud835\udf06\ud835\udc5b\u22c5subscript\ud835\udc34\ud835\udc5b\ud835\udc53subscript\ud835\udf06\ud835\udc5b\u22c5I_{n}(f,\\cdot)-\\Lambda_{n}(f,\\lambda_{n},\\cdot)\\equiv
A_{n}(f,\\lambda_{n},\\cdot)italic_I start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT
( italic_f , \u22c5 ) - roman_\u039b start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT
( italic_f , italic_\u03bb start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT , \u22c5
) \u2261 italic_A start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_f ,
italic_\u03bb start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT , \u22c5 ) have the
same limit distribution, provided that the limit exists.\nThe proof is then completed
by showing that the latter\nlimit exists and can be obtained by an\nargument using
Theorem 1 in which n\ud835\udc5bnitalic_n tends to infinity for a\nfixed small,
but positive\n\u03bb\u2113subscript\ud835\udf06\u2113\\lambda_{\\ell}italic_\u03bb
start_POSTSUBSCRIPT roman_\u2113 end_POSTSUBSCRIPT, to be determined. Thus, this
new\nproof exhibits the asymptotic distribution of\n1n\u2062\u222b0n\u2062tf\u2062(X\u2062(s))\u2062\ud835\udc51s,t\u226501\ud835\udc5bsuperscriptsubscript0\ud835\udc5b\ud835\udc61\ud835\udc53\ud835\udc4b\ud835\udc60differential-d\ud835\udc60\ud835\udc610\\frac{1}{\\sqrt{n}}\\int_{0}^{nt}f(X(s))ds,t\\geq
0divide start_ARG 1 end_ARG start_ARG square-root start_ARG italic_n end_ARG end_ARG
\u222b start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n
italic_t end_POSTSUPERSCRIPT italic_f ( italic_X ( italic_s ) ) italic_d italic_s
, italic_t \u2265 0,\nf\u2208\ud835\udc9f(\u2212A^)\u221212\ud835\udc53subscript\ud835\udc9fsuperscript^\ud835\udc3412f\\in\\mathscr{D}_{(-\\hat{A})^{-\\frac{1}{2}}}italic_f
\u2208 script_D start_POSTSUBSCRIPT ( - over^ start_ARG italic_A end_ARG ) start_POSTSUPERSCRIPT
- divide start_ARG 1 end_ARG start_ARG 2 end_ARG end_POSTSUPERSCRIPT end_POSTSUBSCRIPT,
explicitly\nas the limit of\n1n\u2062\u222b0n\u2062tA^\u2062R\u03bbn\u2062f\u2062(X\u2062(s)),t\u226501\ud835\udc5bsuperscriptsubscript0\ud835\udc5b\ud835\udc61^\ud835\udc34subscript\ud835\udc45subscript\ud835\udf06\ud835\udc5b\ud835\udc53\ud835\udc4b\ud835\udc60\ud835\udc610\\frac{1}{\\sqrt{n}}\\int_{0}^{nt}\\hat{A}R_{\\lambda_{n}}f(X(s)),t\\geq
0divide start_ARG 1 end_ARG start_ARG square-root start_ARG italic_n end_ARG end_ARG
\u222b start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n
italic_t end_POSTSUPERSCRIPT over^ start_ARG italic_A end_ARG italic_R start_POSTSUBSCRIPT
italic_\u03bb start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_POSTSUBSCRIPT
italic_f ( italic_X ( italic_s ) ) , italic_t \u2265 0,\nA^\u2062R\u03bbn\u2062f\u2208\u211bA^^\ud835\udc34subscript\ud835\udc45subscript\ud835\udf06\ud835\udc5b\ud835\udc53subscript\u211b^\ud835\udc34\\hat{A}R_{\\lambda_{n}}f\\in\\mathscr{R}_{\\hat{A}}over^
start_ARG italic_A end_ARG italic_R start_POSTSUBSCRIPT italic_\u03bb start_POSTSUBSCRIPT
italic_n end_POSTSUBSCRIPT end_POSTSUBSCRIPT italic_f \u2208 script_R start_POSTSUBSCRIPT
over^ start_ARG italic_A end_ARG end_POSTSUBSCRIPT,\nfor a sequence of positive
\u201ctuning\u201dparameters \u03bbnsubscript\ud835\udf06\ud835\udc5b\\lambda_{n}italic_\u03bb
start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT.\nSo this new approach\nmay have
added value in\ncomputational and further theoretical refinements of the fclt.",'
- ' "Few-shot Voice Cloning: This follows the central concept of speaker
adaptation. However, the difference is the amount of data required. Thus, the
