DoMINO: Composable Frameworks in Computation

• DoMINO is a diverse set of frameworks featuring composable algorithms and theoretical models across machine learning, simulation, tiling theory, denoising, and hardware design.
• Each framework employs methods like minimal sufficient representations, multi-scale iterative neural operators, and speculative decoding to enhance accuracy, speed, and efficiency.
• Applications span synthetic LLM data generation, CFD surrogate modeling, undecidability in tiling, blind zero-shot denoising, and compute-in-memory for DNNs.

DoMINO

DoMINO refers to a diverse set of algorithms, theoretical constructs, and architectures across computational science, machine learning, mathematical logic, and hardware systems, each leveraging the motif of composability or local-to-global inference. Notable DoMINO frameworks encompass data synthesis for LLMs via minimal sufficient representation, decomposable neural operators for surrogate physical simulation, speculative decoding architectures, undecidability phenomena in tiling theory, zero-shot denoising using combinatorial validation, and compute-in-memory (CIM) hardware for deep neural networks. This entry systematically presents leading DoMINO frameworks as introduced in recent arXiv literature.

1. Minimal Sufficient Representation for Domain-Specific Data Synthesis in LLMs

The DOMINO framework for domain-specific data synthesis enables LLMs to generate synthetic data aligned with implicitly defined domains, solely from a small pool of reference examples, without explicit natural language domain description or prompt engineering (Ye et al., 28 May 2026). Unlike deductive paradigms that rely on human-articulable rules, DOMINO employs an inductive, information-theoretic paradigm based on minimal sufficient representation.

Given $n$ reference samples $x^{(1)},\dots,x^{(n)}$ from a domain $D$ over space $\mathcal{X}$, DOMINO learns:

• Domain-level soft tokens $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$: shared embedding capturing all and only the recurring domain structure.
• Sample-level soft tokens $$S^{(i)} = [s^{(i)}_1, \dots, s^{(i)}_\ell] \in \mathbb{R}^{\ell\times d}$$: unique to each reference sample, absorbing idiosyncratic signal.

The joint objective comprises two terms:

• $$L_1(D^*) = -\frac{1}{n} \sum_{i=1}^n \log p_\theta(x^{(i)}|D^*)$$ (sufficiency)
• $$L_2(D^*, \{S^{(i)}\}) = -\frac{1}{n} \sum_{i=1}^n \log \frac{p_\theta(x^{(i)}|D^*, S^{(i)})}{\sum_{j=1}^n p_\theta(x^{(j)}|D^*, S^{(i)})}$$ (contrastive disentanglement)

$$\mathcal{L}(D^*, \{S^{(i)}\}) = L_1(D^*) + \lambda L_2(D^*, \{S^{(i)}\})$$

After optimization, only $D^*$ is retained for synthetic data generation. This induces a distribution $x^{(1)},\dots,x^{(n)}$0 with provably larger high-probability $x^{(1)},\dots,x^{(n)}$1-support than vanilla prompt tuning, according to the support expansion theorem: $x^{(1)},\dots,x^{(n)}$2 where $x^{(1)},\dots,x^{(n)}$3 is entropy and $x^{(1)},\dots,x^{(n)}$4 is the uniformity gap.

Empirical Results: On code generation benchmarks (e.g., Qwen2.5-Coder-7B-Instruct), fine-tuning on DOMINO-synthesized data increased Pass@1 accuracy by up to 4.63% relative to instruction-tuned baselines; Instruct-Following accuracy rose 3.48% over the base model. t-SNE analyses indicated enhanced distributional coverage and diversity (Ye et al., 28 May 2026).

Significance: DOMINO introduces an inductive, support-expanding synthetic data pipeline robust to implicit, non-articulable domains and provides theoretical guarantees absent in prior methods.

2. Decomposable Multi-scale Iterative Neural Operator for Physical Simulation Surrogates

DoMINO, the Decomposable Multi-scale Iterative Neural Operator, is a machine learning surrogate model for large-scale engineering simulations, such as computational fluid dynamics (CFD) (Ranade et al., 23 Jan 2025). It constructs flow-field predictors directly on point clouds, avoiding mesh downsampling and maintaining scalability.

