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##  Appendix A Data tables

This appendix provides all the numerical values obtained in this analysis.

The inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ differential
$p_{\mathrm{\textsc{t}}}$ yields in $\mathrm{Pb\mbox{--}Pb}$ in centrality
classes are given in Tab. 4. Tables 5 to 8 present the inclusive
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and
associated $\mathrm{Pb\mbox{--}Pb}$ yields as a function of centrality for
$2.5<y<4.0$ and four $p_{\mathrm{\textsc{t}}}$ ranges,
$p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
$p_{\mathrm{\textsc{t}}}\leq 2\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
$2<p_{\mathrm{\textsc{t}}}<5\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
and
$5<p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$.
Tables 9 to 13 show the $p_{\mathrm{\textsc{t}}}$ dependence of the inclusive
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and
associated $\mathrm{Pb\mbox{--}Pb}$ yields for the centrality classes
$\mathrm{0\mbox{--}20\%}$, $\mathrm{20\mbox{--}40\%}$,
$\mathrm{0\mbox{--}40\%}$, $\mathrm{40\mbox{--}90\%}$ and
$\mathrm{0\mbox{--}90\%}$. Table 14 shows the $y$ dependence of the inclusive
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and
associated $\mathrm{Pb\mbox{--}Pb}$ yields for the centrality class
$\mathrm{0\mbox{--}90\%}$ in the $p_{\mathrm{\textsc{t}}}$ range
$p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$.
Then, the inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
$R_{\mathrm{AA}}$ results with a low $p_{\mathrm{\textsc{t}}}$ cut at 0.3
$\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ are presented. The reference
$\mathrm{p\kern-0.50003ptp}$ cross section needed to build the
$R_{\mathrm{AA}}$ was extracted with the method described in [40]. The
inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$
centrality dependence for $2.5<y<4$ in the $p_{\mathrm{\textsc{t}}}$ ranges
$0.3<p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
and
$0.3<p_{\mathrm{\textsc{t}}}<2\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
is shown in Tab. 15. The inclusive
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ in the
$p_{\mathrm{\textsc{t}}}$ range
$0.3<p_{\mathrm{\textsc{t}}}<1\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
for $2.5<y<4$ in four centrality classes $\mathrm{0\mbox{--}90\%}$,
$\mathrm{0\mbox{--}20\%}$, $\mathrm{20\mbox{--}40\%}$ and
$\mathrm{40\mbox{--}90\%}$ is given in Tab. 16. Finally, Tab. 17 presents the
inclusive
$\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{Pb\mbox{--}Pb}}$
and
$\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{Pb\mbox{--}Pb}}\;/\;\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{p\kern-0.35002ptp}}$
ratios as a function of centrality for the $p_{\mathrm{\textsc{t}}}$ intervals
$p_{\mathrm{\textsc{t}}}<3\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and
$3<p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$.