reference audio can range from a few seconds to a maximum of 5 minutes, which
is decided based on previous work, and anything more is challenging to obtain
in real-life scenarios.",'
- source_sentence: ' "For any \u03b3\u2208(0,2\u2062d)\ud835\udefe02\ud835\udc51\\gamma\\in(0,\\sqrt{2d})italic_\u03b3
\u2208 ( 0 , square-root start_ARG 2 italic_d end_ARG ), define a stochastic process\n{P\u03b3(\u03bb)\u2062(\ud835\udc2d):\ud835\udc2d\u2208[0,1]d}conditional-setsuperscriptsubscript\ud835\udc43\ud835\udefe\ud835\udf06\ud835\udc2d\ud835\udc2dsuperscript01\ud835\udc51\\{P_{\\gamma}^{(\\lambda)}(\\mathbf{t}):\\mathbf{t}\\in[0,1]^{d}\\}{
italic_P start_POSTSUBSCRIPT italic_\u03b3 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT
( italic_\u03bb ) end_POSTSUPERSCRIPT ( bold_t ) : bold_t \u2208 [ 0 , 1 ] start_POSTSUPERSCRIPT
italic_d end_POSTSUPERSCRIPT } by\n\n\n(3.52)\n\nP\u03b3(\u03bb)\u2062(\ud835\udc2d):=exp\u2061(\u03b3\u2062Z\u03bb\u2062(\ud835\udc2d)\u2212\u03b322\u2062\ud835\udd3c\u2062[Z\u03bb\u2062(\ud835\udc2d)2])=exp\u2061(\u03b3\u2062Z\u03bb\u2062(\ud835\udc2d)\u2212\u03b322\u2062R\u03bb\u2062(\ud835\udc2d,\ud835\udc2d)).assignsuperscriptsubscript\ud835\udc43\ud835\udefe\ud835\udf06\ud835\udc2d\ud835\udefesubscript\ud835\udc4d\ud835\udf06\ud835\udc2dsuperscript\ud835\udefe22\ud835\udd3cdelimited-[]subscript\ud835\udc4d\ud835\udf06superscript\ud835\udc2d2\ud835\udefesubscript\ud835\udc4d\ud835\udf06\ud835\udc2dsuperscript\ud835\udefe22subscript\ud835\udc45\ud835\udf06\ud835\udc2d\ud835\udc2d\\displaystyle
P_{\\gamma}^{(\\lambda)}(\\mathbf{t}):=\\exp\\Big{(}\\gamma Z_{\\lambda%\n}(\\mathbf{t})-\\frac{\\gamma^{2}}{2}\\mathbb{E}[Z_{\\lambda}(\\mathbf{t})^{2}]\\Big{%\n)}=\\exp\\Big{(}\\gamma
Z_{\\lambda}(\\mathbf{t})-\\frac{\\gamma^{2}}{2}R_{\\lambda}(%\n\\mathbf{t},\\mathbf{t})\\Big{)}.italic_P
start_POSTSUBSCRIPT italic_\u03b3 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( italic_\u03bb
) end_POSTSUPERSCRIPT ( bold_t ) := roman_exp ( italic_\u03b3 italic_Z start_POSTSUBSCRIPT
italic_\u03bb end_POSTSUBSCRIPT ( bold_t ) - divide start_ARG italic_\u03b3 start_POSTSUPERSCRIPT
2 end_POSTSUPERSCRIPT end_ARG start_ARG 2 end_ARG blackboard_E [ italic_Z start_POSTSUBSCRIPT
italic_\u03bb end_POSTSUBSCRIPT ( bold_t ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT
] ) = roman_exp ( italic_\u03b3 italic_Z start_POSTSUBSCRIPT italic_\u03bb end_POSTSUBSCRIPT
( bold_t ) - divide start_ARG italic_\u03b3 start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT
end_ARG start_ARG 2 end_ARG italic_R start_POSTSUBSCRIPT italic_\u03bb end_POSTSUBSCRIPT
( bold_t , bold_t ) ) .",'
sentences:
- ' "In this section, we highlight open challenges and future directions
in network-level ISAC design and the practical implementation of distributed ISAC
systems.",'
- '}'
- ' "Warning: As before, we need to restrict ourselves to a smaller class
of perturbation data (i.e. sufficiently small Hamiltonian perturbations) to ensure
that the element on the right is in \u039b0subscript\u039b0\\Lambda_{0}roman_\u039b
start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, in other words such that for any quilted
strip u\u00af\u00af\ud835\udc62\\underline{u}under\u00af start_ARG italic_u end_ARG
we have \u03c9\u2062(u\u00af)=0\ud835\udf14\u00af\ud835\udc620\\omega(\\underline{u})=0italic_\u03c9
( under\u00af start_ARG italic_u end_ARG ) = 0 if and only if [u\u00af]=0delimited-[]\u00af\ud835\udc620[\\underline{u}]=0[
under\u00af start_ARG italic_u end_ARG ] = 0.",'
