AI reasoning gaps live in the data mix. Alignment can't bridge them.

A compensatory alignment pass, a post-training step meant to sharpen behavior on targeted capabilities, lifted 116 of 120 mid-training cells by an average of 4.32 percentage points. It then closed zero of 240 capability-gap pairs at the 5% threshold and only 30 of 240 at a 10% ratio. A random-data permutation null would have closed 13.8 ± 3.3 pairs at the 5% threshold and 77.9 ± 8.5 at the 10% ratio (P<0.001). The numbers come from a new controlled study of the under-discussed middle of the AI training pipeline, the stage where a model's per-domain data mix is set. The finding, from a preprint on arXiv, is that data choices made at this stage set per-domain ceilings that later training cannot repair.

The stage in question is called mid-training. It sits between pretraining, where a model absorbs the bulk of its world knowledge, and post-training, where a model is shaped into a useful assistant. Mid-training is where a model's per-domain data composition is typically set. In practice that decision is usually made by data availability: if there is more code, the model sees more code; if there is more math, it sees more math. Preprint 2609.09081 asks whether that allocation matters in a measurable way, and whether later training can compensate for it.

The test bed is KOR-Bench, a public logical-reasoning benchmark built around five domains that were designed not to share rules. The base model is Qwen3-8B-Base, with a 4-billion-parameter replication. The team swept 30 different allocations of the five domains across the data-mix simplex, the triangle of all possible five-way mixes, with five seeds per allocation and six configurations withheld from the fit. The evaluation substrate is, by construction, scoped to logical reasoning. The paper does not claim the result generalizes to code, math, or general text.

The first finding: every reasoning domain has an interior optimum in a moderate band. A calibrated permutation test for quadratic interiority gives P≈0.010. Fitted curves on the 8-billion-parameter runs put the per-domain peaks between 9.9% and 35.1% of the mid-training mix. The shape of the curves reproduces in the 4-billion-parameter replication, but the exact peak location does not. More is not better here. A moderate share of any one domain performs best, not the maximum share.

On the 120 mid-training cells, the authors ran a fixed-budget compensatory pass using supervised fine-tuning, the post-training step meant to sharpen a model's behavior on targeted capabilities. SFT raised 116 of 120 cells, by a mean of 4.32 percentage points. The team then asked, cell-by-cell, whether any pair of cells whose mid-training-only accuracies differed by more than a threshold had been pulled inside the threshold. At a 5% threshold, the answer was zero out of 240 pairs. At a 10% ratio, it was 30 out of 240. A random-data permutation null would have bridged 13.8 ± 3.3 pairs at the 5% threshold and 77.9 ± 8.5 at the 10% ratio (P<0.001). The SFT pass did not just fail to close the gaps; it closed fewer than chance.

The team ran an equal-budget uniform control to rule out the obvious objection, that the SFT pass simply lacked the budget to do real work. The control behaved almost identically. The gaps, the authors argue, are structural and set during mid-training, not an artifact of how much SFT the team chose to spend.

Zero coverage of a domain collapses mid-training-only accuracy. That sounds like a clean win for the coverage story, but the team ran a FineWeb-Edu-only control to test what "zero" actually means. FineWeb-Edu is a generic pretraining corpus of educational web text, used here as a placeholder for whatever else a model absorbs while it is supposedly seeing zero of a target domain. The collapse appears to be commingled with generic pretraining drift, not purely a coverage effect. The paper is honest about that. Coverage matters, but the experiment cannot fully separate coverage from drift.

The paper also reports an exploratory allocation it calls θ, which attained the largest full-pipeline gain at +4.36 percentage points, against +0.80 and +0.64 for the controls. The result is marginal under a Welch test, and the authors hedge it accordingly. θ is best read as a direction worth investigating, not a recipe.

For any team that decides how to mix training data, the operational implication is stark: per-domain ceilings are set in the under-named middle of the pipeline, and post-training alignment, the layer most public discussion points to when a model gets something wrong, can lift cells but cannot close the gaps that matter. The paper's reference basis is narrow: a single base-model family, a single logical-reasoning benchmark, and a controlled sweep that does not extend to code, math, or production mid-training mixtures. The negation lands, but it lands inside those bounds. The next test will be whether the same gap-bridging failure shows up on a held-out domain outside KOR-Bench.