$\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times
10^{3}$
---
$p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | $\mathrm{0\mbox{--}20\%}$ | $\mathrm{20\mbox{--}40\%}$ | $\mathrm{40\mbox{--}90\%}$
0.0–0.5 | $3.253\pm 0.386\pm 0.446$ | $1.366\pm 0.081\pm 0.165$ | $0.257\pm 0.017\pm 0.031$
0.5–1.0 | $8.012\pm 0.487\pm 1.087$ | $2.571\pm 0.199\pm 0.310$ | $0.346\pm 0.024\pm 0.042$
1.0–1.5 | $9.909\pm 0.603\pm 1.149$ | $3.494\pm 0.255\pm 0.388$ | $0.533\pm 0.030\pm 0.061$
1.5–2.0 | $8.193\pm 0.505\pm 0.907$ | $2.907\pm 0.194\pm 0.320$ | $0.493\pm 0.037\pm 0.053$
2.0–2.5 | $6.342\pm 0.401\pm 0.701$ | $2.371\pm 0.164\pm 0.260$ | $0.441\pm 0.034\pm 0.049$
2.5–3.0 | $4.759\pm 0.316\pm 0.542$ | $1.997\pm 0.134\pm 0.227$ | $0.270\pm 0.020\pm 0.029$
3.0–3.5 | $2.735\pm 0.183\pm 0.290$ | $1.313\pm 0.087\pm 0.151$ | $0.222\pm 0.016\pm 0.023$
3.5–4.0 | $1.876\pm 0.134\pm 0.201$ | $0.874\pm 0.068\pm 0.092$ | $0.174\pm 0.013\pm 0.018$
4.0–4.5 | $1.075\pm 0.098\pm 0.109$ | $0.483\pm 0.037\pm 0.048$ | $0.108\pm 0.009\pm 0.011$
4.5–5.0 | $0.731\pm 0.069\pm 0.073$ | $0.339\pm 0.030\pm 0.033$ | $0.076\pm 0.007\pm 0.007$
5.0–5.5 | $0.453\pm 0.047\pm 0.045$ | $0.263\pm 0.023\pm 0.026$ | $0.042\pm 0.005\pm 0.004$
5.5–6.0 | $0.345\pm 0.039\pm 0.046$ | $0.132\pm 0.016\pm 0.014$ | $0.028\pm 0.004\pm 0.003$
6.0–8.0 | $0.099\pm 0.009\pm 0.010$ | $0.068\pm 0.005\pm 0.007$ | $0.012\pm 0.001\pm 0.001$
Table 4:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ yields (as defined by Eq. 1) in $p_{\mathrm{\textsc{t}}}$ intervals for the $\mathrm{0\mbox{--}20\%}$, $\mathrm{20\mbox{--}40\%}$ and $\mathrm{40\mbox{--}90\%}$ most central $\mathrm{Pb\mbox{--}Pb}$ collisions. The rapidity range is $2.5<y<4$. Statistical and systematic uncertainties are also reported as $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm statistical~{}uncertainty}\pm{\rm systematic~{}uncertainty}$. A global systematic uncertainty of 4% affects all the values. A 2%, 1% and 2% systematic uncertainty, independent of $p_{\mathrm{\textsc{t}}}$, affects the centrality classes $\mathrm{0\mbox{--}20\%}$, $\mathrm{20\mbox{--}40\%}$ and $\mathrm{40\mbox{--}90\%}$, respectively.  Centrality |  $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ [27] | $Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}\pm{\rm(stat.)}\pm{\rm(syst.)}\times 10^{3}$
---|---|---
$\mathrm{0\mbox{--}10\%}$ | $0.557\pm 0.019\pm 0.024$ | $43.095\pm 1.454\pm 1.049$
$\mathrm{10\mbox{--}20\%}$ | $0.573\pm 0.020\pm 0.022$ | $27.212\pm 0.979\pm 0.501$
$\mathrm{20\mbox{--}30\%}$ | $0.598\pm 0.022\pm 0.020$ | $17.409\pm 0.638\pm 0.188$
$\mathrm{30\mbox{--}40\%}$ | $0.577\pm 0.024\pm 0.025$ | $9.671\pm 0.406\pm 0.211$
$\mathrm{40\mbox{--}50\%}$ | $0.609\pm 0.028\pm 0.030$ | $5.413\pm 0.247\pm 0.041$
$\mathrm{50\mbox{--}60\%}$ | $0.725\pm 0.036\pm 0.043$ | $3.246\pm 0.160\pm 0.050$
$\mathrm{60\mbox{--}70\%}$ | $0.839\pm 0.041\pm 0.058$ | $1.677\pm 0.083\pm 0.024$
$\mathrm{70\mbox{--}80\%}$ | $0.849\pm 0.063\pm 0.068$ | $0.701\pm 0.051\pm 0.014$
$\mathrm{80\mbox{--}90\%}$ | $1.094\pm 0.106\pm 0.104$ | $0.362\pm 0.033\pm 0.008$
Table 5:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of centrality, for $p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 15% (12%) affects all the $R_{\mathrm{AA}}$ (yields) values. Centrality | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ | $Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}\pm{\rm(stat.)}\pm{\rm(syst.)}\times 10^{3}$
---|---|---
$\mathrm{0\mbox{--}10\%}$ | $0.732\pm 0.034\pm 0.041$ | $27.932\pm 1.302\pm 1.282$
$\mathrm{10\mbox{--}20\%}$ | $0.733\pm 0.035\pm 0.028$ | $17.159\pm 0.824\pm 0.383$
$\mathrm{20\mbox{--}30\%}$ | $0.715\pm 0.038\pm 0.024$ | $10.113\pm 0.541\pm 0.115$
$\mathrm{30\mbox{--}40\%}$ | $0.678\pm 0.040\pm 0.033$ | $5.516\pm 0.322\pm 0.182$
$\mathrm{40\mbox{--}50\%}$ | $0.641\pm 0.044\pm 0.032$ | $2.789\pm 0.190\pm 0.064$
$\mathrm{50\mbox{--}60\%}$ | $0.839\pm 0.048\pm 0.056$ | $1.799\pm 0.103\pm 0.070$
$\mathrm{60\mbox{--}90\%}$ | $1.104\pm 0.064\pm 0.078$ | $0.559\pm 0.032\pm 0.016$
Table 6:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of centrality, for $p_{\mathrm{\textsc{t}}}<2\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 15% (12%) affects all the $R_{\mathrm{AA}}$ (yields) values.  Centrality | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ | $Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}\pm{\rm(stat.)}\pm{\rm(syst.)}\times 10^{3}$
---|---|---
$\mathrm{0\mbox{--}10\%}$ | $0.425\pm 0.019\pm 0.017$ | $15.540\pm 0.681\pm 0.379$
$\mathrm{10\mbox{--}20\%}$ | $0.461\pm 0.019\pm 0.016$ | $10.336\pm 0.431\pm 0.168$
$\mathrm{20\mbox{--}30\%}$ | $0.529\pm 0.022\pm 0.018$ | $7.164\pm 0.293\pm 0.106$
$\mathrm{30\mbox{--}40\%}$ | $0.498\pm 0.025\pm 0.027$ | $3.879\pm 0.194\pm 0.153$
$\mathrm{40\mbox{--}50\%}$ | $0.595\pm 0.030\pm 0.029$ | $2.481\pm 0.126\pm 0.049$
$\mathrm{50\mbox{--}60\%}$ | $0.675\pm 0.042\pm 0.041$ | $1.386\pm 0.085\pm 0.037$
$\mathrm{60\mbox{--}90\%}$ | $0.722\pm 0.044\pm 0.050$ | $0.350\pm 0.021\pm 0.009$
Table 7:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of centrality, for $2<p_{\mathrm{\textsc{t}}}<5\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 14% (11%) affects all the $R_{\mathrm{AA}}$ (yields) values.  Centrality | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ | $Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}\pm{\rm(stat.)}\pm{\rm(syst.)}\times 10^{3}$
---|---|---
$\mathrm{0\mbox{--}10\%}$ | $0.280\pm 0.021\pm 0.011$ | $1.093\pm 0.081\pm 0.027$
$\mathrm{10\mbox{--}20\%}$ | $0.282\pm 0.027\pm 0.011$ | $0.677\pm 0.064\pm 0.016$
$\mathrm{20\mbox{--}30\%}$ | $0.410\pm 0.029\pm 0.013$ | $0.594\pm 0.042\pm 0.006$
$\mathrm{30\mbox{--}40\%}$ | $0.540\pm 0.039\pm 0.024$ | $0.449\pm 0.033\pm 0.012$
$\mathrm{40\mbox{--}50\%}$ | $0.529\pm 0.053\pm 0.031$ | $0.236\pm 0.024\pm 0.009$
$\mathrm{50\mbox{--}60\%}$ | $0.587\pm 0.073\pm 0.036$ | $0.129\pm 0.016\pm 0.004$
$\mathrm{60\mbox{--}90\%}$ | $0.644\pm 0.083\pm 0.047$ | $0.033\pm 0.004\pm 0.001$
Table 8:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of centrality, for $5<p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 18% (10%) affects all the $R_{\mathrm{AA}}$ (yields) values.  $p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) |  $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ [27] | $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm(stat.)}\pm{\rm(syst.)}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times 10^{3}$
---|---|---
0–1 | $0.803\pm 0.084\pm 0.113$ | $5.771\pm 0.345\pm 0.748$
1–2 | $0.690\pm 0.052\pm 0.084$ | $9.134\pm 0.411\pm 0.987$
2–3 | $0.505\pm 0.042\pm 0.062$ | $5.539\pm 0.284\pm 0.604$
3–4 | $0.381\pm 0.037\pm 0.046$ | $2.305\pm 0.116\pm 0.247$
4–5 | $0.355\pm 0.052\pm 0.041$ | $0.905\pm 0.068\pm 0.090$
5–6 | $0.282\pm 0.048\pm 0.032$ | $0.388\pm 0.030\pm 0.038$
6–8 | $0.279\pm 0.064\pm 0.032$ | $0.100\pm 0.009\pm 0.010$
Table 9:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of $p_{\mathrm{\textsc{t}}}$ for the $\mathrm{0\mbox{--}20\%}$ centrality class and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 8% (4%) affects all the $R_{\mathrm{AA}}$ (yields) values.  $p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ | $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm(stat.)}\pm{\rm(syst.)}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times 10^{3}$
---|---|---
0–1 | $0.733\pm 0.080\pm 0.097$ | $1.909\pm 0.128\pm 0.229$
1–2 | $0.660\pm 0.051\pm 0.080$ | $3.189\pm 0.154\pm 0.344$
2–3 | $0.543\pm 0.044\pm 0.067$ | $2.167\pm 0.106\pm 0.238$
3–4 | $0.493\pm 0.048\pm 0.060$ | $1.084\pm 0.055\pm 0.117$
4–5 | $0.444\pm 0.063\pm 0.051$ | $0.411\pm 0.027\pm 0.040$
