  We propose a framework within which a robust mechanical definition of
precursors to plastic instabilities, often termed `soft-spots', naturally
emerges. They are shown to be collective displacements (modes) $\hat{z}_0$ that
correspond to local minima of the `barrier function' $b(\hat{z})$. The latter
is derived from the cubic approximation of the variation $\delta
U_{\hat{z}}(s)$ of the potential energy upon displacing particles a distance
$s$ along $\hat{z}$. We show that modes $\hat{z}_0$ corresponding to low-lying
minima of $b(\hat{z})$ lead to transitions over energy barriers in the glass,
and are therefore associated with highly asymmetric variations $\delta
U_{\hat{z}}(s)$ with $s$. We further demonstrate how a heuristic search for
local minima of $b(\hat{z})$ can a-priori detect the locus and geometry of
imminent plastic instabilities with remarkable accuracy, at strains as large as
$\gamma_c-\gamma \sim 10^{-2}$ away from the instability strain $\gamma_c$,
where the non-affine displacements under shear are still largely delocalized.
Our findings suggest that the a-priori detection of plastic instabilities can
be effectively carried out by the investigation of the landscape of
$b(\hat{z})$.
