Arnold uses the OpenImageIO texture cache. From the OIIO Programmer Documentation:

In short, if you have an application that will need to read pixels from many large image files, you can rely on ImageCache to manage all the resources for you. It is reasonable to access thousands of image files totalling hundreds of GB of pixels, efficiently and using a memory footprint on the order of 50 MB.

So, if you’re using tx files (tiled and mipmapped textures), then Arnold can read tiles as required, and use the texture cache to keep memory usage under control.

The reason we don’t read all the textures at once is that many of our customers have (literally) 100+GB of textures, so we use a texture cache that constantly loads small bits of texture data as required, and unloads old data.

By default, the size of the texture cache is 2048KB (as of Arnold 4.2.13.0). The size of the texture cache is set in the Arnold Render Settings.

Max Cache Size
The maximum amount of memory to be used for texture caching. Arnold uses a tile-based cache with a LRU (Least Recently Used) type algorithm, where the least recently used tiles are discarded when the texture caches is full.

Note If we get an error reading a texture, we mark that texture as bad and we never try to read it again. This makes the renderer a lot faster when you have a missing texture, since we won’t ask the file server millions of times to read from a nonexistent file. But in a transient network error case, one bad experience and the rest of your render has the texture missing.