5–6 | $0.399\pm 0.067\pm 0.045$ | $0.200\pm 0.014\pm 0.020$
6–8 | $0.523\pm 0.116\pm 0.059$ | $0.068\pm 0.005\pm 0.007$
Table 10:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of $p_{\mathrm{\textsc{t}}}$ for the $\mathrm{20\mbox{--}40\%}$ centrality class and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 8% (4%) affects all the $R_{\mathrm{AA}}$ (yields) values.  $p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ | $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm(stat.)}\pm{\rm(syst.)}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times 10^{3}$
---|---|---
0–1 | $0.767\pm 0.074\pm 0.105$ | $3.754\pm 0.163\pm 0.472$
1–2 | $0.672\pm 0.046\pm 0.082$ | $6.103\pm 0.212\pm 0.662$
2–3 | $0.515\pm 0.038\pm 0.064$ | $3.865\pm 0.134\pm 0.428$
3–4 | $0.411\pm 0.038\pm 0.049$ | $1.698\pm 0.063\pm 0.178$
4–5 | $0.376\pm 0.051\pm 0.043$ | $0.655\pm 0.033\pm 0.064$
5–6 | $0.315\pm 0.050\pm 0.036$ | $0.296\pm 0.016\pm 0.029$
6–8 | $0.340\pm 0.075\pm 0.038$ | $0.083\pm 0.005\pm 0.008$
Table 11:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of $p_{\mathrm{\textsc{t}}}$ for the $\mathrm{0\mbox{--}40\%}$ centrality class and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 8% (4%) affects all the $R_{\mathrm{AA}}$ (yields) values.  $p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ | $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm(stat.)}\pm{\rm(syst.)}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times 10^{3}$
---|---|---
0–1 | $0.815\pm 0.081\pm 0.107$ | $0.305\pm 0.015\pm 0.036$
1–2 | $0.732\pm 0.059\pm 0.090$ | $0.508\pm 0.028\pm 0.055$
2–3 | $0.617\pm 0.053\pm 0.076$ | $0.354\pm 0.020\pm 0.038$
3–4 | $0.627\pm 0.062\pm 0.074$ | $0.198\pm 0.010\pm 0.020$
4–5 | $0.693\pm 0.097\pm 0.079$ | $0.092\pm 0.006\pm 0.009$
5–6 | $0.489\pm 0.087\pm 0.055$ | $0.035\pm 0.003\pm 0.003$
6–8 | $0.646\pm 0.150\pm 0.072$ | $0.012\pm 0.001\pm 0.001$
Table 12:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of $p_{\mathrm{\textsc{t}}}$ for the $\mathrm{40\mbox{--}90\%}$ centrality class and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 9% (4%) affects all the $R_{\mathrm{AA}}$ (yields) values.  $p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) |  $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ [27] | $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm(stat.)}\pm{\rm(syst.)}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times 10^{3}$
---|---|---
0–1 | $0.779\pm 0.076\pm 0.106$ | $1.857\pm 0.081\pm 0.230$
1–2 | $0.677\pm 0.047\pm 0.083$ | $2.993\pm 0.104\pm 0.323$
2–3 | $0.519\pm 0.038\pm 0.064$ | $1.896\pm 0.064\pm 0.206$
3–4 | $0.425\pm 0.039\pm 0.051$ | $0.855\pm 0.029\pm 0.089$
4–5 | $0.405\pm 0.054\pm 0.047$ | $0.343\pm 0.015\pm 0.033$
5–6 | $0.322\pm 0.052\pm 0.036$ | $0.147\pm 0.007\pm 0.015$
6–8 | $0.364\pm 0.079\pm 0.041$ | $0.043\pm 0.002\pm 0.004$
Table 13:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of $p_{\mathrm{\textsc{t}}}$ for the $\mathrm{0\mbox{--}90\%}$ centrality class and $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 8% (4%) affects all the $R_{\mathrm{AA}}$ (yields) values.  $y$ |  $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ [27] | $\mathrm{d}^{2}Y_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}/\mathrm{d}y\mathrm{d}p_{\mathrm{\textsc{t}}}\pm{\rm(stat.)}\pm{\rm(syst.)}(\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc)^{-1}\,\times 10^{3}$
---|---|---
2.50–2.75 | $0.631\pm 0.087\pm 0.088$ | $1.509\pm 0.114\pm 0.191$
2.75–3.00 | $0.747\pm 0.068\pm 0.097$ | $1.387\pm 0.058\pm 0.162$
3.00–3.25 | $0.632\pm 0.048\pm 0.094$ | $1.120\pm 0.039\pm 0.154$
3.25–3.50 | $0.566\pm 0.044\pm 0.088$ | $0.891\pm 0.032\pm 0.130$
3.50–3.75 | $0.467\pm 0.041\pm 0.070$ | $0.733\pm 0.025\pm 0.101$
3.75–4.00 | $0.395\pm 0.050\pm 0.050$ | $0.528\pm 0.029\pm 0.058$
Table 14:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ and $\mathrm{Pb\mbox{--}Pb}$ yields as a function of $y$ for the $\mathrm{0\mbox{--}90\%}$ centrality class and $p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 8% (4%) affects all the $R_{\mathrm{AA}}$ (yields) values.  | $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$
---|---
Centrality | $0.3<p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ | $0.3<p_{\mathrm{\textsc{t}}}<2\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
$\mathrm{0\mbox{--}10\%}$ | $0.545\pm 0.017\pm 0.026$ | $0.745\pm 0.041\pm 0.042$
$\mathrm{10\mbox{--}20\%}$ | $0.560\pm 0.018\pm 0.021$ | $0.736\pm 0.036\pm 0.028$
$\mathrm{20\mbox{--}30\%}$ | $0.594\pm 0.020\pm 0.020$ | $0.716\pm 0.038\pm 0.025$
$\mathrm{30\mbox{--}40\%}$ | $0.570\pm 0.021\pm 0.025$ | $0.671\pm 0.040\pm 0.032$
$\mathrm{40\mbox{--}50\%}$ | $0.592\pm 0.025\pm 0.029$ | $0.619\pm 0.045\pm 0.032$
$\mathrm{50\mbox{--}60\%}$ | $0.715\pm 0.033\pm 0.044$ | $0.801\pm 0.049\pm 0.054$
$\mathrm{60\mbox{--}70\%}$ | $0.805\pm 0.043\pm 0.057$ | $\Biggr{\\}}0.959\pm 0.057\pm 0.067$
$\mathrm{70\mbox{--}80\%}$ | $0.778\pm 0.062\pm 0.064$
$\mathrm{80\mbox{--}90\%}$ | $0.887\pm 0.097\pm 0.088$
Table 15:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ as a function of centrality, for $0.3<p_{\mathrm{\textsc{t}}}<8\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $0.3<p_{\mathrm{\textsc{t}}}<2\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in the rapidity range $2.5<y<4.0$. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 15% affects all the $R_{\mathrm{AA}}$ values.  Centrality |  $R_{\mathrm{AA}}\pm{\rm(stat.)}\pm{\rm(syst.)}$ for $0.3<p_{\mathrm{\textsc{t}}}<1\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
---|---
$\mathrm{0\mbox{--}90\%}$ | $0.775\pm 0.057\pm 0.113$
$\mathrm{0\mbox{--}20\%}$ | $0.803\pm 0.066\pm 0.123$
$\mathrm{20\mbox{--}40\%}$ | $0.733\pm 0.067\pm 0.103$
$\mathrm{40\mbox{--}90\%}$ | $0.688\pm 0.057\pm 0.098$
Table 16:  Inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\mathrm{AA}}$ for $2.5<y<4.0$ in the centrality classes $\mathrm{0\mbox{--}90\%}$, $\mathrm{0\mbox{--}20\%}$, $\mathrm{20\mbox{--}40\%}$ and $\mathrm{40\mbox{--}90\%}$ for the lowest $p_{\mathrm{\textsc{t}}}$ range when the $0.3\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ $p_{\mathrm{\textsc{t}}}$ cut is applied. Statistical and systematic uncertainties are also reported. A global systematic uncertainty of 8%, 8%, 8% and 9% affect the $R_{\mathrm{AA}}$ values, respectively.  $p_{\mathrm{\textsc{t}}}$ ($\,\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | Centrality | $\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{Pb\mbox{--}Pb}}$ | $\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{Pb\mbox{--}Pb}}\;/\;\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{p\kern-0.35002ptp}}$
---|---|---|---
0–3 | $\mathrm{0\mbox{--}20\%}$ |  $<0.012$ (95% CL) |  $<0.65$ (95% CL)
0–3 | $\mathrm{20\mbox{--}40\%}$ | $0.017\pm 0.010\pm 0.004$ | $0.86\pm 0.51\pm 0.23$
0–3 | $\mathrm{40\mbox{--}60\%}$ | $0.013\pm 0.012\pm 0.006$ | $0.65\pm 0.65\pm 0.30$
0–3 | $\mathrm{60\mbox{--}90\%}$ | $0.029\pm 0.012\pm 0.004$ | $1.49\pm 0.62\pm 0.27$
3–8 | $\mathrm{0\mbox{--}20\%}$ |  $<0.046$ (95% CL) |  $<1.71$ (95% CL)
3–8 | $\mathrm{20\mbox{--}60\%}$ |  $<0.033$ (95% CL) |  $<1.24$ (95% CL)
Table 17:  Inclusive
$\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{Pb\mbox{--}Pb}}$
and
$\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{Pb\mbox{--}Pb}}\;/\;\left[\psi\mathrm{(2S)}/\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi\right]_{\mathrm{p\kern-0.35002ptp}}$
ratios as a function of centrality for two $p_{\mathrm{\textsc{t}}}$
intervals. Statistical and systematic uncertainties are reported when the
value is not given as an upper limit.

