Llemma: NLP, Math & Robotics Insights

• Llemma is a multifaceted term covering canonical lemmatization in NLP, mathematical language models for reasoning, and robotics benchmarks for multi-robot manipulation.
• Neural architectures, including dual-encoder setups and instruction-tuned LLMs, achieve high accuracy and cross-lingual generalization in lemmatization.
• Robotics applications under the LEMMA benchmark demonstrate modular planning and expert demonstrations while exposing challenges in ambiguous instructions and low-level control.

Llemma encompasses multiple meanings in contemporary computational linguistics and machine learning. It principally refers to the mathematical notion of a lemma (the canonical dictionary form of a word), the process of lemmatization (mapping surface forms to lemmas), specialized neural models for lemmatization, and—more recently—open-access LLMs for mathematical reasoning named “Llemma.” It also appears as an acronym in robotics: LEMMA (Learning Language-Conditioned Multi-Robot Manipulation). This article provides a comprehensive survey of technical definitions, key methodologies, state-of-the-art results, and emergent research areas.

1. Mathematical and Linguistic Definitions

Within NLP, a lemma is defined as the canonical dictionary form of a word, capturing all its inflectional variants. Lemmatization is the mapping function:

$f : \text{surface form} \to \text{lemma}$

with context-sensitive extensions $f:(V^n, C)\to L^n$ for token sequences in sentential context (Toporkov et al., 8 Oct 2025). This mapping is essential for indexing, semantic equivalence detection, and reducing sparsity in IR, MT, and summarization (El-Shishtawy et al., 2014, El-Shishtawy et al., 2012).

In a mathematical context, “Lemma” denotes a subsidiary proposition used in the proof of larger theorems. However, recent works have appropriated the term to designate pre-trained LLMs (e.g., “Llemma: An Open LLM for Mathematics” (Azerbayev et al., 2023)) and mathematical object recovery techniques (e.g., token subspace topology (Robinson et al., 19 Mar 2025)).

2. Neural Architectures for Lemmatization

Sequence-to-sequence neural models represent the dominant paradigm for lemmatization across languages (Milintsevich et al., 2021). The base system comprises:

• An encoder (typically BiLSTM) ingesting surface forms, POS tags, and morphological features.
• A decoder LSTM, which generates the lemma in character-by-character fashion using attention over the encoder states.

Enhancements include dual-encoder architectures, where an auxiliary BiLSTM ingests external lemma candidates (e.g., outputs from Apertium or Unimorph):

$$p(y_t|\cdots) = \operatorname{softmax}(W_o [s_t; c_t^{\text{orig}}; c_t^{\text{cand}}] + b_o)$$

This allows for on-the-fly combination of neural predictions and candidate lexicon entries, improving out-of-vocabulary accuracy (+1.11%) and yielding an average lemma-token accuracy of 97.25% across 23 Universal Dependencies languages—statistically significant over Stanford Stanza and previous baselines (Milintsevich et al., 2021).

3. In-Context Lemmatization with LLMs

Recent empirical work establishes that instruction-tuned LLMs (e.g., Mistral-Large-Instruct-2407, Llama-3.3-70B-Instruct, Claude-3.7-Sonnet) attain state-of-the-art contextual lemmatization via in-context learning, even absent domain- or language-specific training data (Toporkov et al., 8 Oct 2025). The canonical setup:

• Input sentence as a word-per-line list.
• 4-shot basic prompt with high-error examples from the development set.
• Output in TSV format (word, lemma).

In 12 typologically distinct languages, large LLMs matched or outperformed supervised fine-tuned encoders in Turkish, Czech, Russian, Finnish, and others, with word-level accuracy up to 0.97 and sentence-level accuracy up to 0.65. This approach is highly sensitive to prompt design and model scale; smaller variants (≤8B parameters) lag behind significantly. A plausible implication is that LLMs have internalized morphological regularities via massive scale pre-training, enabling cross-lingual generalization in lemmatization.

