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To study the set of torsion classes of a finite dimensional basic algebra, weuse a decomposition, called sign-decomposition, parametrized by elements of$\{\pm1\}^n$ where $n$ is the number of simple modules. If $A$ is an algebrawith radical square zero, then for each $\epsilon \in \{\pm1\}^n$ there is ahereditary algebra $A_{\epsilon}^!$ with radical square zero and a bijectionbetween the set of torsion classes of $A$ associated to $\epsilon$ and the setof faithful torsion classes of $A_{\epsilon}^!$. Furthermore, this bijectionpreserves the property of being functorially finite. As an application in$\tau$-tilting theory, we prove that the number of support $\tau$-tiltingmodules over Brauer line algebras (resp. Brauer odd-cycle algebras) having $n$edges is $\binom{2n}{n}$ (resp. $2^{2n-1}$).

Classifying torsion classes for algebras with radical square zero via sign decomposition