##  Appendix B The ALICE Collaboration

J. Adamorg40&D. Adamováorg83&M.M. Aggarwalorg87&G. Aglieri Rinellaorg36&M.
Agnelloorg111&N. Agrawalorg48&Z. Ahammedorg132&S.U. Ahnorg68&I.
Aimoorg94,org111&S. Aiolaorg137&M. Ajazorg16&A. Akindinovorg58&S.N.
Alamorg132&D. Aleksandrovorg100&B. Alessandroorg111&D. Alexandreorg102&R.
Alfaro Molinaorg64&A. Aliciorg105,org12&A. Alkinorg3&J.R.M. Almarazorg119&J.
Almeorg38&T. Altorg43&S. Altinpinarorg18&I. Altsybeevorg131&C. Alves Garcia
Pradoorg120&C. Andreiorg78&A. Andronicorg97&V. Anguelovorg93&J.
Anielskiorg54&T. Antičićorg98&F. Antinoriorg108&P. Antonioliorg105&L.
Aphecetcheorg113&H. Appelshäuserorg53&S. Arcelliorg28&N. Armestoorg17&R.
Arnaldiorg111&I.C. Arseneorg22&M. Arslandokorg53&B. Audurierorg113&A.
Augustinusorg36&R. Averbeckorg97&M.D. Azmiorg19&M. Bachorg43&A.
Badalàorg107&Y.W. Baekorg44&S. Bagnascoorg111&R. Bailhacheorg53&R.
Balaorg90&A. Baldisseriorg15&F. Baltasar Dos Santos Pedrosaorg36&R.C.
Baralorg61&A.M. Barbanoorg111&R. Barberaorg29&F. Barileorg33&G.G.
Barnaföldiorg136&L.S. Barnbyorg102&V. Barretorg70&P. Bartaliniorg7&K.
Barthorg36&J. Bartkeorg117&E. Bartschorg53&M. Basileorg28&N. Bastidorg70&S.
Basuorg132&B. Bathenorg54&G. Batigneorg113&A. Batista Camejoorg70&B.
Batyunyaorg66&P.C. Batzingorg22&I.G. Beardenorg80&H. Beckorg53&C.
Beddaorg111&N.K. Beheraorg49,org48&I. Belikovorg55&F. Belliniorg28&H. Bello
Martinezorg2&R. Bellwiedorg122&R. Belmontorg135&E. Belmont-Morenoorg64&V.
Belyaevorg76&G. Bencediorg136&S. Beoleorg27&I. Berceanuorg78&A.
Bercuciorg78&Y. Berdnikovorg85&D. Berenyiorg136&R.A. Bertensorg57&D.
Berzanoorg36,org27&L. Betevorg36&A. Bhasinorg90&I.R. Bhatorg90&A.K.
Bhatiorg87&B. Bhattacharjeeorg45&J. Bhomorg128&L. Bianchiorg122&N.
Bianchiorg72&C. Bianchinorg135,org57&J. Bielčíkorg40&J. Bielčíkováorg83&A.
Bilandzicorg80&R. Biswasorg4&S. Biswasorg79&S. Bjelogrlicorg57&J.T.
Blairorg118&F. Blancoorg10&D. Blauorg100&C. Blumeorg53&F. Bockorg93,org74&A.
Bogdanovorg76&H. Bøggildorg80&L. Boldizsárorg136&M. Bombaraorg41&J.
Bookorg53&H. Borelorg15&A. Borissovorg96&M. Borriorg82&F. Bossúorg65&E.
Bottaorg27&S. Böttgerorg52&P. Braun-Munzingerorg97&M. Bregantorg120&T.
Breitnerorg52&T.A. Brokerorg53&T.A. Browningorg95&M. Brozorg40&E.J.
Bruckenorg46&E. Brunaorg111&G.E. Brunoorg33&D. Budnikovorg99&H.
Bueschingorg53&S. Bufalinoorg27,org111&P. Buncicorg36&O. Buschorg128,org93&Z.
Butheleziorg65&J.B. Buttorg16&J.T. Buxtonorg20&D. Caffarriorg36&X. Caiorg7&H.
Cainesorg137&L. Calero Diazorg72&A. Calivaorg57&E. Calvo Villarorg103&P.
Cameriniorg26&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg28&J. Castillo
Castellanosorg15&A.J. Castroorg125&E.A.R. Casulaorg25&C. Cavicchioliorg36&C.
Ceballos Sanchezorg9&J. Cepilaorg40&P. Cerelloorg111&J. Cerkalaorg115&B.
Changorg123&S. Chapelandorg36&M. Chartierorg124&J.L. Charvetorg15&S.
Chattopadhyayorg132&S. Chattopadhyayorg101&V. Chelnokovorg3&M. Cherneyorg86&C.
Cheshkovorg130&B. Cheynisorg130&V. Chibante Barrosoorg36&D.D.
Chinellatoorg121&P. Chochulaorg36&K. Choiorg96&M. Chojnackiorg80&S.
Choudhuryorg132&P. Christakoglouorg81&C.H. Christensenorg80&P.
Christiansenorg34&T. Chujoorg128&S.U. Chungorg96&Z. Chunhuiorg57&C.
Cicaloorg106&L. Cifarelliorg12,org28&F. Cindoloorg105&J. Cleymansorg89&F.
Colamariaorg33&D. Colellaorg36,org33,org59&A. Colluorg25&M. Colocciorg28&G.
Conesa Balbastreorg71&Z. Conesa del Valleorg51&M.E. Connorsorg137&J.G.
Contrerasorg11,org40&T.M. Cormierorg84&Y. Corrales Moralesorg27&I. Cortés
Maldonadoorg2&P. Corteseorg32&M.R. Cosentinoorg120&F. Costaorg36&P.
Crochetorg70&R. Cruz Albinoorg11&E. Cuautleorg63&L. Cunqueiroorg36&T.
Dahmsorg92,org37&A. Daineseorg108&A. Danuorg62&D. Dasorg101&I.
Dasorg101,org51&S. Dasorg4&A. Dashorg121&S. Dashorg48&S. Deorg120&A. De
Caroorg31,org12&G. de Cataldoorg104&J. de Cuvelandorg43&A. De Falcoorg25&D. De
Gruttolaorg12,org31&N. De Marcoorg111&S. De Pasqualeorg31&A.
Deistingorg97,org93&A. Delofforg77&E. Dénesorg136&G. D’Erasmoorg33&D. Di
Bariorg33&A. Di Mauroorg36&P. Di Nezzaorg72&M.A. Diaz Corcheroorg10&T.
Dietelorg89&P. Dillensegerorg53&R. Diviàorg36&Ø. Djuvslandorg18&A.
Dobrinorg57,org81&T. Dobrowolskiorg770&D. Domenicis Gimenezorg120&B.
Dönigusorg53&O. Dordicorg22&T. Drozhzhovaorg53&A.K. Dubeyorg132&A.
Dublaorg57&L. Ducrouxorg130&P. Dupieuxorg70&R.J. Ehlersorg137&D. Eliaorg104&H.
Engelorg52&B. Erazmusorg36,org113&I. Erdemirorg53&F. Erhardtorg129&D.
Eschweilerorg43&B. Espagnonorg51&M. Estienneorg113&S. Esumiorg128&J.
Eumorg96&D. Evansorg102&S. Evdokimovorg112&G. Eyyubovaorg40&L.
Fabbiettiorg37,org92&D. Fabrisorg108&J. Faivreorg71&A. Fantoniorg72&M.
Faselorg74&L. Feldkamporg54&D. Feleaorg62&A. Felicielloorg111&G.