4. Lemma-Level Evaluation and Information Retrieval

Lemmatization improves text matching and evaluation in highly inflected languages. The lemma-based ROUGE methodology replaces surface n-gram counting with lemma n-grams:

$$\text{LemmaROUGE-N} = \frac{\sum_{S \in \text{Refs}} \text{count}_\text{match}(\ell\text{-gram})}{\sum_{S \in \text{Refs}} \text{count}(\ell\text{-gram})}$$

For Arabic, this yields a 10–30% relative gain in F-measure over surface-level ROUGE in summarization evaluation (El-Shishtawy et al., 2014). Rule-based, root-pattern Arabic lemmatizers achieve superior accuracy in both closed and open settings (94.8% on known text; 89.15% on unseen text) compared to statistical taggers, particularly by preserving semantic unity across inflections and avoiding over-conflation (El-Shishtawy et al., 2012).

5. Mathematical LLMs: Llemma

“Llemma” designates open base LLMs for mathematics, obtained via continued pretraining of Code Llama on “Proof-Pile-2” (55B tokens of scientific papers, math web data, and mathematical code) (Azerbayev et al., 2023). Technical specifications:

• Llemma-7B: 32 layers, $d=4096$, context length 4096 tokens, Rotary Positional Embedding (RoPE) contraction ($\theta=10^4$).
• Llemma-34B: 40 layers, $d=6144$, context length 4096 tokens, RoPE base $\theta=10^6$.

On the MATH benchmark, Llemma-34B achieves 25.0% accuracy (greedy decode), 43.1% (self-consistency), equaling or exceeding the unreleased Minerva-62B and outperforming all open base models. Integrated tool-use (Python REPL, SymPy) and formal proving (Isabelle, Lean tactic prediction on miniF2F) demonstrate capability without downstream fine-tuning. All code, weights, and data are openly released; this provides a viable foundation for mathematics-specialist “LLMs” and reproducible scientific workflows.

6. Probing Token Space Topology via Structured Prompts

Recent advances utilize LLMs to reconstruct their hidden token embedding space $\iota(T)\subset X$ up to homeomorphism (Robinson et al., 19 Mar 2025). Theoretical guarantee is given by multijet transversality (Thom’s theorem): for generic maps, the structured-prompting algorithm recovers the topology (dimension, connectivity, stratification) of token subspace. Empirical results on Llemma-7B show:

• Recovery of stratified base dimensions (5–15) across 32,016 tokens, matching the ground truth histogram.
• Fidelity in topological invariants (volume–radius, persistent homology) within the embedding.
• Limitations include variance from probability estimation, incomplete checks for full homeomorphism, and model-specific “genericity.”

This approach generalizes to other nonlinear autoregressive models and may illuminate deep connections between input–output behavior and latent geometry.

7. Robotics Benchmark: LEMMA

In robotics, LEMMA refers to a benchmark environment for language-conditioned multi-robot manipulation (Gong et al., 2023). LEMMA consists of eight procedurally generated tabletop tasks including “tool use” and “tool passing” and provides 6,400 expert demonstrations with language annotations. Core technical components:

• Modular hierarchical planning (Episodic Transformer + CLIPort), decomposing high-level language into sub-tasks and joint-space trajectories.
• Metrics: Episode Success Rate, Sub-Task Accuracy, Temporal Error.
• Results: 43.2% success (baseline), 74.8% (with oracle allocation), strong drop for ambiguous instructions and long-horizon tasks.
• Failure modes: misallocation, out-of-order primitives, and low-level grounding errors.

Extensions proposed include SE(3) manipulation, richer robot morphologies, unscripted language via LLMs, real–world transfer, and joint end-to-end optimization.

8. Limitations, Controversies, and Future Directions

Several open challenges persist:

• Lemmatizers remain heavily language- and dialect-dependent in rule-based forms; LLMs require prompt engineering and large parameter counts for robust performance.
• Automated probing of token topology measures only local dimension and partial homological equivalence; global invariants may remain unresolved.
• In mathematical problem-solving, even large models lag in harder problem categories (e.g., geometry, precalculus) and may hallucinate plausible–but–incorrect solutions.
• Robotics benchmarks like LEMMA highlight gaps in semantic understanding, multi-agent planning, and realistic physics.

A plausible implication is that scaling up LLMs, integrating structured neural–symbolic combinations, and advancing corpus curation will be required for continued progress. The “Llemma” suite—in both mathematical language modeling and token topology probing—serves as a canonical reference point for future work in linguistically and mathematically grounded AI.