- source_sentence: ' "For the regular planar lattice graphs, \ud835\udca2\u25b3,\ud835\udca2\u25a1,\ud835\udca2\u2394subscript\ud835\udca2\u25b3subscript\ud835\udca2\u25a1subscript\ud835\udca2\u2394\\mathcal{G}_{\\triangle},\\,\\mathcal{G}_{\\square},\\,\\mathcal{G}_{\\hexagon}caligraphic_G
start_POSTSUBSCRIPT \u25b3 end_POSTSUBSCRIPT , caligraphic_G start_POSTSUBSCRIPT
\u25a1 end_POSTSUBSCRIPT , caligraphic_G start_POSTSUBSCRIPT \u2394 end_POSTSUBSCRIPT,\n\n\n\nvol\u27c2\u2062(G)=vol\u2062(G)=vol\u25c6\u2062(G)+vol\u25c6\u2062(G\u2217)=2\u2062\u03c0\u2062m\u2062(p\u2062(z,w))=2\u2062\u03c0\u2062zGfd.superscriptvolperpendicular-to\ud835\udc3avol\ud835\udc3asuperscriptvol\u25c6\ud835\udc3asuperscriptvol\u25c6superscript\ud835\udc3a2\ud835\udf0bm\ud835\udc5d\ud835\udc67\ud835\udc642\ud835\udf0bsubscriptsuperscript\ud835\udc67fd\ud835\udc3a{\\rm
vol}^{\\perp}(G)={\\rm vol}(G)={\\rm vol}^{\\lozenge}(G)+{\\rm vol}^{\\lozenge}%\n(G^{*})=2\\pi\\,\\mathrm{m}(p(z,w))=2\\pi\\,z^{\\rm
fd}_{G}.roman_vol start_POSTSUPERSCRIPT \u27c2 end_POSTSUPERSCRIPT ( italic_G
) = roman_vol ( italic_G ) = roman_vol start_POSTSUPERSCRIPT \u25c6 end_POSTSUPERSCRIPT
( italic_G ) + roman_vol start_POSTSUPERSCRIPT \u25c6 end_POSTSUPERSCRIPT ( italic_G
start_POSTSUPERSCRIPT \u2217 end_POSTSUPERSCRIPT ) = 2 italic_\u03c0 roman_m (
italic_p ( italic_z , italic_w ) ) = 2 italic_\u03c0 italic_z start_POSTSUPERSCRIPT
roman_fd end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT .\n\n\n\nThus,
the lower bound in Conjecture\u00a01 holds with equality.",'
sentences:
- ' "Let F\ud835\udc39Fitalic_F denote a target model, which will now be
trained on a modified dataset Dp\u2062o\u2062i\u2062s\u2062o\u2062n\u2062e\u2062d=D\u2217subscript\ud835\udc37\ud835\udc5d\ud835\udc5c\ud835\udc56\ud835\udc60\ud835\udc5c\ud835\udc5b\ud835\udc52\ud835\udc51superscript\ud835\udc37D_{poisoned}=D^{*}italic_D
start_POSTSUBSCRIPT italic_p italic_o italic_i italic_s italic_o italic_n italic_e
italic_d end_POSTSUBSCRIPT = italic_D start_POSTSUPERSCRIPT \u2217 end_POSTSUPERSCRIPT,
where D\u2217superscript\ud835\udc37D^{*}italic_D start_POSTSUPERSCRIPT \u2217
end_POSTSUPERSCRIPT is a surreptitiously modified version of the clean training
dataset D\ud835\udc37Ditalic_D. The aim of data poisoning F\ud835\udc39Fitalic_F
is creating a poisoned model F\u2217superscript\ud835\udc39F^{*}italic_F start_POSTSUPERSCRIPT
\u2217 end_POSTSUPERSCRIPT that makes incorrect predictions, often without an
observable degradation in its overall accuracy. Data poisoning compromises the
model integrity by introducing systematic biases that serve the attacker\u2019s
objectives while evading detection during model training.",'
- ' "Figure 2 illustrates a comparison between the observed low-medium resolution
and the high-resolution spectral profiles of the oxygen A band, depicting observations
of (telluric) molecular oxygen. The upper panel of Figure 2 shows low to medium
resolution telluric oxygen features. These were obtained from the ESO Science
Archive Facility using X-shooter[141] observations during February and March 2024
by the UVES team, as part of Program ID: 60.A-9022(c), OB ID:2024672, 2024624
and 2024822, at various resolutions with short exposures (12 seconds). The results
indicate that higher resolution enables the observation of more detailed features
within the molecular oxygen spectrum, revealing the signal more distinctly within
each spectral line. The lower panel of Figure 2 shows performance tests for future
HRS instrumentation by observing the Sun through the Earth\u2019s atmosphere.