Feofilovorg131&J. Ferenceiorg83&A. Fernández Téllezorg2&E.G. Ferreiroorg17&A.
Ferrettiorg27&A. Festantiorg30&V.J.G. Feuillardorg70,org15&J.
Figielorg117&M.A.S. Figueredoorg124,org120&S. Filchaginorg99&D.
Finogeevorg56&E.M. Fioreorg33&M.G. Fleckorg93&M. Florisorg36&S.
Foertschorg65&P. Fokaorg97&S. Fokinorg100&E. Fragiacomoorg110&A.
Francesconorg30,org36&U. Frankenfeldorg97&U. Fuchsorg36&C. Furgetorg71&A.
Fursorg56&M. Fusco Girardorg31&J.J. Gaardhøjeorg80&M. Gagliardiorg27&A.M.
Gagoorg103&M. Gallioorg27&D.R. Gangadharanorg74&P. Ganotiorg88&C. Gaoorg7&C.
Garabatosorg97&E. Garcia-Solisorg13&C. Gargiuloorg36&P. Gasikorg92,org37&M.
Germainorg113&A. Gheataorg36&M. Gheataorg62,org36&P. Ghoshorg132&S.K.
Ghoshorg4&P. Gianottiorg72&P. Giubellinoorg36&P. Giubilatoorg30&E. Gladysz-
Dziadusorg117&P. Glässelorg93&D.M. Goméz Coralorg64&A. Gomez Ramirezorg52&P.
González-Zamoraorg10&S. Gorbunovorg43&L. Görlichorg117&S. Gotovacorg116&V.
Grabskiorg64&L.K. Graczykowskiorg134&K.L. Grahamorg102&A. Grelliorg57&A.
Grigorasorg36&C. Grigorasorg36&V. Grigorievorg76&A. Grigoryanorg1&S.
Grigoryanorg66&B. Grinyovorg3&N. Grionorg110&J.F. Grosse-
Oetringhausorg36&J.-Y. Grossiordorg130&R. Grossoorg36&F. Guberorg56&R.
Guernaneorg71&B. Guerzoniorg28&K. Gulbrandsenorg80&H. Gulkanyanorg1&T.
Gunjiorg127&A. Guptaorg90&R. Guptaorg90&R. Haakeorg54&Ø. Haalandorg18&C.
Hadjidakisorg51&M. Haiducorg62&H. Hamagakiorg127&G. Hamarorg136&A.
Hansenorg80&J.W. Harrisorg137&H. Hartmannorg43&A. Hartonorg13&D.
Hatzifotiadouorg105&S. Hayashiorg127&S.T. Heckelorg53&M. Heideorg54&H.
Helstruporg38&A. Herghelegiuorg78&G. Herrera Corralorg11&B.A. Hessorg35&K.F.
Hetlandorg38&T.E. Hildenorg46&H. Hillemannsorg36&B. Hippolyteorg55&R.
Hosokawaorg128&P. Hristovorg36&M. Huangorg18&T.J. Humanicorg20&N.
Hussainorg45&T. Hussainorg19&D. Hutterorg43&D.S. Hwangorg21&R. Ilkaevorg99&I.
Ilkivorg77&M. Inabaorg128&M. Ippolitovorg76,org100&M. Irfanorg19&M.
Ivanovorg97&V. Ivanovorg85&V. Izucheevorg112&P.M. Jacobsorg74&S.
Jadlovskaorg115&C. Jahnkeorg120&H.J. Jangorg68&M.A. Janikorg134&P.H.S.Y.
Jayarathnaorg122&C. Jenaorg30&S. Jenaorg122&R.T. Jimenez Bustamanteorg97&P.G.
Jonesorg102&H. Jungorg44&A. Juskoorg102&P. Kalinakorg59&A. Kalweitorg36&J.
Kaminorg53&J.H. Kangorg138&V. Kaplinorg76&S. Karorg132&A. Karasu Uysalorg69&O.
Karavichevorg56&T. Karavichevaorg56&L. Karayanorg93,org97&E. Karpechevorg56&U.
Kebschullorg52&R. Keidelorg139&D.L.D. Keijdenerorg57&M. Keilorg36&K.H.
Khanorg16&M.M. Khanorg19&P. Khanorg101&S.A. Khanorg132&A. Khanzadeevorg85&Y.
Kharlovorg112&B. Kilengorg38&B. Kimorg138&D.W. Kimorg44,org68&D.J.
Kimorg123&H. Kimorg138&J.S. Kimorg44&M. Kimorg44&M. Kimorg138&S. Kimorg21&T.
Kimorg138&S. Kirschorg43&I. Kiselorg43&S. Kiselevorg58&A. Kisielorg134&G.
Kissorg136&J.L. Klayorg6&C. Kleinorg53&J. Kleinorg36,org93&C. Klein-
Bösingorg54&A. Klugeorg36&M.L. Knichelorg93&A.G. Knospeorg118&T.
Kobayashiorg128&C. Kobdajorg114&M. Kofaragoorg36&T. Kolleggerorg97,org43&A.
Kolojvariorg131&V. Kondratievorg131&N. Kondratyevaorg76&E. Kondratyukorg112&A.
Konevskikhorg56&M. Kopcikorg115&M. Kourorg90&C. Kouzinopoulosorg36&O.
Kovalenkoorg77&V. Kovalenkoorg131&M. Kowalskiorg117&G. Koyithatta
Meethaleveeduorg48&J. Kralorg123&I. Králikorg59&A. Kravčákováorg41&M.
Krelinaorg40&M. Kretzorg43&M. Krivdaorg59,org102&F. Krizekorg83&E.
Kryshenorg36&M. Krzewickiorg43&A.M. Kuberaorg20&V. Kučeraorg83&T.
Kugathasanorg36&C. Kuhnorg55&P.G. Kuijerorg81&A. Kumarorg90&J. Kumarorg48&L.
Kumarorg79,org87&P. Kurashviliorg77&A. Kurepinorg56&A.B. Kurepinorg56&A.
Kuryakinorg99&S. Kushpilorg83&M.J. Kweonorg50&Y. Kwonorg138&S.L. La
Pointeorg111&P. La Roccaorg29&C. Lagana Fernandesorg120&I. Lakomovorg36&R.
Langoyorg42&C. Laraorg52&A. Lardeuxorg15&A. Lattucaorg27&E. Laudiorg36&R.
Leaorg26&L. Leardiniorg93&G.R. Leeorg102&S. Leeorg138&I. Legrandorg36&F.
Lehasorg81&R.C. Lemmonorg82&V. Lentiorg104&E. Leograndeorg57&I. León
Monzónorg119&M. Leoncinoorg27&P. Lévaiorg136&S. Liorg7,org70&X. Liorg14&J.
Lienorg42&R. Lietavaorg102&S. Lindalorg22&V. Lindenstruthorg43&C.
Lippmannorg97&M.A. Lisaorg20&H.M. Ljunggrenorg34&D.F. Lodatoorg57&P.I.
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Mahajanorg90&S.M. Mahmoodorg22&A. Maireorg55&R.D. Majkaorg137&M.
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Rochaorg64&E. Meninnoorg31&J. Mercado Pérezorg93&M. Meresorg39&Y.
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Laraorg81&E. Perez Lezamaorg53&V. Peskovorg53&Y. Pestovorg5&V.
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Zhuorg18,org7&J. Zhuorg113,org7&X. Zhuorg7&A. Zichichiorg12,org28&A.
Zimmermannorg93&M.B. Zimmermannorg54,org36&G. Zinovjevorg3&M. Zyzakorg43

