ReST Algorithm: Diverse Domain Innovations

• ReST algorithm refers to a suite of diverse computational methods, each tailored for efficiency, accuracy, and robustness across different domains.
• Its implementations span from jet substructure analysis in collider physics and distributed evolutionary computation to robust sparse recovery techniques.
• REST also enhances program verification, video action recognition, accelerated language model decoding, and robust DNN training with empirically validated gains.

The term "ReST algorithm" refers to a diverse set of computational methods, each independently named "ReST" or "REST" in the literature, spanning areas such as jet substructure in collider physics, distributed evolutionary computation, robust neural sparse recovery, program verification via term rewriting, generative action recognition, accelerated LLM decoding, robust DNN training, and, most recently, reinforcement learning with LLMs for code reasoning. Each instance exploits unique domain-specific technical strategies but the unifying theme is algorithmic innovation aimed at efficiency, accuracy, and robustness in large-scale or challenging computational scenarios.

1. Rest Frame Subjet Algorithm for Jet Physics

The Rest Frame Subjet Algorithm was introduced to address the identification of hadronic decays from highly boosted color singlet particles (such as Higgs, W, or Z bosons) at colliders (Kim, 2010). The core strategy involves:

• Rest Frame Boosting and Clustering: The fat jet, reconstructed in the laboratory frame using SISCone, is boosted to its own rest frame. This is achieved via Lorentz transformation so that its four-momentum is $(m^{\text{jet}}_\text{inv}, 0,0,0)$. In this frame, decay substructure is enhanced: decay into $N$ partons naturally exhibits $N$ hard, well-isolated subjets.
• Subjet Reclustering: Constituents are re-clustered in the rest frame using SISCone with a smaller radius $R_\text{subjet}$ and overlap threshold, then reordered by energy to select the $N$ hardest subjets.
• N-subjettiness ($\tau_N^j$) Observable: Define

$$\tau_N^j = \frac{2}{(m_\text{inv}^\text{jet})^2} \sum_{k \in J} \min \{q_1 \cdot p_k, q_2 \cdot p_k, ..., q_N \cdot p_k \}$$

where $p_k$ are constituent four-momenta in the lab frame and $q_i$ are the $N$ subjet momenta.

Signal jets from $N$-prong hadronic decays produce low $\tau_N^j$ values, sharply discriminating them from QCD jets—especially effective with additional b-tagging for $H \to b\bar{b}$. In LHC analyses (e.g., $pp \to HZ, HW$), combining $\tau_2^j < 0.08$ and b-tagging yields a signal statistical significance of about $2\sigma$ at $\mathcal{L} \sim 30\,\text{fb}^{-1}$, $14\,\text{TeV}$. IR and collinear safety is rigorously preserved via SISCone and construction of $\tau_N^j$.

2. REST in Distributed Evolutionary Computation

REST, as Representational State Transfer, is utilized for orchestrating distributed evolutionary algorithms where client nodes evaluate the fitness of evolved individuals (Castillo et al., 2011). The key features include:

• REST Protocol as Middleware: RESTful endpoints (over HTTP, built in Perl/Dancer) mediate between a central EA "master" and distributed "slaves." Slaves download the fitness function, evaluate individuals (e.g., MLP architectures), and submit fitness results back to the master.
• Parallelization via Master–Slave Model: The master manages population evolution; slaves perform the compute-intensive evaluation—most notably, MLP training and validation with varying hidden layer size, weight initializations, and learning rates.
• Scalability and Speedup: For the Glass dataset, speedup from 1215s to 424s is observed with four slaves—demonstrating non-linear but substantial parallel efficiency.

REST's protocol-agnostic nature suggests general applicability to distributed metaheuristics and scientific computing bottlenecks dominated by expensive objective evaluations.

3. Robust lEarned Shrinkage-Thresholding (REST) for Sparse Recovery

REST (Robust lEarned Shrinkage-Thresholding) is an algorithm unrolling technique designed to solve sparse inverse problems under sample-dependent model mismatch (Pu et al., 2021).

