The Bidirectional Texture Function (BTF) is a data-driven solution to render materials with complex appearance. A typical capture contains tens of thousands of images of a material sample under varying viewing and lighting conditions. While capable of faithfully recording complex light interactions in the material, the main drawback is the massive memory requirement, both for storing and rendering, making effective compression of BTF data a critical component in practical applications. Common compression schemes used in practice are based on matrix factorization techniques, which preserve the discrete format of the original dataset. While this approach generalizes well to different materials, rendering with the compressed dataset still relies on interpolating between the closest samples. Depending on the material and the angular resolution of the BTF, this can lead to blurring and ghosting artefacts. An alternative approach uses analytic model fitting to approximate the BTF data, using continuous functions that naturally interpolate well, but whose expressive range is often not wide enough to faithfully recreate materials with complex non-local lighting effects (subsurface scattering, inter-reflections, shadowing and masking...). In light of these observations, we propose a neural network-based BTF representation inspired by autoencoders: our encoder compresses each texel to a small set of latent coefficients, while our decoder additionally takes in a light and view direction and outputs a single RGB vector at a time. This allows us to continuously query reflectance values in the light and view hemispheres, eliminating the need for linear interpolation between discrete samples. We train our architecture on fabric BTFs with a challenging appearance and compare to standard PCA as a baseline. We achieve competitive compression ratios and high-quality interpolation/extrapolation without blurring or ghosting artifacts.