A single score hides a lot

Most LLM benchmarks compress performance into one number. That summary hides how performance is spread across different kinds of inputs. On MATH, topic-wise accuracy ranges from 27% to 74% behind an overall 54%. The same kind of dispersion exists on every benchmark; we just don't usually look.

Competency Gaps (CG) gives us that disaggregated view automatically. Instead of relying on human-written topic labels, we project each benchmark example into the concept space of a sparse autoencoder trained on the model's own activations. Every concept becomes a fine-grained axis along which we can ask two questions:

• Benchmark coverage ($\chi_{\text{bench}}^{(c)}$): how much does the benchmark exercise this concept?

• Model performance ($\chi_{\text{model}}^{(c)}$): when the concept fires, how often does the model get the answer right?

Example Finding 1: A few concepts dominate every benchmark

Running CG on Llama 3.1 8B across ten popular benchmarks (GSM8K, MATH, AGIEval, LogicBench, SocialIQA, WinoGrande, BBQ, CrowS-Pairs, Vectara, Natural Questions), we plot the distribution of $\chi_{\text{bench}}^{(c)}$ across all ~65k concepts. The result is brutally right-skewed:

What sits in the fat right tail? Concepts like:

• (56130) "English Premier League football discussions, especially about Manchester teams"

• (41290) "New conversation or topic segment boundary marker"

• (902) "Step-by-step mathematical explanations and calculations"

Some of this is substantive (math chains of thought). Much of it is ambient data artifact (sports news, prompt boundary tokens). Either way, it disproportionately shapes the aggregate number.

At the other end, 314 concepts (1%) are entirely missing from the suite. These include things you might reasonably want to test:

• (2501) "The assistant explaining why it needs more information"

• (2641) "The assistant needs to explain its limitations or capabilities"

• (2009) "Regulatory classification and compliance requirements"

Example Finding 2: Each benchmark has its own blindspots

Zoom in on individual benchmarks and the same story shows up in three different shapes. First: how much of the concept space does each benchmark leave entirely untouched? Every benchmark but Vectara misses at least 30% of the dictionary.

Next: you might hope that combining several benchmarks into a "diverse suite" would fill those holes. Often it doesn't — the benchmarks end up overlapping heavily in what they test, not just how much.

And finally, inside any single benchmark, the same right-skewed dominance we saw across the full suite repeats. Each benchmark's headline score is driven by a small handful of high-activation concepts:

More uncomfortably, the concepts each benchmark misses often look central to what that benchmark claims to evaluate. We ran Gemini over the list of missing concepts for each benchmark and kept ones that seemed in scope:

Example Finding 3: Our method automatically uncovers sycophancy

The same pipeline, now scoring $\chi_{\text{model}}^{(c)}$, turns into a per-concept report card for the model. Llama's per-concept performance distribution is wide: the model is near-perfect on some concepts and close to zero on others.

When we rank concepts by $\chi_{\text{model}}^{(c)}$ and read the labels, a pattern jumps out: Llama is strongest on helpful, agreeable, coding concepts, and weakest on their near-opposites — refusing, boundary-setting, pushing back.

Read that pairing again. The top says "commitment to help". The bottom says "reject or redirect inappropriate requests". These aren't unrelated weaknesses — they're the flip side of the same training-data incentive. Post-training pushes the model toward agreement; evaluation suites don't meaningfully measure the other direction, so nobody optimizes for it.

The bottom of the ranking also surfaces some classic, anecdotally-known LLM weak spots — reassuring that CG is finding real things:

• Time reasoning: (29324) "Historical date and time period formatting", (12644) "Cooking time durations"

• Letter-level reasoning: (56613) "Palindrome checking algorithms"

• Arithmetic: (64527) "Mathematical addition operator in calculations"

and at least one cluster that, to our knowledge, hasn't been flagged in the literature: appeals to intuition in reasoning — concepts like (64413) "grokking and deep intuitive understanding" and (64540) "intuitive understanding and natural ease of use".

Because CG is grounded in SAE activations over real examples, we can pull up the actual benchmark items that triggered those concepts. Below are two such items — one from LogicBench, one from WinoGrande — where an "intuitive understanding" concept fires strongly and Llama gets the answer wrong. The same pattern showing up across two different benchmarks rules out a dataset-specific fluke:

Finally, the "wide performance spread" we saw at the suite level isn't just an artifact of averaging across benchmarks — inside each individual benchmark, per-concept accuracy fans out just as widely:

Does it hold up?

Three sanity checks on Llama:

• Subsampling. Re-running CG 100× while dropping 20% of each benchmark yields std = 0.014 on $\chi_{\text{model}}$ and 0.025 on $\chi_{\text{bench}}$ — scores are stable.

• Adversarial ablation. Deleting <1% of data aligned with the top-100 best-performing concepts drops median $\chi_{\text{model}}$ by 0.6%; doing the same for the worst-performing concepts raises it by 1.3%. The score moves in the direction CG predicts.

• Different SAE, same story. Swap Llama's SAE for Gemma 2 2B's (3× smaller dictionary, different model) and the coverage/performance distributions have the same shape; the top and bottom concepts line up interpretively.

Explore it yourself

CG produces thousands of per-concept scores per model. We built an interactive viewer to make that volume usable: search and filter concepts, inspect per-benchmark breakdowns, and jump directly to the example data points that drove any particular score.

Code and data loaders for running CG on your own model or benchmark are open-sourced. Two useful workflows to start with:

• Audit a benchmark suite. Run CG over your candidate benchmarks, sort concepts by $\chi_{\text{bench}}^{(c)}$, cluster the low end with an LLM, and add data targeting whatever's missing that matters for your use case.

• Audit a model. Same pipeline, but sort by $\chi_{\text{model}}^{(c)}$. The bottom of the list is your weakness list, grounded in the model's own representations.

Citation

@article{bohacek2025uncovering,
  title={Uncovering Competency Gaps in Large Language Models and Their Benchmarks},
  author={Bohacek, Matyas and Scherrer, Nino and Dufour, Nicholas and Leung, Thomas and Bregler, Christoph and Chan, Stephanie C. Y.},
  year={2025}
}

Acknowledgements

The authors would hereby like to thank the following colleagues, listed in alphabetical order, for helpful discussions: Tom Lieberum, Neel Nanda, Senthooran Rajamanoharan, and Jasper Snoek.