These profiles demonstrate the measurement outcomes obtained using two types of
interferometers: Michelson-based and FPI-based. Firstly, the FTS from the National
Solar Observatory at Kitt Peak [126] reported R=700,000 in the oxygen A-band.
Secondly, the FIOS-demo[133] showcases spectral profiles based on a chained FPI
array with a spectral resolution of R=250,000. This resolution can potentially
increase up to R=350,000 with the addition of each array. The throughput of each
additional unit, however, decreases by 10-15% [50]. One benefit of achieving this
level of resolution is the increase in signal-to-noise ratio and the sampling
frequency for each spectral line, which may reduce the required observing time,
as predicted in [46, 93].",'
- ' "At this point, we can reconcile what we observe with the evidence from
the last paragraphs on TFP in Figure 5. We argue that a critical mass is needed
in either case to record a significant impact of the exporting activity. At lower
levels of exporting activity, the company starts to benefit from economies of
scale but also needs to invest in productive capacity. To keep up with the technological
frontier is costly, and it often requires an upgrade of obsolete tangible assets.
We argue that the combined evidence of rising operational capacity (sales and
costs) and investment in fixed assets explains why we observe a negative albeit
small productivity loss in an intermediate range of export intensity. It is only
when the company operates abroad at a larger scale that positive albeit small
TFP gains come as a consequence of exporting. In this case, we argue, economies
of scale become evident and the capital adjustment unveils its impact on firms\u2019
performance.",'
- source_sentence: ' "To generate queer warmth phrases, we employed persona
prompting to adapt our SAE warmth phrases (see Table\u00a04). Three distinct personas
were designed and used as prompts to produce iterations of the 14 SAE warmth phrases.
Each phrase was processed through all three persona prompts (see Table\u00a08),
resulting in a total of 42 unique queer warmth phrases. The final set of phrases
is presented below.",'
sentences:
- ' "title": "Always skip attention",'
- ' "To generate queer warmth phrases, we employed persona prompting to adapt
our SAE warmth phrases (see Table\u00a04). Three distinct personas were designed
and used as prompts to produce iterations of the 14 SAE warmth phrases. Each phrase
was processed through all three persona prompts (see Table\u00a08), resulting
in a total of 42 unique queer warmth phrases. The final set of phrases is presented
below.",'
- ' "Assuming an adequately sized Bloom filter, the proportion of false positives
is small, ensuring that XAcomsuperscriptsubscript\ud835\udc4b\ud835\udc34comX_{A}^{\\text{com}}italic_X
start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT start_POSTSUPERSCRIPT com end_POSTSUPERSCRIPT
and XBcomsuperscriptsubscript\ud835\udc4b\ud835\udc35comX_{B}^{\\text{com}}italic_X
start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT com end_POSTSUPERSCRIPT
are highly similar. This minimizes the occurrence of similar but non-identical
buckets, thereby mitigating the redundancy issue inherent in bucketing. Furthermore,
the use of bucketing not only detects false positives but also ensures convergence,
addressing the limitation of Bloom filters alone. This combined approach is analogous
to the RSync protocol, where Bloom filters act as the weak checksum and bucketing
serves as the strong checksum.",'
pipeline_tag: sentence-similarity
library_name: sentence-transformers
---
# SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2
This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [sentence-transformers/all-MiniLM-L6-v2](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2). It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.
## Model Details
### Model Description
- **Model Type:** Sentence Transformer
- **Base model:** [sentence-transformers/all-MiniLM-L6-v2](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2) <!-- at revision c9745ed1d9f207416be6d2e6f8de32d1f16199bf -->
- **Maximum Sequence Length:** 256 tokens
- **Output Dimensionality:** 384 dimensions
- **Similarity Function:** Cosine Similarity
<!-- - **Training Dataset:** Unknown -->
<!-- - **Language:** Unknown -->
<!-- - **License:** Unknown -->
### Model Sources
- **Documentation:** [Sentence Transformers Documentation](https://sbert.net)
- **Repository:** [Sentence Transformers on GitHub](https://github.com/UKPLab/sentence-transformers)
- **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers)
### Full Model Architecture
```
SentenceTransformer(
(0): Transformer({'max_seq_length': 256, 'do_lower_case': False}) with Transformer model: BertModel
(1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
(2): Normalize()
)
```
## Usage
### Direct Usage (Sentence Transformers)
First install the Sentence Transformers library:
```bash
pip install -U sentence-transformers
```
Then you can load this model and run inference.
