In Vision, David Marr proposed that an information-processing device is fully understood only when it is described at three levels (Marr, 1982, p. 25): the computational (what is the goal of the computation, why is it appropriate, what is the logic of the strategy?), the algorithmic or representational (how are input and output represented, and what algorithm transforms one into the other?) and the implementational (how is all this realized physically?). The levels are coupled, but only loosely: one computation admits many algorithms, and one algorithm many substrates (see multiple realizability). His example is a cash register: the computational theory explains why it adds rather than multiplies (1982, p. 22). And his most quoted analogy: "trying to understand perception by studying only neurons is like trying to understand bird flight by studying only feathers" (1982, p. 27).
Ku et al. (2026) propose applying the scheme to LLMs. At the computational level one starts from what we do know, the training objective: next-token prediction. From it follows that a model will do better when the correct answer is probable; GPT-4 counts the letters in a list well when the answer is 30 (97% accuracy) and badly when it is 29 (17%) (2026, p. 3). At the algorithmic level, methods from experimental psychology apply, such as the analysis of systematic errors; at the implementational level, circuits, activation patching and sparse autoencoders, analogues of the techniques of neuroscience (2026, p. 3).
There is an instructive tension. For Millière & Buckner (2024b), mechanistic interpretability targets, like systems neuroscience, the algorithmic level (2024b, sec. 2.5); Ku and colleagues place those tools at the implementational level, and grant that neural networks blur the boundary (2026, p. 12). In a network, where does the algorithm end and the hardware begin?
The levels also organize philosophical debates. The dispute between GOFAI and connectionism is partly an argument about the level at which cognition is explained, and the "Redescription Fallacy" consists in thinking that a description at the implementational level ("it just multiplies matrices") rules out capacities at the computational one (Millière & Buckner, 2024a, sec. 3). Dennett (1987) offers another hierarchy: the physical, design and intentional stances (1987, pp. 16–17).