The language-model head maps a hidden state of width D to a vocabulary of size V, so its transpose can return at most D independent directions to the Transformer. Godey and Artzi argue that this severe projection is a harmful optimization bottleneck. We separate the geometry from the causal claim. Our backward-only intervention keeps the ordinary logits and the exact LM-head parameter update while reducing only the rank of the gradient sent into the Transformer. Across five paired seeds on byte-level and BPE-8192 WikiText-2 models, reducing backward rank increases validation loss. An equally ranked factorized forward head, however, increases loss substantially more. At half rank in the larger model, the backward-only loss increase is 0.0586 (95% CI [0.0167, 0.1005]), while the factorized forward head increases loss by 0.1795 ([0.1547, 0.2042]). The vocabulary-space residual also contributes to the ordinary LM-head update, and removing that contribution is harmful. Additional controls show that repeated-token failures are confounded by the number of independently sampled symbols, that adding never-target output classes does not impair learning, and that projection diagnostics do not reliably predict progress in our runs. Tested auxiliary feedback routes do not beat tuned backpropagation. These results confirm strong geometric compression but do not establish that it is a harmful optimization bottleneck.
Statistical subword tokenizers can process arbitrary text, but their units need not align with lexical or grammatical structure. This is especially important for Tamil, where a written word may encode stem changes, case, number, tense, agreement, voice, clitics, and linked verbs. We present a Tamil morphology system extending the open-source ThamizhiMorph analyzer and generator, together with a byte-exact semantic tokenizer and a learned hierarchical word composer. Twelve finite-state transducers analyze words into lemmas and grammatical features, while character and byte fallbacks preserve exact reconstruction. We compare a flat morphology tokenizer, a signal-preserving word composer, and tokenizers based on Sarvam-1, AI4Bharat IndicBERTv2, and BrahmicTokenizer-131K. All systems use the same 69,591 Tamil-English training pairs, 18.97-million-parameter encoder-decoder, 40,000 updates, target tokenizer, optimizer, positional method, and generation settings. On a protected 3,539-row IN22 and FLORES+ evaluation, morphology-flat achieves the best pooled scores: 10.63 BLEU, 35.26 chrF++, and 0.6276 COMETKiwi. Relative to AI4Bharat, the strongest external-tokenizer baseline, these are improvements of 7.2%, 3.2%, and 2.6%. The word composer scores 10.30, 34.88, and 0.6241, improving on AI4Bharat by 3.8%, 2.1%, and 2.0%. The composer reduces mean global source states from 71.48 to 29.08, a 59.3% reduction, and is estimated to require 9-21% fewer inference FLOPs depending on decoder caching. Its remaining quality gap is concentrated in longer FLORES+ sentences. These results show that explicit Tamil morphology improves translation under a fixed small-model budget, while hierarchical composition substantially reduces sequence length and estimated inference cost.
