A hand opening is easy to describe in ordinary language. In a scene representation, it can be awkward. The gap between two fingers appears, surfaces that were close together separate, and visibility changes quickly.
HyperNeRF is interesting because it addresses changes in scene topology through an expanded representation. Rather than asking every frame to be a straightforward deformation of one fixed three-dimensional arrangement, it introduces additional dimensions in which the family of shapes can be represented more flexibly.
A simple deformation works well when there is a clear correspondence. Bend a rubber object and each part can be followed from its original location to its new one. The object changes shape, but the relationship between its parts remains manageable.
Opening a mouth illustrates a harder case. A dark interior becomes visible between surfaces that were previously close together. A system trying to explain everything with a smooth mapping into one canonical arrangement can be forced into uncomfortable compromises around those boundaries. The problem is not merely that the object moves quickly.
Extra dimensions provide room for arrangements that are difficult to separate in ordinary space. A useful analogy is a road crossing another road. In a flat drawing they meet; with a height coordinate, one can pass over the other. The analogy is only conceptual, but it helps explain why changing the representation can remove a restriction that a more powerful optimizer alone would struggle with.
This still leaves a substantial reconstruction problem. The system has to learn from images, estimate which changes belong together, and synthesize views that were not directly observed. A more flexible representation can explain more variation, but it also needs enough evidence to constrain that flexibility.
I would pay particular attention to regions near contact and separation: fingers, lips, folds and objects passing one another. A broad, slowly moving surface may look good under several methods. The difficult transitions reveal whether the representation can keep geometry and appearance coherent when the arrangement changes.
There is a separate question about what the result is useful for. Rendering a plausible new viewpoint of captured motion is different from obtaining an editable character rig. The learned representation does not automatically expose a named elbow joint or a control for opening the mouth. An application must respect the kind of control the method actually offers.
For me, the paper's appeal is the connection between the visual failure and the mathematical choice. If a scene cannot comfortably fit inside the assumptions of a representation, increasing detail may preserve the wrong structure more accurately. Giving the model a different space to work in can be the more productive move.
It is also a reminder to inspect transitions, not just states. Closed and open may both look convincing as isolated images. The path between them is where a dynamic scene reveals what its representation understands.