```python
from sentence_transformers import SentenceTransformer
# Download from the 🤗 Hub
model = SentenceTransformer("Stergios-Konstantinidis/MNLP_M2_document_encoder")
# Run inference
sentences = [
' "To generate queer warmth phrases, we employed persona prompting to adapt our SAE warmth phrases (see Table\\u00a04). Three distinct personas were designed and used as prompts to produce iterations of the 14 SAE warmth phrases. Each phrase was processed through all three persona prompts (see Table\\u00a08), resulting in a total of 42 unique queer warmth phrases. The final set of phrases is presented below.",',
' "To generate queer warmth phrases, we employed persona prompting to adapt our SAE warmth phrases (see Table\\u00a04). Three distinct personas were designed and used as prompts to produce iterations of the 14 SAE warmth phrases. Each phrase was processed through all three persona prompts (see Table\\u00a08), resulting in a total of 42 unique queer warmth phrases. The final set of phrases is presented below.",',
' "title": "Always skip attention",',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]
# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]
```
<!--
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<details><summary>Click to see the direct usage in Transformers</summary>
</details>
-->
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### Downstream Usage (Sentence Transformers)
You can finetune this model on your own dataset.
<details><summary>Click to expand</summary>
</details>
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*List how the model may foreseeably be misused and address what users ought not to do with the model.*
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*What are the known or foreseeable issues stemming from this model? You could also flag here known failure cases or weaknesses of the model.*
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*What are recommendations with respect to the foreseeable issues? For example, filtering explicit content.*
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## Training Details
### Training Dataset
#### Unnamed Dataset
* Size: 21,000 training samples
* Columns: <code>sentence_0</code>, <code>sentence_1</code>, and <code>label</code>
* Approximate statistics based on the first 1000 samples:
| | sentence_0 | sentence_1 | label |
|:--------|:------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------|:------------------------------------------------|
| type | string | string | int |
| details | <ul><li>min: 3 tokens</li><li>mean: 173.22 tokens</li><li>max: 256 tokens</li></ul> | <ul><li>min: 3 tokens</li><li>mean: 170.67 tokens</li><li>max: 256 tokens</li></ul> | <ul><li>0: ~66.60%</li><li>1: ~33.40%</li></ul> |
* Samples:
| sentence_0 | sentence_1 | label |
|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------|
| <code> "the user may robustify the design by selecting a suitable A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG. Only the choice of A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG has an impact at an algorithmic level and, normally, A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG is tuned to a set A\ud835\udc34Aitalic_A that, in the user\u2019s mind, captures, and suitably describes, possible adversarial actions. Still, we remark that our results hold true for any choice of A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG and A\ud835\udc34Aitalic_A (with A^\u2286A^\ud835\udc34\ud835\udc34\\widehat{A}\\subseteq Aover^ start_ARG italic_A end_ARG \u2286 italic_A), so accommodating situations in which, e.g., the user envisages adversarial actions of a certain type and, yet, he is willing to theoretically test the robustness of the design against actions of higher magnitude. One simple example of this situation occurs when the design is done...