## Affiliation notes

0Deceased

idp3817696Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn
Institute of Nuclear, Physics, Moscow, Russia

idp5959776Also at: University of Kansas, Lawrence, Kansas, United States

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi”, Rome, Italy

org13Chicago State University, Chicago, Illinois, USA

org14China Institute of Atomic Energy, Beijing, China

org15Commissariat à l’Energie Atomique, IRFU, Saclay, France

org16COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org17Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org18Department of Physics and Technology, University of Bergen, Bergen,
Norway

org19Department of Physics, Aligarh Muslim University, Aligarh, India

org20Department of Physics, Ohio State University, Columbus, Ohio, United
States

org21Department of Physics, Sejong University, Seoul, South Korea

org22Department of Physics, University of Oslo, Oslo, Norway

org23Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari,
Italy

org24Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN
Rome, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org27Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org30Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org31Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org35Eberhard Karls Universität Tübingen, Tübingen, Germany

org36European Organization for Nuclear Research (CERN), Geneva, Switzerland

org37Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org38Faculty of Engineering, Bergen University College, Bergen, Norway

org39Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org40Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org41Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org42Faculty of Technology, Buskerud and Vestfold University College,
Vestfold, Norway

org43Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org44Gangneung-Wonju National University, Gangneung, South Korea

org45Gauhati University, Department of Physics, Guwahati, India

org46Helsinki Institute of Physics (HIP), Helsinki, Finland

org47Hiroshima University, Hiroshima, Japan

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore (IITI), India

org50Inha University, Incheon, South Korea

org51Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org52Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org53Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org54Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org55Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org56Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org57Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org58Institute for Theoretical and Experimental Physics, Moscow, Russia

org59Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org60Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org61Institute of Physics, Bhubaneswar, India

org62Institute of Space Science (ISS), Bucharest, Romania

org63Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org64Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org65iThemba LABS, National Research Foundation, Somerset West, South Africa

org66Joint Institute for Nuclear Research (JINR), Dubna, Russia

org67Konkuk University, Seoul, South Korea

org68Korea Institute of Science and Technology Information, Daejeon, South
Korea

org69KTO Karatay University, Konya, Turkey

org70Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org71Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org72Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org73Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org74Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org75Lawrence Livermore National Laboratory, Livermore, California, United
States

org76Moscow Engineering Physics Institute, Moscow, Russia

org77National Centre for Nuclear Studies, Warsaw, Poland

org78National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org79National Institute of Science Education and Research, Bhubaneswar, India

org80Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org81Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org82Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org83Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org84Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org85Petersburg Nuclear Physics Institute, Gatchina, Russia

org86Physics Department, Creighton University, Omaha, Nebraska, United States

org87Physics Department, Panjab University, Chandigarh, India

org88Physics Department, University of Athens, Athens, Greece

org89Physics Department, University of Cape Town, Cape Town, South Africa

org90Physics Department, University of Jammu, Jammu, India

org91Physics Department, University of Rajasthan, Jaipur, India

org92Physik Department, Technische Universität München, Munich, Germany

org93Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org94Politecnico di Torino, Turin, Italy

org95Purdue University, West Lafayette, Indiana, United States

org96Pusan National University, Pusan, South Korea

org97Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany

org98Rudjer Bošković Institute, Zagreb, Croatia

org99Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org100Russian Research Centre Kurchatov Institute, Moscow, Russia

org101Saha Institute of Nuclear Physics, Kolkata, India

org102School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org103Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org104Sezione INFN, Bari, Italy

org105Sezione INFN, Bologna, Italy

org106Sezione INFN, Cagliari, Italy

org107Sezione INFN, Catania, Italy

org108Sezione INFN, Padova, Italy

org109Sezione INFN, Rome, Italy

org110Sezione INFN, Trieste, Italy

org111Sezione INFN, Turin, Italy

org112SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org113SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

org114Suranaree University of Technology, Nakhon Ratchasima, Thailand

org115Technical University of Košice, Košice, Slovakia

org116Technical University of Split FESB, Split, Croatia

org117The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org118The University of Texas at Austin, Physics Department, Austin, Texas,
USA

org119Universidad Autónoma de Sinaloa, Culiacán, Mexico

org120Universidade de São Paulo (USP), São Paulo, Brazil

org121Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org122University of Houston, Houston, Texas, United States

org123University of Jyväskylä, Jyväskylä, Finland

org124University of Liverpool, Liverpool, United Kingdom

org125University of Tennessee, Knoxville, Tennessee, United States

org126University of the Witwatersrand, Johannesburg, South Africa

org127University of Tokyo, Tokyo, Japan

org128University of Tsukuba, Tsukuba, Japan

org129University of Zagreb, Zagreb, Croatia

org130Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France

org131V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org132Variable Energy Cyclotron Centre, Kolkata, India

org133Vinča Institute of Nuclear Sciences, Belgrade, Serbia

org134Warsaw University of Technology, Warsaw, Poland

org135Wayne State University, Detroit, Michigan, United States

org136Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org137Yale University, New Haven, Connecticut, United States

org138Yonsei University, Seoul, South Korea

org139Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany


#  LLaVA-Phi: Efficient Multi-Modal Assistant with Small Language Model

Yichen Zhu1, Minjie Zhu1,2, Ning Liu1, Zhicai Ou1, Xiaofeng Mou1, Jian Tang1
1Midea Group, 2East China Normal University

###### Abstract

In this paper, we introduce LLaVA-$\phi$ (LLaVA-Phi), an efficient multi-modal
assistant that harnesses the power of the recently advanced small language
model, Phi-2, to facilitate multi-modal dialogues. LLaVA-Phi marks a notable
advancement in the realm of compact multi-modal models. It demonstrates that
even smaller language models, with as few as 2.7B parameters, can effectively
engage in intricate dialogues that integrate both textual and visual elements,
provided they are trained with high-quality corpora. Our model delivers
commendable performance on publicly available benchmarks that encompass visual
comprehension, reasoning, and knowledge-based perception. Beyond its
remarkable performance in multi-modal dialogue tasks, our model opens new
avenues for applications in time-sensitive environments and systems that
require real-time interaction, such as embodied agents. It highlights the
potential of smaller language models to achieve sophisticated levels of
understanding and interaction, while maintaining greater resource efficiency.
The project is available at https://github.com/zhuyiche/llava-phi.