Architecture:

• The computational domain $x^{(1)},\dots,x^{(n)}$5 is partitioned into overlapping patches $x^{(1)},\dots,x^{(n)}$6, each with local neural operators $x^{(1)},\dots,x^{(n)}$7.
• The global solution is refined via fixed-point–style iterations: $x^{(1)},\dots,x^{(n)}$8, with $x^{(1)},\dots,x^{(n)}$9 assembled by partition-of-unity.
• Multi-scale geometry encoding is achieved by ball-query point-convolutions of various radii, mapping the surface point cloud into structured feature grids.
• CNN blocks propagate local to global geometry, allowing final local geometry descriptors $D$0 to be extracted for prediction at each query point.

Training and Validation:

• Loss: sums of (area-weighted) mean squared errors for both volume and surface fields, plus $D$1 regularization.
• Tested on the DrivAerML dataset (500 car morphs, 150M+ cells), achieving mean relative $D$2 errors $D$30.15–0.2 for surface and $D$40.2–0.5 for volume fields. Inference time is under 1 s per geometry, representing a $D$5–$D$6 speed-up over conventional CFD while retaining high $D$7 accuracy for aerodynamic quantities (Ranade et al., 23 Jan 2025).

Comparative Analysis:

• DoMINO attains lower or comparable errors than MeshGraphNet, Point-DeepONet, or Fourier Neural Operators, but operates on realistic unstructured 3D domains and delivers both surface and volume predictions.

Limitations and Directions:

• Does not enforce incompressibility or exact PDE residuals. Higher transverse velocity errors noted; hybrid physics-informed training and adaptive multiresolution are proposed improvements.

3. Decoupling Causal Modeling from Autoregressive Drafting in Speculative Decoding

The Domino speculative decoding framework addresses the cost-quality trade-off in LLM inference acceleration (Huang et al., 28 May 2026). In speculative decoding, a cheap draft model predicts a block of future tokens, which the target model then verifies.

Domino Architecture:

• Parallel Draft Backbone: Generates block-parallel hidden states $D$8 using context $D$9 from the verified prefix.
• Domino Head: For $\mathcal{X}$0, a GRU encodes the prefix-dependent causal state $\mathcal{X}$1, outputting a low-rank logit correction $\mathcal{X}$2 to refine the draft logits, modeling intra-block dependencies efficiently: $\mathcal{X}$3 where $\mathcal{X}$4.
• Teacher-forced and curriculum-annealed training first fortify the parallel backbone, then transition to the full Domino head, avoiding shortcutting and collapse.

Complexity: The total per-block cost is $\mathcal{X}$5, where the GRU and correction are orders of magnitude cheaper than repeated full transformer decoding.

Results:

• On Qwen3-8B with block size $\mathcal{X}$6, Domino achieved up to $\mathcal{X}$7 end-to-end speedup (Transformers backend) and $\mathcal{X}$8 throughput gain (SGLang concurrency), exceeding alternatives such as DFlash and EAGLE-3 (Huang et al., 28 May 2026).

Limitations: Domino is inference-focused; training cost is unaffected. Optimizations are hardware-specific (A100 GPUs via Triton). Block size is fixed; dynamic and adaptive block budgeting are proposed extensions.

4. Domino Problem and Undecidability on Rhombus Subshifts

The Domino problem generalizes the undecidability of Wang tile plane tilings to tilings by rhombus-shaped tiles and arbitrary subshifts $\mathcal{X}$9 (Menibus et al., 2023). The $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$0-Domino problem asks: given a finite tileset $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$1 (coloured rhombi) and a subshift $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$2, does an infinite $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$3-tiling $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$4 exist with $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$5?