</code> | <code> "the user may robustify the design by selecting a suitable A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG. Only the choice of A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG has an impact at an algorithmic level and, normally, A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG is tuned to a set A\ud835\udc34Aitalic_A that, in the user\u2019s mind, captures, and suitably describes, possible adversarial actions. Still, we remark that our results hold true for any choice of A^^\ud835\udc34\\widehat{A}over^ start_ARG italic_A end_ARG and A\ud835\udc34Aitalic_A (with A^\u2286A^\ud835\udc34\ud835\udc34\\widehat{A}\\subseteq Aover^ start_ARG italic_A end_ARG \u2286 italic_A), so accommodating situations in which, e.g., the user envisages adversarial actions of a certain type and, yet, he is willing to theoretically test the robustness of the design against actions of higher magnitude. One simple example of this situation occurs when the design is done...</code> | <code>1</code> |
| <code> "Aha Moment of R1-Reward. Through our task design and reward function formulation, the R1-Reward model effectively learns the reward modeling task structure during the SFT phase. Following reinforcement learning, it reduces the length of reasoning to enhance efficiency. Visual examples of the model\u2019s output appear in Figures\u00a03 and\u00a06. The model autonomously learns a process to assess response quality. It first defines the goal, analyzes the image, attempts to solve the problem, and provides an answer. Based on this, the model evaluates Response 1 and Response 2, compares the two outputs, and gives a final ranking. Simultaneously, the model demonstrates different reflection patterns. In Figure\u00a03, the model encounters an error in its calculation, but after rechecking the bar chart, it recognizes the mistake and recalculates to obtain the correct result. In Figure\u00a06, the model misunderstands the problem. However, after outputting \u201cWait, re-reading the ...</code> | <code> "In an ideal case, the hole made after the punch doesn\u2019t move and keeps the size of the needle. Then the hole is filled with a subsequent paint layer, if it is not made in the top layer.",</code> | <code>0</code> |
| <code> "In our search for the optimal parameters, we evaluated all possible combinations presented in Section\u00a03.3. To do this, we aggregated the results for each specific parameter configuration and computed the mean metrics. This approach allowed us to isolate the effects of each parameter under evaluation.",</code> | <code> "We employ RWP to model the movement of humans within the indoor space and use the Matern hard-core process (MHCP) to model static obstacles, such as furniture or static humans, in the environment [15].",</code> | <code>0</code> |
* Loss: [<code>ContrastiveTensionLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#contrastivetensionloss)
### Training Hyperparameters
#### Non-Default Hyperparameters
- `per_device_train_batch_size`: 3
- `per_device_eval_batch_size`: 3
- `num_train_epochs`: 10
- `multi_dataset_batch_sampler`: round_robin
#### All Hyperparameters
<details><summary>Click to expand</summary>
- `overwrite_output_dir`: False
- `do_predict`: False
- `eval_strategy`: no
- `prediction_loss_only`: True
- `per_device_train_batch_size`: 3
- `per_device_eval_batch_size`: 3
- `per_gpu_train_batch_size`: None
- `per_gpu_eval_batch_size`: None
- `gradient_accumulation_steps`: 1
- `eval_accumulation_steps`: None
- `torch_empty_cache_steps`: None
- `learning_rate`: 5e-05
- `weight_decay`: 0.0
- `adam_beta1`: 0.9
- `adam_beta2`: 0.999
- `adam_epsilon`: 1e-08
- `max_grad_norm`: 1
- `num_train_epochs`: 10
- `max_steps`: -1
- `lr_scheduler_type`: linear