• Robust Objective and Unrolling: Contrasted with standard LISTA, REST optimizes

$$\min_x \frac{\|y - Ax\|_2^2}{1+\|x\|_2^2} + \lambda \|x\|_1,$$

where $y = (A+E)x + e$ and $E$ reflects unknown measurement operator perturbation. REST layers are constructed from proximal gradient descent of this robustified cost, with each iteration including normalization by $1+\|x\|_2^2$ and additional learnable matrices.

• Superior Robustness: Results on compressive sensing and SAR imaging show REST achieves lower MSEs and better robustness to operator mismatch compared to LISTA, BP, robust ISTA, and MU-GAMP—particularly under sample-wise variable $E$.

REST's normalization and learnable operator matrices are necessary architectural elements conferring sample-wise adaptability in practical inverse problems.

4. REST for Program Verification: Online Term Rewriting

REST is also a flexible, termination-safe, online term rewriting framework that integrates with program verification environments (Grannan et al., 2022).

• Termination via Dynamic Ordering: REST explores rewrite paths and refines term ordering constraints at each step, ensuring that every path is oriented by an instance from a family of thin, well-quasi-orderings (not just strict simplification orderings).
• RPQO (Recursive Path Quasi-Ordering): Permits associative/commutative equations to be applied in both directions, enabling cycles such as $X + Y \approx Y + X$ without global orientation conflicts.
• Integration with Liquid Haskell: Automates lemma application in refinement type proofs, interleaving rewriting with logical evaluation, and guarantees termination (mitigating E-matching loops common in SMT solvers).

REST, via RPQO and online ordering constraint algebra, provides both flexibility and theoretical safety, reducing manual effort in proof construction while avoiding divergence.

5. REST in Generative Action Recognition

REST (REtrieve & Self-Train) is a generative, open-world video/action recognition framework (Bulat et al., 2022).

• Pseudo-Caption Self-Training: Adapt BLIP (a vision-LLM) to video via a temporal adapter (3D depth-wise convolution across frames) and generate action-specific pseudo-captions via prompting; use standard LLMing loss for fine-tuning.
• CLIP-Based Caption Retrieval: Augment the set of training captions by retrieving diverse pseudo-captions using CLIP similarity in both video–video and video–text spaces, thereby mitigating confirmation bias from self-generated captions.
• Label-Free Open-World Recognition: REST avoids ground-truth action labels, enabling scalable training on unannotated video. Evaluation leverages a CLIP-based Text Accuracy Metric mapping generated captions to action class names.

Compared to direct label fine-tuning (which incurs severe overfitting), REST achieves competitive zero-shot action recognition, with practical advantages in interpretability and scalability.

6. REST for Accelerated LLM Decoding

REST (Retrieval-Based Speculative Decoding) accelerates LLM inference by substituting the draft model in speculative decoding with non-parametric retrieval (He et al., 2023).

• Exact-Match Retrieval and Trie Construction: For a given context, retrieve longest-suffix-matching continuations from a pre-built datastore (suffix arrays over pretrain/fine-tune corpora). Build a Trie over continuations; select high-frequency candidate sequences as "draft tokens."
• Plug-and-Play Acceleration: The draft tokens are jointly verified in parallel with a tree attention mask in the large LM—no additional model training is required.
• Empirical Performance: Achieves speedups of $1.62\times$–$2.36\times$ on 7B/13B code and text LMs on benchmarks like HumanEval and MT-Bench, with token latency drops from $27.89$ to $11.82$ ms/token in representative settings.

This approach is domain-adaptable (via datastore construction) and reduces LLM inference cost without any retraining overhead.

7. REST for Group-Robust Sparse Training of DNNs

REST (Reweighted Sparse Training) addresses poor minority-group generalization due to bias-aligned spurious correlations in overparameterized DNNs (Zhao et al., 2023).

• Sparse Training with Group Reweighting: Trains a subnetwork $f(x;\theta_s)$ with a fixed sparsity constraint rather than post-hoc pruning. Group weights $\beta_{P^e}$ upweight loss from bias-conflicting or minority groups, directly in the loss function.
• Dynamic Prune-and-Grow Paradigm: Iterative parameter pruning by magnitude and regrowth maintains fixed sparsity; sparse training from scratch is found to be more robust than dense-to-sparse pruning.
• Empirical Findings: On datasets such as Colored MNIST, CIFAR-10-C, and BFFHQ, REST achieves up to $28\%$ accuracy improvement for $0.5\%$ bias-conflicting samples, with only $2\%$ of original FLOPs and $1.6\%$ inference computation (e.g., 0.056M/11.17M parameters for ResNet-18).

