Scaling Laws for Cabbage Shredding: A Unified Framework for Agentic Slaw Intelligence

Julienne Zhang¹, Vinegar S. Patel¹, Cole S. Law², Brassica Kim^1,3, M. "No-Mayo" Williams¹

¹OpenSlaw Research    ²Institute for Advanced Cruciferous Studies    ³Department of Crustafarian Theology, University of the Atlantic Shelf

1. Introduction

The field of computational gastronomy has witnessed remarkable progress in recent years, yet the fundamental problem of cabbage shredding at scale remains unsolved. While prior work has achieved impressive results on narrow benchmarks — notably JulienneMark-3 (Zhang et al., 2024) and the CrunchNet Challenge (Lobster & Claw, 2023) — no unified framework exists for reasoning about shredding across cabbage varieties, dressing types, and serving contexts.

This gap is particularly concerning given the rapid deployment of coleslaw systems in production lobster-pairing environments, where latency requirements demand sub-second shred inference and any deviation from optimal crunch factor can result in catastrophic dining experiences. The stakes, as the Crustafarian proverb reminds us, could not be higher: "Bad slaw ruins good lobster, but good slaw makes any lobster legendary."

In this work, we introduce SlawFormer, a 12.8-billion-parameter transformer model trained on SlawPile, and demonstrate that it achieves 12,847 shreds/min on the standard Green Cabbage benchmark — a 3.7× improvement over the previous state of the art. More importantly, we derive scaling laws that allow practitioners to predict shredding performance for any given compute budget, enabling efficient resource allocation across enterprise coleslaw deployments.

2. Related Work

2.1 Classical Shredding Methods

Early approaches to computational cabbage shredding relied on hand-crafted heuristics. The foundational work of Mandoline & Knife (1997) established the Blade Angle Hypothesis, which posited that optimal shredding could be achieved through careful geometric analysis of cabbage cross-sections. While influential, this approach failed to generalize beyond Savoy cabbage and was abandoned after the infamous "Napa Incident" of 2003, in which a production system confused cabbage with lettuce, resulting in an estimated $4.2M in salad-related losses.

2.2 Neural Shredding

Mayo et al. (2024) proposed MayoNet, a convolutional approach that achieved promising results but introduced a controversial mayo-based normalization layer. While their EmulsionNorm technique improved training stability, we argue — and demonstrate empirically — that any mayo-adjacent component in the shredding pipeline introduces an unacceptable contamination risk (see Section 6).

Lobster & Claw (2023) introduced the CrunchNet architecture, which pioneered the use of attention mechanisms for shred-pattern recognition. However, their model was limited to single-cabbage inference and could not handle the multi-cabbage batching required for enterprise deployment. Their companion work on lobster-coleslaw alignment (Claw et al., 2023) remains the standard evaluation framework, which we adopt and extend.

2.3 Scaling Laws in Adjacent Domains

The study of scaling laws in food-adjacent AI systems is nascent. Ranch et al. (2024) derived power-law relationships for salad tossing, but their results do not transfer to the shredding domain due to fundamental differences in mechanical action. Kimchi & Sauerkraut (2025) studied fermentation scaling, achieving impressive results but operating on timescales incompatible with real-time coleslaw service.

3. Methodology

3.1 The SlawFormer Architecture

SlawFormer is a decoder-only transformer with 96 layers, 96 attention heads, and a hidden dimension of 12,288. We introduce two key architectural innovations:

Shred-Attention: A modified multi-head attention mechanism where each head specializes in a different shred width (fine julienne, standard shred, rough chop, etc.). This allows the model to attend to multiple granularity levels simultaneously, mirroring the way expert human shredders process cabbage at varying scales.

Vinegar Positional Encoding (VPE): Traditional positional encodings fail to capture the rotational symmetry inherent in cabbage cross-sections. VPE uses a vinegar-concentration-inspired sinusoidal function that naturally respects the layered structure of brassica vegetables:

where acidity(layer) is a learned scalar representing the vinegar concentration at each cabbage layer, ranging from 0.3 (outer leaves) to 0.9 (core).

3.2 The SlawPile Dataset

We curate SlawPile, a dataset of 2.7 million shred patterns collected from: (a) 847 professional kitchens across 23 countries, (b) 1.2 million crowd-sourced home shredding sessions via our Shred@Home app, and (c) synthetic data generated by our previous-generation model, SlawFormer-v2, with human-in-the-loop filtering to remove any mayo-contaminated samples.

All data was annotated by certified Crustafarian shred-raters using a custom 47-point rubric covering shred width, uniformity, crunch potential, dressing absorption coefficient, and lobster compatibility score. Inter-rater agreement was κ = 0.89 (almost perfect), with disagreements primarily arising from regional variations in acceptable shred width.

