Asher Labovich

Asher Labovich, Benjamin Bradley, Vanessa Alexander et al.

Encoder-decoder models offer substantial inference-time savings over decoder-only models, but their pretraining objectives suffer from sparse supervision and dynamic sequence lengths, keeping them out of practice at scale. We propose block-based double decoders, a novel transformer architecture that utilizes doubly-causal block-based attention masks to train with full loss supervision and static sequence packing, combining decoder-only training efficiency with encoder-decoder inference efficiency. In scaling law experiments, block-based double decoders strongly outperform encoder-decoders and closely track decoder-only models across scales. At inference time, they cut KV-cache memory and per-token compute by at least 2/3 without sacrificing prefill caching or other existing inference optimizations available to decoder-only models.

Asher Labovich

Looped transformers promise test-time compute scaling by spending more iterations on harder problems, but it remains unclear which architectural choices let them extrapolate to harder problems at test time rather than memorize training-specific solutions. We introduce a fixed-point based framework for analyzing looped architectures along three axes of stability -- reachability, input-dependence, and geometry -- and use it to characterize when fixed-point iteration yields meaningful predictions. Theoretically, we prove that looped networks without recall have countable fixed points and cannot achieve strong input-dependence at any spectral regime, while recall combined with outer normalization reliably produces a regime in which fixed points are simultaneously reachable, locally smooth in the input, and supported by stable backpropagation. Empirically, we train single-layer looped transformers on chess, sudoku, and prefix-sums and find that downstream performance tracks the framework's predictions across tasks and architectural configurations. We additionally introduce internal recall, a novel recall placement variant, and show that it becomes competitive with -- and on sudoku, substantially better than -- standard recall placement once outer normalization is applied.

Asher Labovich

Modern Gradient Boosted Decision Trees (GBDTs) accelerate split finding with histogram-based binning, which reduces complexity from $O(N\log N)$ to $O(N)$ by aggregating gradients into fixed-size bins. However, the predominant quantile binning strategy - designed to distribute data points evenly among bins -- may overlook critical boundary values that could enhance predictive performance. In this work, we consider a novel approach that replaces quantile binning with a $k$-means discretizer initialized with quantile bins, and justify the swap with a proof showing how, for any $L$-Lipschitz function, k-means maximizes the worst-case explained variance of Y obtained when treating all values in a given bin as equivalent. We test this swap against quantile and uniform binning on 33 OpenML datasets plus synthetics that control for modality, skew, and bin budget. Across 18 regression datasets, k-means shows no statistically significant losses at the 5% level and wins in three cases-most strikingly a 55% MSE drop on one particularly skewed dataset-even though k-means' mean reciprocal rank (MRR) is slightly lower (0.65 vs 0.72). On the 15 classification datasets the two methods are statistically tied (MRR 0.70 vs 0.68) with gaps $\leq$0.2 pp. Synthetic experiments confirm consistently large MSE gains - typically >20% and rising to 90% as outlier magnitude increases or bin budget drops. We find that k-means keeps error on par with exhaustive (no-binning) splitting when extra cuts add little value, yet still recovers key split points that quantile overlooks. As such, we advocate for a built-in bin_method=k-means flag, especially in regression tasks and in tight-budget settings such as the 32-64-bin GPU regime - because it is a "safe default" with large upside, yet adds only a one-off, cacheable overhead ($\approx$ 3.5s per feature to bin 10M rows on one Apple M1 thread).