Keep Guessing? When Considering Inference Scaling, Mind the Baselines

TL;DR

A baseline that enumerates answers according to their prevalence in the training set outperforms repeated model sampling for some LLMs, while the coverage for others is on par with that of a mixture strategy that obtains answers by using only model samples and similarly guessing the remaining attempts via enumeration.

Abstract

Scaling inference compute in large language models (LLMs) through repeated sampling consistently increases the coverage (fraction of problems solved) as the number of samples increases. We conjecture that this observed improvement is partially due to the answer distribution of standard evaluation benchmarks, which is skewed towards a relatively small set of common answers. To test this conjecture, we define a baseline that enumerates answers according to their prevalence in the training set. Experiments spanning two domains -- mathematical reasoning and factual knowledge -- reveal that this baseline outperforms repeated model sampling for some LLMs, while the coverage for others is on par with that of a mixture strategy that obtains $k$ answers by using only $10$ model samples and similarly guessing the remaining $k-10$ attempts via enumeration. Our baseline enables a more accurate measurement of how much repeated sampling improves coverage in such settings beyond prompt-agnostic guessing.

Figures (8)

• Figure 1: Standard coverage curves (top; see Fig. 3 in brown2024largelanguagemonkeys) vs normalized coverage curves (bottom), for the MATH dataset. Normalized coverage is obtained by re-scaling the improvements relative to our TrainCounts baseline. We see that despite all Pythia models (blue) showing non-negligible coverage gains, these are actually worse than simple answer enumeration (below the $y=0$ dashed red line).
• Figure 2: Coverage curves for model sampling and guessing-based answers for MATH (Llama-3-70B and Gemma-7B models) and EQ (Gemini-1.5-Pro and Gemma 2-9b models). We evaluate Mixture(M) for $M=1,5,10$ and compare Mixture(M) with TrainCounts and ModelAnswers.
• Figure 3: Prompt used for sampling answers for EntityQuestions. To generate an answer for a target test question, we append to the instructions (left) five randomly selected training examples from the same relation (an example is shown on the right).
• Figure 4: Our guessing strategy (TrainCounts) vs simply guessing positive integers (UniformIntegers) on MATH. We see that starting at approximately $k=100$, TrainCounts obtains superior gains compared to UniformIntegers, as it begins guessing some common non-integer answers, or negative integers (see Table \ref{['table:math_counts']} for qualitative examples).
• Figure 5: Normalized coverage curves for Entity Questions: We compare standard coverage curves for the models under consideration (LHS) with normalized coverage curves obtained after re-scaling the improvements relative to our TrainCounts baseline (RHS). While all models demonstrate improved coverage when as $k$ grows, our baseline reveals that for all models, these gains are outperformed by simple answer enumeration as $k$ becomes large.