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        <title>Why Does Low-Rank Adaptation Work for Hindi-English Code-Mixing? A Geometric Analysis</title>
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            <namePart type="given">Kengatharaiyer</namePart>
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    <abstract>Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large language models, yet why it works particularly well for code-mixed text remains unexplained. We propose that LoRA’s efficiency stems from geometric structure in multilingual pre-trained models: code-mixed embeddings concentrate in low-dimensional cross-lingual subspaces. Through spectral analysis of mBERT and MuRIL on Hindi-English (Hinglish) data, we establish that pre-trained attention weights have effective ranks of 437–441, while LoRA updates (r = 4,8,16) exhibit ranks of 2.1–5.9—a 136× average compression. Cross-lingual geometry measured via Centered Kernel Alignment shows Hinglish embeddings align strongly with Hindi (CKA=0.279) but weakly with English (0.093), compared to a monolingual baseline of 0.074. Statistical tests (Wilcoxon p \ensuremath&lt; 10\ensuremath-19) and permutation ablations confirm these differences are robust. We interpret the convergence of geometric overlap (3.77× baseline) and empirical compression (136×) as evidence that low-rank adaptation exploits pre-existing multilingual structure. Findings are demonstrated on token-level language identification; extensions to other language pairs and tasks remain open questions.</abstract>
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%0 Conference Proceedings
%T Why Does Low-Rank Adaptation Work for Hindi-English Code-Mixing? A Geometric Analysis
%A Vishwakarma, Shashank
%A Kumar, Rakesh
%Y Sarveswaran, Kengatharaiyer
%Y Vaidya, Ashwini
%S Proceedings of the Second workshop on Challenges in Processing South Asian Languages (CHiPSAL2026)
%D 2026
%8 May
%I ELRA Language Resources Association (ELRA)
%C Palma de Mallorca, Spain
%F vishwakarma-kumar-2026-low
%X Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large language models, yet why it works particularly well for code-mixed text remains unexplained. We propose that LoRA’s efficiency stems from geometric structure in multilingual pre-trained models: code-mixed embeddings concentrate in low-dimensional cross-lingual subspaces. Through spectral analysis of mBERT and MuRIL on Hindi-English (Hinglish) data, we establish that pre-trained attention weights have effective ranks of 437–441, while LoRA updates (r = 4,8,16) exhibit ranks of 2.1–5.9—a 136× average compression. Cross-lingual geometry measured via Centered Kernel Alignment shows Hinglish embeddings align strongly with Hindi (CKA=0.279) but weakly with English (0.093), compared to a monolingual baseline of 0.074. Statistical tests (Wilcoxon p \ensuremath< 10\ensuremath-19) and permutation ablations confirm these differences are robust. We interpret the convergence of geometric overlap (3.77× baseline) and empirical compression (136×) as evidence that low-rank adaptation exploits pre-existing multilingual structure. Findings are demonstrated on token-level language identification; extensions to other language pairs and tasks remain open questions.
%R 10.63317/55yuuwkijgj9
%U https://aclanthology.org/2026.chipsal-1.13/
%U https://doi.org/10.63317/55yuuwkijgj9
%P 127-136

Markdown (Informal)

[Why Does Low-Rank Adaptation Work for Hindi-English Code-Mixing? A Geometric Analysis](https://aclanthology.org/2026.chipsal-1.13/) (Vishwakarma & Kumar, CHiPSAL 2026)

• Why Does Low-Rank Adaptation Work for Hindi-English Code-Mixing? A Geometric Analysis (Vishwakarma & Kumar, CHiPSAL 2026)

ACL

• Shashank Vishwakarma and Rakesh Kumar. 2026. Why Does Low-Rank Adaptation Work for Hindi-English Code-Mixing? A Geometric Analysis. In Proceedings of the Second workshop on Challenges in Processing South Asian Languages (CHiPSAL2026), pages 127–136, Palma de Mallorca, Spain. ELRA Language Resources Association (ELRA).