Heuristic Computational Matrix Method for Marathi Grammar Checker

1. Introduction

Marathi, spoken by over 80 million people, is a morphologically rich IndoAryan language. Its complex inflectional system, flexible word order, and extensive use of postpositions make automated grammar checking a nontrivial task. Traditional rulebased approaches quickly become unwieldy, while pure statistical models suffer from data sparsity. The Heuristic Computational Matrix Method (HCMM) offers a hybrid solution that merges linguistic heuristics with a matrixbased computational framework, providing high accuracy with manageable computational overhead.

2. Core Concepts

2.1 Computational Matrix

At the heart of HCMM lies a multidimensional matrix M that represents the interaction between three primary linguistic axes:

• Lexical Class (L): nouns, verbs, adjectives, adverbs, postpositions, etc.
• Morphosyntactic Features (F): gender, number, case, tense, aspect, mood.
• Contextual Position (C): sentenceinitial, medial, final; and surrounding token patterns.

An entry M[L,F,C] stores a weighted heuristic score indicating the likelihood that a token with the specified properties appears correctly in that context. Scores are populated through:

• Corpusderived frequencies.
• Expert linguistic rules encoded as weight adjustments.
• Feedback loop from user corrections.

2.2 Heuristic Layer

Heuristics supplement raw matrix values to handle exceptions that pure statistics cannot capture. Examples include:

• Agreement rules for gender and number between a noun and its adjective.
• Verbsubject concord in compound sentences.
• Preferred postposition usage after specific case markers.

3. Processing Pipeline

1. Tokenisation & Morphological Tagging: The input sentence is split using a Unicodeaware tokenizer and each token is assigned a preliminary morphological tag (e.g., NounMascSing).
2. Matrix Lookup: For each token, the algorithm retrieves the probability vector from M based on its lexical class, features, and positional index.
3. Heuristic Adjustment: Heuristic functions evaluate neighbouring tokens and adjust scores to enforce agreement and syntactic constraints.
4. Decision Making: The final score determines whether the token is accepted, flagged, or suggested for replacement.
5. Correction Generation: If a token is flagged, a ranked list of alternative forms is produced by consulting the matrix and the underlying lexicon.

4. Sample Implementation (JavaScript)

The following short snippet illustrates how a simplified HCMM could be realised in a browser environment. It assumes that matrix and heuristics objects have been populated elsewhere.

/* Simplified HCMM core */function checkMarathiGrammar(sentence) {    const tokens = tokenize(sentence);               // custom tokeniser    const tags = morphologicalTagger(tokens);        // returns [{token, class, features}]    const errors = [];    for (let i = 0; i < tags.length; i++) {        const {token, class: L, features: F} = tags[i];        const C = i;                                 // simple positional index        let score = matrix.get(L, F, C) || 0;        // Apply heuristics that involve neighbouring tokens        score += heuristics.agreement(tags, i);        score += heuristics.postPosition(tags, i);        if (score < 0.5) {                           // threshold tuned on validation set            const suggestions = generateSuggestions(token, L, F);            errors.push({position: i, token, suggestions});        }    }    return errors;}

5. Advantages Over Conventional Methods

• Hybrid Strength: By blending statistical evidence with rulebased heuristics, HCMM mitigates both data sparsity and rule explosion.
• Scalability: The matrix can be compressed using sparse representations, allowing deployment on modest hardware such as smartphones.
• Explainability: Each flagged error can be traced back to a specific matrix entry and heuristic rule, facilitating transparent feedback to users.
• Adaptability: New linguistic phenomena (e.g., emerging slang) can be integrated by simply updating the matrix or adding a heuristic without retraining a full model.

6. Evaluation Results

HCMM was evaluated on a curated corpus of 10,000 Marathi sentences drawn from news articles, literature, and social media. The performance metrics compared to a stateoftheart neural grammar checker are summarised below:

The higher precision stems from HCMMs strict heuristic enforcement, while recall benefits from the matrixs coverage of lesscommon forms. The latency advantage demonstrates suitability for realtime editor plugins.

7. Extending the Method

Future work can broaden HCMM in several directions:

• Dynamic Matrix Update: Incorporate an online learning module that continuously refines matrix weights from user corrections.
• Crosslingual Transfer: Leverage similarities with other IndoAryan languages (e.g., Hindi, Gujarati) to bootstrap matrix entries for lowresource dialects.
• Integration with SpeechtoText: Extend the pipeline to detect grammatical errors in transcribed speech, where prosodic cues may aid heuristic evaluation.

8. Conclusion

The Heuristic Computational Matrix Method offers a pragmatic yet powerful architecture for Marathi grammar checking. By representing linguistic interactions in a structured matrix and complementing them with targeted heuristics, HCMM achieves a balance of accuracy, speed, and interpretability that pure rulebased or purely statistical models lack. Its modular nature makes it an attractive foundation for both research prototypes and productiongrade language tools.

For more details, source code and a live demo, visit the GitHub repository or contact the authors at info@hcmm-marathi.org.