##  1 Introduction

Large vision language models, including Flamingo [1], GPT-4V [30], and Gemini
[33], have exhibited remarkable proficiency in executing instructions,
engaging in multi-turn dialogues, and handling image-based question-answering
tasks. The progression of open-source vision language models has been
significantly propelled by the rapid advancement of open-source Large Language
Models like LLaMA [34] and Vicuna [5]. These developments primarily focus on
leveraging language models with a minimum of 7B parameters, integrated with a
vision encoder to enhance visual comprehension. However, this approach often
results in increased test time and reduced inference speed, which are less
than ideal for time-sensitive or real-time interactive applications, such as
autonomous driving and robotics. This leads to an important inquiry: How
effectively can small vision-language assistants perform in comparison?

Gemini [33] has blazed a trail for multi-modal models in mobile technology.
Its streamlined variant, Gemini-Nano, boasts 1.8/3.25 billion parameters and
is deployable on mobile devices. However, details like the model architecture,
training data, and training methodologies remain proprietary and inaccessible
to the public. In the realm of small language models, there have been notable
advancements: TinyGSM [23], with 2.6 billion parameters, achieves over 80%
accuracy on the GSM8k [7] benchmark. Additionally, models such as Phi [13]
have demonstrated capabilities in language understanding, commonsense
reasoning, and code generation, rivaling larger language models like
LLaMA-2-7B. This progress underscores the significant strides being made in
the efficiency and effectiveness of smaller-scale language models.

In this paper, we introduce LLaVA-Phi, a compact vision-language assistant
powered by a small language model. Our work combines the powerful open-sourced
multi-modal model, LLaVA-1.5 [24], with the best-performing open-sourced small
language models, Phi-2 [21]. We follow a two-stage training pipeline and
leverage high-quality visual instruction tuning data from LLaVA. LLaVA-Phi was
evaluated across eight diverse benchmarks. Despite possessing only 3 billion
parameters, it achieves performance comparable to, or even surpassing, some
larger multi-modal models that are three times larger. Notably, LLaVA-Phi-3B
demonstrates exceptional proficiency in ScienceQA [28], outperforming existing
large multi-modal models. Additionally, we qualitatively demonstrate LLaVA-
Phi’s strong generalization ability in handling challenging questions,
generating code based on instructions, and solving mathematical problems.

##  2 Related Work

The rapid advancements in Large Language Models (LLMs) have significantly
propelled the development of vision-language models based on LLMs. These
models, representing a departure from the capabilities of the pre-LLM era, are
equipped with advanced question-answering and visual comprehension skills.
This progress is enabled by using LLMs as language encoding modules. Notable
research in this domain includes the LLaVA-family [25, 24, 32, 26], the BLIP-
family [20, 8], MiniGPT-4 [36], and others. Each has demonstrated significant
advancements in managing visual-centric dialogues. However, a common
limitation of these open-sourced Vision-Language Models (VLMs) is their
substantial computational demands, typically ranging from 7B to 65B
parameters. This requirement poses challenges for deployment on edge or mobile
devices, especially in real-time applications. Gemini [33], a leader in this
field, has released three versions of vision-language models, including the
compact Gemini-Nano with 1.8B/3.25B parameters, tailored for smartphones.
However, their models and data are not open-sourced. Another initiative,
MobileVLM [6], has developed mobileLLaMA with 2.7B parameters to facilitate
smaller vision-language models. Our paper explores and demonstrates the
effectiveness of integrating vision-language models with open-sourced, smaller
language models, assessing their potential and efficiency in a variety of
applications.

Figure 1: LLaVA-Phi is adept at identifying and responding to complex
questions with empathetic reasoning.

Figure 2: LLaVA-Phi can generate useful codes based on visual input and
commands.

Figure 3: LLaVA-Phi is capable of performing accurate OCR on mathematical
equations and solving them correspondingly..

##  3 LLaVA-Phi

Our overall network architecture is similar to LLaVA-1.5. We use the pre-
trained CLIP ViT-L/14 with a resolution of 336x336 as the visual encoder. A
two-layer MLP is adopted to improve the connection of the visual encoder and
LLM.

Table 1: Multi-modal evaluation on multi-modal benchmarks. Benchmark names are
abbreviated due to space limits. $\text{VQA}^{\text{v2}}$ [12]; GQA [16];
VizWiz [14]; $\text{SQA}^{\text{I}}$: ScienceQA-IMG [28];
$\text{VQA}^{\text{T}}$: TextVQA [31]; POPE [22]; MME [10]; MMB: MMBench [27];
SEED: SEED-Bench [18]; MM-Vet [35].

Method | LLM | $\text{VQA}^{\text{v2}}$ | VizWiz | $\text{SQA}^{\text{I}}$ | $\text{VQA}^{\text{T}}$ | POPE | MME | MMB | MMVet
---|---|---|---|---|---|---|---|---|---
Gemini-Nano2 [33] | N/A (3.25B) | 67.5 | - | - | 65.9 | - | - | - | -
OpenFlamingo [2] | MBT (7B) | - | - | - | 33.6 | - | - | 4.6 | -
BLIP-2 [20] | Vicuna (13B) | 41.0 | 19.6 | 61.0 | 42.5 | 85.3 | 1293.8 | - | 22.4
InstructBLIP [8] | Vicuna (7B) | - | 34.5 | 60.5 | 50.1 | - | - | 36.0 | 26.2
InstructBLIP [8] | Vicuna (13B) | - | 33.4 | 63.1 | 50.7 | 78.9 | 1212.8 | - | 25.6
MiniGPT-4 [36] | Vicuna (7B) | - | - | - | - | - | 581.7 | 23.0 | 22.1
Shikra [4] | Vicuna (13B) | 77.4 | - | - | - | - | - | 58.8 | -
Otter [19] | LLaMA (7B) | - | - | - | - | - | 1292.3 | 48.3 | 24.6
Qwen-VL [3] | Qwen (7B) | 78.8 | 35.2 | 67.1 | 63.8 | - | - | 38.2 | -
Qwen-VL-Chat [3] | Qwen (7B) | 78.2 | 38.9 | 68.2 | 61.5 | - | 1487.5 | 60.6 | -
IDEFICS-9B [17] | LLaMA (7B) | 50.9 | 35.5 | - | 25.9 | - | - | 48.2 | -
IDEFICS-80B [17] | LLaMA (65B) | 60.0 | 36.0 | - | 30.9 | - | - | 54.5 | -
LLaMA-Adapter-v2 [11] | LLaMA (7B) | - | - | - | - | - | 1328.4 | 39.5 | 31.4
LLaVA [25] | Vicuna (7B) | - | - | - | - | - | 502.8 | 36.2 | 28.1
LLaVA-1.5 [24] | Vicuna (7B) | 78.5 | 50.0 | 66.8 | 58.2 | 85.9 | 1510.7 | 64.3 | 30.5
MobileVLM [6] | M-LLaMA (2.7B) | - | - | 61.0 | 47.5 | 84.9 | 1288.9 | 59.6 | -
LLaVA-Phi | Phi-2 (2.7B) | 71.4 | 35.9 | 68.4 | 48.6 | 85.0 | 1335.1 | 59.8 | 28.9