REST demonstrates that carefully reweighted sparse training can deliver robust generalization and substantial efficiency gains across diverse groups.

8. REST for LLM RL – Code Reasoning

ReST-RL, combining an improved Reinforced Self-Training (ReST) data-generating paradigm with Group Relative Policy Optimization (GRPO) and a test-time value model Monte Carlo Tree Search (VM-MCTS), advances code reasoning with LLMs (Zhoubian et al., 27 Aug 2025).

• Optimized ReST Data Assembly: Multiple candidate solution traces are generated for each prompt; traces with high reward variance and passing thresholded criteria are decomposed to extract informative partial traces, sampled for training data. Low-variance prompts are filtered out.
• Integration with GRPO: The constructed examples—combining questions and partial solution traces—are used in GRPO updates, which are based on group-level advantage estimation and clipped policy ratio/KL penalties. Increased reward variance directly improves RL signal effectiveness.
• Test-Time Decoding (VM-MCTS): A value model (VM), trained via MCTS roll-outs, predicts the expected reward for each partial state. Decoding uses VM-guided MCTS with UCT-style exploration:

$$S' = \arg\max [v_{S'} + c \sqrt{(\ln N_S + 1)/(N_{S'} + \epsilon)}]$$

where $v_{S'}$ is the VM's predicted value for state $S'$.

• Empirical Improvements: On coding benchmarks (HumanEval, BigCodeBench, APPS), ReST-RL achieves $6$–$9\%$ average pass@1 improvement over both naive GRPO and other RL/decoding baselines.

The methodology provides significant advances in reward signal richness for policy optimization and at test time yields more accurate, verifiable code reasoning through value model-backed search.

9. Cross-Domain Patterns and Nomenclature

Across these instances, "REST" or "ReST" is not a unified method but rather an acronym variably invoking physical rest frames (physics), Representational State Transfer (distributed computation protocols), robust algorithm unrolling (sparse recovery), reweighted sparse training (group robustness), reinforcement learning from self-training (LLMs), retrieval-enhanced speculative decoding (LLM efficiency), and retrieval-based self-training (VLMs/video). This diversity underscores the importance of explicit context when referencing a "REST" or "ReST" algorithm in the literature.

The consistent traits are principled algorithmic modifications, often featuring self-supervision, retrieval, or decoupled computation, yielding gains in statistical efficiency, resource utilization, or generalization. For each domain, empirical validation is performed on representative benchmarks with relevant metrics (statistical significance at LHC, accuracy/worst-group accuracy in DNNs, speedup in LMs, pass rates in code reasoning, etc.), with source code frequently provided for reproducibility.

10. Summary Table

Domain	REST / ReST Algorithm Purpose	Notable Metric / Finding
High-energy physics	Jet substructure, signal discrimination	$2\sigma$ at $30$ fb$^{-1}$, $14$ TeV (Kim, 2010)
Distributed computation	Parallelize EA fitness evaluation	Non-linear speedup (Castillo et al., 2011)
Sparse recovery	Robustness to model mismatch via normalization + unfolding	Achieves lower MSE under mismatch (Pu et al., 2021)
Program verification	Dynamic, terminating term rewriting with RPQO	Outperforms static orderings; terminates when SMT E-matching fails (Grannan et al., 2022)
Video action recognition	Generative open-vocab pseudo-captioning	Zero-shot accuracy competitive with CLIP-based models (Bulat et al., 2022)
LLM decoding	Datastore-based speculative decoding	$1.62\times$–$2.36\times$ speedup (He et al., 2023)
Group-robust DNNs	Reweighted in-situ sparse training	$28\%$ improvement on bias-conflicting samples (Zhao et al., 2023)
LLM code reasoning	RL with variance-boosted self-training and value-model MCTS	$6$–$9\%$ pass@1 gain over RL baselines (Zhoubian et al., 27 Aug 2025)

Each REST/ReST variant is independently motivated by the demands of its specific field but represents an exemplar of tailored algorithmic design for scalable, robust, or interpretable AI and computational science.