- `lr_scheduler_kwargs`: {}
- `warmup_ratio`: 0.0
- `warmup_steps`: 0
- `log_level`: passive
- `log_level_replica`: warning
- `log_on_each_node`: True
- `logging_nan_inf_filter`: True
- `save_safetensors`: True
- `save_on_each_node`: False
- `save_only_model`: False
- `restore_callback_states_from_checkpoint`: False
- `no_cuda`: False
- `use_cpu`: False
- `use_mps_device`: False
- `seed`: 42
- `data_seed`: None
- `jit_mode_eval`: False
- `use_ipex`: False
- `bf16`: False
- `fp16`: False
- `fp16_opt_level`: O1
- `half_precision_backend`: auto
- `bf16_full_eval`: False
- `fp16_full_eval`: False
- `tf32`: None
- `local_rank`: 0
- `ddp_backend`: None
- `tpu_num_cores`: None
- `tpu_metrics_debug`: False
- `debug`: []
- `dataloader_drop_last`: False
- `dataloader_num_workers`: 0
- `dataloader_prefetch_factor`: None
- `past_index`: -1
- `disable_tqdm`: False
- `remove_unused_columns`: True
- `label_names`: None
- `load_best_model_at_end`: False
- `ignore_data_skip`: False
- `fsdp`: []
- `fsdp_min_num_params`: 0
- `fsdp_config`: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
- `tp_size`: 0
- `fsdp_transformer_layer_cls_to_wrap`: None
- `accelerator_config`: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
- `deepspeed`: None
- `label_smoothing_factor`: 0.0
- `optim`: adamw_torch
- `optim_args`: None
- `adafactor`: False
- `group_by_length`: False
- `length_column_name`: length
- `ddp_find_unused_parameters`: None
- `ddp_bucket_cap_mb`: None
- `ddp_broadcast_buffers`: False
- `dataloader_pin_memory`: True
- `dataloader_persistent_workers`: False
- `skip_memory_metrics`: True
- `use_legacy_prediction_loop`: False
- `push_to_hub`: False
- `resume_from_checkpoint`: None
- `hub_model_id`: None
- `hub_strategy`: every_save
- `hub_private_repo`: None
- `hub_always_push`: False
- `gradient_checkpointing`: False
- `gradient_checkpointing_kwargs`: None
- `include_inputs_for_metrics`: False
- `include_for_metrics`: []
- `eval_do_concat_batches`: True
- `fp16_backend`: auto
- `push_to_hub_model_id`: None
- `push_to_hub_organization`: None
- `mp_parameters`:
- `auto_find_batch_size`: False
- `full_determinism`: False
- `torchdynamo`: None
- `ray_scope`: last
- `ddp_timeout`: 1800
- `torch_compile`: False
- `torch_compile_backend`: None
- `torch_compile_mode`: None
- `include_tokens_per_second`: False
- `include_num_input_tokens_seen`: False
- `neftune_noise_alpha`: None
- `optim_target_modules`: None
- `batch_eval_metrics`: False
- `eval_on_start`: False
- `use_liger_kernel`: False
- `eval_use_gather_object`: False
- `average_tokens_across_devices`: False
- `prompts`: None
- `batch_sampler`: batch_sampler
- `multi_dataset_batch_sampler`: round_robin
</details>
### Training Logs
<details><summary>Click to expand</summary>
| Epoch | Step | Training Loss |
|:------:|:-----:|:-------------:|
| 0.0714 | 500 | 1.8871 |
| 0.1429 | 1000 | 1.7445 |
| 0.2143 | 1500 | 1.7138 |
| 0.2857 | 2000 | 1.699 |
| 0.3571 | 2500 | 1.6729 |
| 0.4286 | 3000 | 1.6864 |
| 0.5 | 3500 | 1.6718 |
| 0.5714 | 4000 | 1.6754 |
| 0.6429 | 4500 | 1.6747 |
| 0.7143 | 5000 | 1.6709 |
| 0.7857 | 5500 | 1.6797 |
| 0.8571 | 6000 | 1.6768 |
| 0.9286 | 6500 | 1.6694 |
| 1.0 | 7000 | 1.6754 |
| 1.0714 | 7500 | 1.6632 |
| 1.1429 | 8000 | 1.6643 |
| 1.2143 | 8500 | 1.6553 |
| 1.2857 | 9000 | 1.6626 |
| 1.3571 | 9500 | 1.6734 |
| 1.4286 | 10000 | 1.673 |
| 1.5 | 10500 | 1.6611 |
| 1.5714 | 11000 | 1.671 |
| 1.6429 | 11500 | 1.6762 |
| 1.7143 | 12000 | 1.6717 |
| 1.7857 | 12500 | 1.6599 |
| 1.8571 | 13000 | 1.681 |
| 1.9286 | 13500 | 1.6715 |
| 2.0 | 14000 | 1.6815 |
| 2.0714 | 14500 | 1.6304 |
| 2.1429 | 15000 | 1.6351 |
| 2.2143 | 15500 | 1.648 |
| 2.2857 | 16000 | 1.6538 |
| 2.3571 | 16500 | 1.6396 |
| 2.4286 | 17000 | 1.632 |
| 2.5 | 17500 | 1.6497 |
| 2.5714 | 18000 | 1.6526 |
