LLM system cards should report the upper bound on the model’s opaque serial depth, following the methodology proposed by Brown-Cohen et al. in Quantifying the Necessity of Chain of Thought through Opaque Serial Depth.
Currently, the most we know about frontier models’ opaque serial depths comes from occasional lab statements like Jakub Pachocki’s claim about Astra: “The depth of the computation graph for our present frontier models, including Astra, is within a factor of two of GPT-4.” This is annoyingly vague. Here are some questions it raises:
What counts as a node in the computation graph? Is it a layer, one attention/MLP module, one sequential matmul operation? As long as architectures are similar, the factor-of-two comparison is meaningful either way, but GPT-4 and GPT-6 are likely architecturally quite different, which could make a comparison that uses layers as the atomic objects in a computation graph misleading. I want to give OpenAI the benefit of doubt and assume that they wouldn’t use a misleading definition of a node, but the huge increase in no-CoT time horizons is difficult to reconcile with Pachocki’s statement.
Is the computation graph defined in terms of serial depth between interpretable information bottlenecks or in some other way? For example, if information can flow from later layers to earlier ones between token positions, does the computation graph get deeper? Again, given that Pachocki’s statement was directly addressed at neuralese fears, I’d like to think that it isn’t deliberately misleading in this sense, but a more precise statement would give me a lot more peace of mind.
What even is the reference point? We don’t really know the opaque serial depth of GPT-4 either.
Brown-Cohen et al. have proposed a clean definition of opaque serial depth: unroll the model into a circuit whose gates are two-input associative operations (add, multiply, max, min) and single-input piecewise-analytic functions (attention, softmax, etc all get decomposed into these), mark tokens as interpretable, and take the longest path that never passes through an interpretable node. This yields a single number that should be in every system card and provides minimal information about the architecture. It would likely tell competitors when you’ve started using looped transformers or dramatically increased the layer count, but those things can be inferred from rumors and no-CoT time horizons anyway. The gains for the safety community would be significant: we would be able to track how opaque serial depth has changed over time and forecast future trends, study the relationship between opaque serial depth and no-CoT time horizons, and spend less effort on speculation based on no-CoT time horizons.
Based on a skim, you may be interested in this MATS project