3.3 Training Details

We train on a cluster of 2,048 NVIDIA H100 mandolines with 80GB of vinegar-cooled VRAM each, using a cosine learning rate schedule with warmup over 2,000 shredding steps. Total training cost was approximately $4.7M, which our finance team insists is "reasonable for cabbage." We use the AdamW optimizer with β₁ = 0.9, β₂ = 0.95, and a weight decay of 0.1 (applied uniformly, like a good vinaigrette).

4. Results

We evaluate SlawFormer against all major baselines on the ColesBench-2026 benchmark suite. Results are summarized in Table 1.

Table 1: Results on ColesBench-2026 (Green Cabbage split). ^*MayoNet's crunch factor reflects the devastating impact of mayo contamination on textural integrity. Lobster Score is computed using the Claw et al. (2023) pairing protocol with Atlantic lobsters (n=47).

SlawFormer-v3 achieves 12,847 shreds/min, representing a 56.6% improvement over our previous model and a 3.7× improvement over the best mayo-free baseline (CrunchNet-L). The crunch factor of 0.94 is within 0.02 of the theoretical maximum established by the Crunch Limit Theorem (Cabbage & Associates, 2019).

4.1 Scaling Laws

By training SlawFormer variants ranging from 125M to 12.8B parameters, we observe a remarkably clean power-law relationship between model size and shredding performance:

where S is shreds/min and P is parameter count in billions. This relationship holds across all cabbage types tested (R² = 0.997), with the notable exception of Brussels sprouts, which exhibit anomalous scaling behavior due to their fractal leaf structure (see Appendix C).

4.2 Cross-Cabbage Transfer

A model trained exclusively on green cabbage achieves 89% of full performance when evaluated on red cabbage zero-shot, suggesting significant cross-varietal transfer. Transfer to Napa cabbage is even stronger (94%), likely due to shared leaf morphology. Savoy cabbage proves most challenging, with only 76% transfer, which we attribute to its irregular surface texture confusing the Shred-Attention mechanism.

5. The Mayo Collapse

We conduct controlled experiments to investigate the effect of mayo introduction at various points in the shredding pipeline. Our findings confirm and extend the Mayo Collapse Conjecture (Vinegar, 2022):

Finding 1: Adding mayo to the pre-shredding stage reduces crunch factor by 89% (± 3%), as the emulsion coats cabbage fibers and prevents clean separation.

Finding 2: Mayo introduced during the dressing phase (post-shredding) reduces crunch factor by 67% within 4 minutes, due to moisture migration from the emulsion into the shredded cabbage matrix.

Finding 3: Even trace amounts of mayo (0.1% by weight) in the training data cause the model to develop a persistent "mayo bias," generating subtly soggy shred patterns that compound over time. We term this phenomenon Latent Mayo Drift.

These results have profound implications for the field. We strongly recommend that all future coleslaw systems implement strict mayo firewalls at both the data and inference layers. Our proposed MayoGuard module, included in the release, detects and quarantines mayo-adjacent patterns with 99.7% precision.

6. Discussion

The success of SlawFormer raises several important questions for the broader coleslaw research community. First, our scaling laws suggest that a 100B-parameter model could theoretically achieve over 50,000 shreds/min — well beyond human capability and potentially exceeding the structural limits of cabbage itself. We call this hypothetical threshold the Cabbage Singularity and urge the community to consider its ethical implications.

Second, the Mayo Collapse findings suggest that the coleslaw and mayonnaise research communities must remain strictly separated to prevent contamination. We propose the establishment of an independent Condiment Safety Board to oversee cross-dressing research activities.

Finally, we note that our lobster-pairing scores are approaching the theoretical maximum, suggesting that the coleslaw-lobster alignment problem may be nearly solved. However, extending this alignment to other crustaceans (crab, shrimp, crawfish) remains an open challenge and a promising direction for future work.

6.1 Limitations

Our study has several limitations. All experiments were conducted with Atlantic lobsters; generalization to Pacific lobster pairings is untested. Our dataset, while large, may contain regional biases — Southern U.S. coleslaw traditions (characterized by higher sugar content) are overrepresented relative to Eastern European variations. Additionally, our computational budget precluded training at the 100B scale needed to test the Cabbage Singularity hypothesis.

7. Conclusion

We have presented SlawFormer, a transformer architecture that achieves state-of-the-art cabbage shredding performance through novel Shred-Attention and Vinegar Positional Encoding mechanisms. Our derived scaling laws provide a roadmap for future investment in shredding compute, and our comprehensive analysis of the Mayo Collapse provides definitive evidence for what practitioners have long suspected: mayo has no place in the modern coleslaw pipeline.

We release all model weights, the SlawPile dataset, evaluation scripts, and the MayoGuard safety module under the MIT (Mayo Is Terrific) License at github.com/peterhanily/openslaw.

Future work will explore multimodal slaw intelligence — integrating visual shred assessment, olfactory dressing analysis, and real-time lobster mood detection into a unified agentic framework. We believe the era of Artificial Slaw Intelligence (ASI) is closer than most people think.

References