###  3.1 Training

Supervised fine-tuning on Phi-2. The publicly released Phi-2 model has not
undergone fine-tuning. Previous research indicates that even a small amount of
high-quality data can significantly enhance performance in areas such as
mathematics, language reasoning, and coding tasks. In light of this, we
employed supervised fine-tuning to further train Phi-2 using a select set of
premium data. This data was organized in the Vicuna format. For our Supervised
Fine-Tuning (SFT) data, we utilized ShareGPT from an open-source platform. The
training was conducted over two epochs, beginning with an initial learning
rate of 3e-5, which was linearly decreased over time. Our findings suggest
that while this step might be optional, applying SFT to Phi-2 does result in
modest improvements across most benchmarks.

Training LLaVA-Phi. Our training approach follows the pipeline used for
LLaVA1.5, consisting of a pre-training stage and a subsequent instruction
tuning phase. Initially, we kept the vision encoder and Phi-2 static, focusing
exclusively on training the efficient projector. This step is followed by a
comprehensive fine-tuning of both the projector and the language model (LLM),
aiming to enhance their capabilities in visual comprehension and language
processing.

For pre-training, we utilize a filtered subset of the CC-595K dataset [24]
over one epoch, applying an initial learning rate of 1e-3 and a batch size of
256. Then, we finetune the model on LLaVA-Instruct-150K dataset for 1 epoch at
a learning rate of 2e-5 and a batch size of 256. We implement a weight decay
of 0.1 and utilize the Adam optimizer, characterized by momentum parameters of
0.9 and 0.98, and an epsilon value of 1e-7. We fine-tune all parameters in LLM
instead of using LoRA.

Computational Cost. Similar to LLaVA1.5, our training process is structured in
two stages. For LLaVA-Phi, the pretraining phase takes 1.5 hours, followed by
8 hours dedicated to visual instruction tuning, utilizing 8 A100 GPUs. The
integration of techniques such as LoRA [15] and QLoRA [9] has the potential to
significantly reduce training time, a possibility we plan to explore in future
work.

###  3.2 Qualitative Results

We present several examples that demonstrate the remarkable generalization
capabilities of LLaVA-Phi, comparing its outputs with those of the
LLaVA-1.5-13B models. In Figure 1, a meme is displayed, and we ask the vision-
language assistant to explain why this meme is considered humorous. While
LLaVA-1.5-13B provides a reasonable interpretation based on the image, LLaVA-
Phi’s response is more empathetic, highlighting the humor by associating the
dog’s ’laid-back demeanor’ with the ’stress or fatigue’ typically associated
with a ’new workweek’.

In the second example, we instructed the model to generate Python code for
converting an Excel table into a bar chart, as illustrated in Figure 2.
LLaVA-1.5-13B generated a simplistic code snippet that only reads the table
and prints it, diverging from the instructions to create a plot. In contrast,
LLaVA-Phi accurately comprehended the task, providing instructions to read the
table, add a title and labels, and correctly plot the bar chart using
matplotlib. We believe this enhanced code generation capability stems from
Phi-2, which was pre-trained on a large corpus of code snippets and is
primarily used for code generation.

The third challenge involves solving a simple math problem, requiring the
model to accurately recognize text through OCR and then perform the necessary
mathematical computations, as shown in Figure 3. LLaVA-1.5-13B, while
providing a step-by-step computation based on the image, incorrectly
recognized the numbers and mathematical symbols. In contrast, our proposed
LLaVA-Phi, without providing a chain-of-thought reasoning, still produces the
correct answer. Our quantitative results on ScienceQA further confirm that
LLaVA-Phi excels in these types of question-answering tasks.

##  4 Experiments

We rigorously evaluated LLaVA-Phi using an extensive array of academic
benchmarks specifically designed for multi-modal models. These included tests
for general question-answering such as VQA-v2 [12], VizWizQA [14], ScienceQA
[28], and TextQA [31], as well as more specialized assessments like POPE [22]
for evaluating object hallucination, and MME [10], MMBench [27], and MMVet
[35] for a comprehensive evaluation of diverse multi-modal abilities, such as
visual understanding and visual commonsense reasoning.

These benchmarks are meticulously structured to challenge and scrutinize
complex multi-modal tasks. We benchmarked LLaVA-Phi against a variety of
state-of-the-art, large vision-language models, as detailed in Table 1. It is
important to note that both our method and LLaVA1.5 utilize the same publicly
available datasets for pre-training and visual instruction fine-tuning.

Our model demonstrated a capacity for visual-based question-answering,
surpassing many existing large multi-modal models. Remarkably, LLaVA-Phi
outperformed models that use 7B-parameter or larger Large Language Models
(LLMs) as their backbone, such as IDEFICS [17] and InstructBLIP [8]. A
particularly notable achievement was our model’s best performance on ScienceQA
[28]. We attribute this success to the Phi-2 language model, which has been
specifically trained on code generation and mathematical corpora, thereby
enhancing our multi-modal model’s prowess in math-based question-answering.

In the comprehensive multi-modal benchmark of MMBench [27], LLaVA-Phi showed
significantly superior performance compared to many existing 7B-LLM-based
vision-language models. For example, our model outperformed Otter by 11.5% and
InstructBLIP by 23.8%. This underscores the effectiveness of LLaVA-Phi in
handling complex multi-modal tasks, reinforcing the potential of smaller, more
efficient models in the rapidly evolving field of multi-modal models.

We also compared to MobileVLM [6], a concurrent work that builds up an
efficient vision-language model. Across all five benchmarks, our LLaVA-Phi
consistently outperforms their method. It’s important to note that the margins
of lead are modest, with the exception of ScienceQA. We attribute this
performance disparity primarily to the differences in the pretraining stages
of the language models.

##  5 Conclusion, Limitation, and Future Works

We introduce LLaVA-Phi, a vision language assistant developed using the
compact language model Phi-2. Our work demonstrates that such small vision-
language models can perform effectively on standard benchmarks when combined
with the LLaVA training methodology and a select dataset of high-quality data.
The primary goal of our project is to aid the community in creating
lightweight, multi-modal models capable of vision-language reasoning,
optimized for operation on edge devices. This innovation paves the way for
deploying multi-modal assistants in time-sensitive applications, such as
robotics.

Limitations. Given that Phi-2 utilizes the codegen-mono [29] tokenizer and our
model has not been specifically fine-tuned for following multilingual
instructions, our LLaVA-Phi architecture is unable to process instructions in
multiple languages, including Chinese.

Future Works. As language models have become significantly smaller in size
compared to traditional vision-language models, they have become more
accessible and affordable for the research community to explore fundamental
concepts in vision-language integration. In future work, we plan to examine
the impact of the size of the visual encoder and refine the training
strategies for small language models, including approaches like direct
preference optimization and RLHF, among other techniques. These efforts aim to
further reduce model size while enhancing performance.

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