Galactic-scale structure is of particular interest since it provides important clues to dark matter properties and its observation is improving. Weakly interacting massive particles (WIMPs) behave as cold dark matter on galactic scales, while beyond-WIMP candidates suppress galactic-scale structure formation. Suppression in the linear matter power spectrum has been conventionally characterized by a single parameter, the thermal warm dark matter mass. On the other hand, the shape of suppression depends on the underlying mechanism. It is necessary to introduce multiple parameters to cover a wide range of beyond-WIMP models. Once multiple parameters are introduced, it becomes harder to share results from one side to the other. In this work, we propose adopting neural network technique to facilitate the communication between the two sides. To demonstrate how to work out in a concrete manner, we consider a simplified model of light feebly interacting massive particles. ♦1 We refer readers to Ref. [10] for a recent review of gravitational probes of DM properties. ♦2 Prominent examples are the missing satellite problem [13][14][15][16][17], core-cusp problem [18][19][20][21], and toobig-to-fail problem [22][23][24][25][26][27]. We refer readers to Ref.[28] for a recent review and further details. Stateof-the-art hydrodynamical simulations have been demonstrating that astrophysical processes also play an important role [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. There have also been reports that small-scale issues persist even in state-of-the-art hydrodynamical simulations [47][48][49][50][51][52][53][54][55]. To our best knowledge, it is still controversial if astrophysical processes fully resolve the small-scale issues.One can work out each step independently by parametrizing the linear matter power spectrum. See the red flow in Fig. 1. A single parameter has been adopted conventionally: the thermal WDM mass m WDM . ♦3 On the other hand, a single parameter is not enough to cover a wide range of beyond-WIMP scenarios. For this purpose, Ref.[88] introduces the 3parameter ({α, β, γ}) characterization of the linear matter power spectrum. On one side, one (likely particle physicist) can construct a map of model parameters onto {α, β, γ}. On the other side, one (likely astrophysicist) can provide observational constraints on {α, β, γ}, as indeed done for the Lyman-α forest data in Ref. [89]. By combining results from the two sides, one can obtain observational constraints on a given beyond-WIMP scenario. Nevertheless, once multiple parameters are introduced, it becomes hard to share results from one side to the other.In this respect, we propose building ready-to-use networks: one maps model parameters onto {α, β, γ}; and another maps {α, β, γ} onto observables. One can use these networks to examine models without repeating the aforementioned time-consuming procedure. Ideally, it would be the most efficient if one obtained analytic maps, but in reality, it is hard to establish such analytic maps....