Step 1: Recall the thermal decomposition of alkali metal nitrates.
On heating, alkali metal nitrates generally form nitrites:
\[
2MNO_3 \rightarrow 2MNO_2+O_2
\]
This behavior is shown by:
\[
\mathrm{Na,\ K,\ Rb,\ Cs}
\]
Step 2: Observe the given reaction carefully.
The given reaction is:
\[
2MNO_3 \rightarrow M_2O+2NO_2+\frac{1}{2}O_2
\]
Here nitrate decomposes into oxide directly.
Step 3: Identify the exception among alkali metals.
Lithium nitrate behaves differently due to the small size and high polarizing power of lithium ion.
Lithium nitrate decomposes as:
\[
4LiNO_3 \rightarrow 2Li_2O+4NO_2+O_2
\]
This matches the given reaction pattern.
Step 4: Final conclusion.
Therefore, the metal \(M\) is
\[
\boxed{\mathrm{Li}}
\]