Main Results:

• For any non-empty subshift $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$6, the $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$7-Domino problem is $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$8-hard.
• If $D^* = [d_1,\dots,d_k] \in \mathbb{R}^{k\times d}$9 is effective (forbidden patterns list is computable), then $$S^{(i)} = [s^{(i)}_1, \dots, s^{(i)}_\ell] \in \mathbb{R}^{\ell\times d}$$0-Domino is $$S^{(i)} = [s^{(i)}_1, \dots, s^{(i)}_\ell] \in \mathbb{R}^{\ell\times d}$$1-complete.
• Proof leverages reductions from the classical Wang Domino problem, using recurrent shape gadgets to encode square-tiling behavior in rhombic domains. Penrose subshifts and other aperiodic tilings inherit this undecidability (Menibus et al., 2023).

Implications: No geometric subshift of rhombus tilings admits a decidable Domino problem. This situates these problems firmly at the first level of the arithmetic hierarchy, regardless of local complexity restrictions.

5. Blind Zero-Shot Denoising via Domino Tilings

DoMINO ("Domino Denoise") is a blind zero-shot denoising framework combining a semi blind-spot convolutional network and a combinatorial "Pixel Domino Tiling" validation strategy (Lequyer et al., 2022).

Algorithmic Pipeline:

• Network: 12-layer partial-convolutional network with ReLU activations, masking 20% of inputs (blind spot) and leaking 0.1% of unmasked pixels for gradient update.
• Training: Binary cross-entropy loss over masked pixels; single-image zero-shot regime.
• Validation Stopping: Pixel Domino Tiling partitions pixels into matched pairs using minimum-cost perfect matchings (computed via the Jonker–Volgenant Hungarian-type algorithm). Validation PSNR is measured by predicting one half of the tiling from the other. Early stopping is triggered once rolling average PSNR ceases to increase.

Performance:

• Achieves an average PSNR improvement of 0.28 dB and a 3× speedup over Self2Self on Set12 (Gaussian noise), and PSNR = 23.48 dB, SSIM = 0.68 on real microscopy (better than all other blind zero-shot methods) (Lequyer et al., 2022).

Broader Applicability: The domino-tiling criterion is architecture-agnostic and usable as a general-purpose zero-shot validation or early-stopping scheme.

6. Tailored Computing-in-Memory (CIM) Architecture for DNNs

The Domino CIM processor is a two-dimensional mesh architecture for deep neural networks, designed to overcome memory bottlenecks by minimizing data movement through local computation (Zhou et al., 2021).

Key Components:

• Each tile comprises a Rifm router (input feature map), processing element (1T1R ReRAM crossbar, integrators, SAR-ADC), and Rofm router (output/partial sums).
• Dataflows exploit both intra-memory MAC execution and inter-memory (router-based) on-the-move summation.
• Distributed instruction scheduling: Tiles maintain local static schedule tables, increment counters, and execute convolution, pooling, or FC operations via localized logic.

Results: Achieved 1.15–9.49× increased power efficiency (normalized to 8-bit, 1 V, 45 nm—up to 25.92 TOPS/W), and 1.57–12.96× higher throughput over state-of-the-art CIM accelerators across several benchmark CNN models (Zhou et al., 2021).

Trade-offs and Extensions: Crossbar size, PE utilization, block mapping strategy, and local instruction scheduling offer design flexibility. Limitations include static scheduling, restrictions in supporting highly dynamic control, and analog variability in memory elements.

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References:

• "Domain-Specific Data Synthesis for LLMs via Minimal Sufficient Representation Learning" (Ye et al., 28 May 2026)
• "DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulations" (Ranade et al., 23 Jan 2025)
• "Domino: Decoupling Causal Modeling from Autoregressive Drafting in Speculative Decoding" (Huang et al., 28 May 2026)
• "The Domino problem is undecidable on every rhombus subshift" (Menibus et al., 2023)
• "Domino Denoise: An Accurate Blind Zero-Shot Denoiser using Domino Tilings" (Lequyer et al., 2022)
• "Domino: A Tailored Network-on-Chip Architecture to Enable Highly Localized Inter- and Intra-Memory DNN Computing" (Zhou et al., 2021)