| 2.6429 | 18500 | 1.6346 |
| 2.7143 | 19000 | 1.6548 |
| 2.7857 | 19500 | 1.6549 |
| 2.8571 | 20000 | 1.6438 |
| 2.9286 | 20500 | 1.6448 |
| 3.0 | 21000 | 1.6435 |
| 3.0714 | 21500 | 1.589 |
| 3.1429 | 22000 | 1.6075 |
| 3.2143 | 22500 | 1.6084 |
| 3.2857 | 23000 | 1.6061 |
| 3.3571 | 23500 | 1.6121 |
| 3.4286 | 24000 | 1.6168 |
| 3.5 | 24500 | 1.6022 |
| 3.5714 | 25000 | 1.6164 |
| 3.6429 | 25500 | 1.6132 |
| 3.7143 | 26000 | 1.6036 |
| 3.7857 | 26500 | 1.6077 |
| 3.8571 | 27000 | 1.6241 |
| 3.9286 | 27500 | 1.6224 |
| 4.0 | 28000 | 1.6023 |
| 4.0714 | 28500 | 1.5479 |
| 4.1429 | 29000 | 1.5569 |
| 4.2143 | 29500 | 1.5611 |
| 4.2857 | 30000 | 1.5413 |
| 4.3571 | 30500 | 1.5568 |
| 4.4286 | 31000 | 1.5458 |
| 4.5 | 31500 | 1.5405 |
| 4.5714 | 32000 | 1.5707 |
| 4.6429 | 32500 | 1.557 |
| 4.7143 | 33000 | 1.5561 |
| 4.7857 | 33500 | 1.5698 |
| 4.8571 | 34000 | 1.546 |
| 4.9286 | 34500 | 1.5589 |
| 5.0 | 35000 | 1.5692 |
| 5.0714 | 35500 | 1.5029 |
| 5.1429 | 36000 | 1.5087 |
| 5.2143 | 36500 | 1.4882 |
| 5.2857 | 37000 | 1.5116 |
| 5.3571 | 37500 | 1.5016 |
| 5.4286 | 38000 | 1.4988 |
| 5.5 | 38500 | 1.5065 |
| 5.5714 | 39000 | 1.5089 |
| 5.6429 | 39500 | 1.5104 |
| 5.7143 | 40000 | 1.4937 |
| 5.7857 | 40500 | 1.4974 |
| 5.8571 | 41000 | 1.5095 |
| 5.9286 | 41500 | 1.5064 |
| 6.0 | 42000 | 1.5119 |
| 6.0714 | 42500 | 1.4572 |
| 6.1429 | 43000 | 1.4732 |
| 6.2143 | 43500 | 1.4534 |
| 6.2857 | 44000 | 1.4598 |
| 6.3571 | 44500 | 1.4626 |
| 6.4286 | 45000 | 1.4486 |
| 6.5 | 45500 | 1.4677 |
| 6.5714 | 46000 | 1.4705 |
| 6.6429 | 46500 | 1.4757 |
| 6.7143 | 47000 | 1.4724 |
| 6.7857 | 47500 | 1.4744 |
| 6.8571 | 48000 | 1.4571 |
| 6.9286 | 48500 | 1.4571 |
| 7.0 | 49000 | 1.4549 |
| 7.0714 | 49500 | 1.4198 |
| 7.1429 | 50000 | 1.4328 |
| 7.2143 | 50500 | 1.4322 |
| 7.2857 | 51000 | 1.4191 |
| 7.3571 | 51500 | 1.4355 |
| 7.4286 | 52000 | 1.4409 |
| 7.5 | 52500 | 1.4366 |
| 7.5714 | 53000 | 1.4378 |
| 7.6429 | 53500 | 1.4229 |
| 7.7143 | 54000 | 1.4386 |
| 7.7857 | 54500 | 1.453 |
| 7.8571 | 55000 | 1.419 |
| 7.9286 | 55500 | 1.4215 |
| 8.0 | 56000 | 1.4248 |
| 8.0714 | 56500 | 1.4184 |
| 8.1429 | 57000 | 1.4059 |
| 8.2143 | 57500 | 1.4011 |
| 8.2857 | 58000 | 1.3962 |
| 8.3571 | 58500 | 1.4134 |
| 8.4286 | 59000 | 1.4104 |
| 8.5 | 59500 | 1.3924 |
| 8.5714 | 60000 | 1.4062 |
| 8.6429 | 60500 | 1.4117 |
| 8.7143 | 61000 | 1.4192 |
| 8.7857 | 61500 | 1.402 |
| 8.8571 | 62000 | 1.3998 |
| 8.9286 | 62500 | 1.4087 |
| 9.0 | 63000 | 1.4203 |
| 9.0714 | 63500 | 1.389 |
| 9.1429 | 64000 | 1.4049 |
| 9.2143 | 64500 | 1.3897 |
| 9.2857 | 65000 | 1.3839 |
| 9.3571 | 65500 | 1.3712 |
| 9.4286 | 66000 | 1.3908 |
| 9.5 | 66500 | 1.3986 |
| 9.5714 | 67000 | 1.4014 |
| 9.6429 | 67500 | 1.3919 |
| 9.7143 | 68000 | 1.404 |
| 9.7857 | 68500 | 1.3921 |
| 9.8571 | 69000 | 1.3918 |
| 9.9286 | 69500 | 1.4046 |
| 10.0 | 70000 | 1.3923 |
</details>
### Framework Versions
- Python: 3.12.8
- Sentence Transformers: 3.4.1
- Transformers: 4.51.3
- PyTorch: 2.5.1+cu124
- Accelerate: 1.3.0
- Datasets: 3.6.0
- Tokenizers: 0.21.0
## Citation
### BibTeX
#### Sentence Transformers
```bibtex
@inproceedings{reimers-2019-sentence-bert,
title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
author = "Reimers, Nils and Gurevych, Iryna",
booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
month = "11",
year = "2019",
publisher = "Association for Computational Linguistics",
url = "https://arxiv.org/abs/1908.10084",
}
```
#### ContrastiveTensionLoss
```bibtex
@inproceedings{carlsson2021semantic,
title={Semantic Re-tuning with Contrastive Tension},
author={Fredrik Carlsson and Amaru Cuba Gyllensten and Evangelia Gogoulou and Erik Ylip{"a}{"a} Hellqvist and Magnus Sahlgren},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=Ov_sMNau-PF}
}
```
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