{ "source_file": "0930", "source_platform": "Hashnode", "author": "Aman Jain", "title_listed": "Does a Wider Embedding Space Help More on Diverse Data?", "keywords": "", "domain": "大模型算法", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://curious-pm.hashnode.dev/does-a-wider-embedding-space-help-more-on-diverse-data", "publish_date": "2026-07-20", "corpus_stage": "", "notes": "", "id": "5fc4a4dffbdb", "collected_at": "2026-10-02T14:11:44", "title": "Does a Wider Embedding Space Help More on Diverse Data?", "body_markdown": "Does a Wider Embedding Space Help More on Diverse Data?\nExploring model width, topic diversity, and next-token prediction with a small GPT model\nUpdated\nJuly 20, 2026\n•\n7\nmin read\n•\nView as Markdown\nA\nAman Jain\nProduct manager learning to build AI from the inside out — from LLM architecture to product applications.\nPart of series\nInside GPT: Experiments and Trade-offs\nTL;DR\nIncreasing the embedding dimension from\n32 to 64\nimproved validation loss in both the low- and high-diversity training conditions.\nMost of the improvement appeared between\n32 and 48 dimensions\n; the gain from 48 to 64 was smaller.\nTraining on diverse data produced better performance on a shared, multi-topic validation set at every model width.\nAt the aggregate level, width did not help substantially more on diverse data. However, the per-cluster results showed that wider models improved more consistently across topics after diverse training.\nIn this setup, the\n48-dimensional model looked like a reasonable quality-versus-compute balance\n.\nGitHub:\nView the complete code and experiment notebooks\nIn the previous experiment, I explored how model size, depth, and compute affected training.\nThis time, I wanted to isolate a narrower question:\nDoes increasing the embedding dimension improve next-token prediction—and does it help more when the training data contains a broader range of topics?\nMy intuition was that a larger embedding space would give the model more room to represent relationships between words, contexts, and topics.\nBut there was an important caveat: in my GPT implementation,\nemb_dim\ndoes more than control the initial token embeddings. It also determines the hidden width used throughout the transformer.\nSo this was really a\nmodel-width experiment\n, not a perfectly isolated test of the embedding table.\nExperiment setup\nI trained models using three embedding dimensions:\nModel\nEmbedding dimension\nHead dimension\nParameters\nNarrow\n32\n8\n3.27M\nMedium\n48\n12\n4.94M\nWide\n64\n16\n6.64M\nEverything else remained fixed:\nfour attention heads;\nfour transformer blocks;\ncontext length of 128;\nthe same optimizer and learning-rate schedule;\n200,192 training tokens per run.\nI also created two token-matched WikiText corpora:\nLow diversity:\narticles selected from one topic cluster.\nHigh diversity:\narticles sampled across six topic clusters.\nEvery model was evaluated on its matched validation set and on a shared, diverse validation set.\nResearch on model scaling has shown that model capacity, data, and compute interact rather than operating independently. Other work has also explored separating embedding size from hidden-layer capacity and the importance of pretraining-data composition.\nHypothesis\nI expected wider models to achieve lower validation loss because they could represent richer relationships.\nI also expected the benefit of width to be larger for the high-diversity corpus, since the model needed to represent a wider range of topics and vocabulary patterns.\nThe first part of the hypothesis held up.\nThe second was more complicated.\nWider models achieved lower loss\nValidation loss improved as embedding dimension increased in both conditions.\nDataset condition\nemb_dim=32\nemb_dim=48\nemb_dim=64\nLow-diversity matched validation\n6.7012\n6.5637\n6.5253\nHigh-diversity validation\n7.1411\n7.0909\n7.0636\nThe gains were not linear.\nFor the low-diversity corpus:\n32 → 48 improved loss by\n0.1375\n48 → 64 improved it by\n0.0384\nFor the high-diversity corpus:\n32 → 48 improved loss by\n0.0502\n48 → 64 improved it by\n0.0273\nSo width helped, but the returns diminished.\nThe 48-dimensional model captured much of the improvement while using fewer parameters and less compute than the 64-dimensional model.\nTop-1 accuracy also peaked at 48 dimensions in both matched-validation comparisons, although validation loss continued to improve at 64 dimensions.\nThat is possible because accuracy only checks whether the highest-ranked token was correct, while cross-entropy loss evaluates the full predicted probability distribution.\nDiverse training improved generalization\nI evaluated every model on the same shared, diverse validation set.\nEmbedding dimension\nLow-diversity training\nHigh-diversity training\n32\n7.3023\n7.1411\n48\n7.2350\n7.0909\n64\n7.2144\n7.0636\nAt every width, the models trained on diverse data performed better on the shared diverse evaluation.\nThis suggests a fairly intuitive pattern:\nThe low-diversity models became better specialists, while the high-diversity models became better generalists.\nThe Pile and later data-mixture research similarly emphasize that the composition and coverage of pretraining data can meaningfully affect cross-domain performance.\nDid width help more on diverse data?\nAt the aggregate level, not really.\nOn the shared validation set, increasing width from 32 to 64 improved loss by:\n0.0879\nafter low-diversity training;\n0.0775\nafter high-diversity training.\nThose improvements were similar. The overall validation score therefore did not support a strong interaction between width and topic diversity.\nBut the per-cluster results added useful nuance.\nPer-cluster results\nAfter high-diversity training, increasing width from 32 to 64 improved loss in\nall six clusters\n.\nAfter low-diversity training, width improved four clusters, barely changed one, and slightly worsened another.\nTraining condition\nAverage 32 → 64 improvement\nHigh diversity\n0.1148\nLow diversity\n0.0479\nThe effect varied substantially across topics.\nFor the high-diversity models:\nCluster 5 improved by\n0.1655\nCluster 2 improved by\n0.1520\nCluster 1 improved by\n0.1345\nCluster 0 improved by only\n0.0280\nSo additional width did not benefit every topic equally.\nThe low-diversity model was especially strong on one cluster but considerably weaker on most of the others. The high-diversity model performed better on five of six clusters at 64 dimensions.\nThat supports a more nuanced version of the original hypothesis:\nWider representations did not create a much larger aggregate benefit on diverse data, but they produced broader and more consistent gains across individual topics.\nQuality versus cost\nIncreasing\nemb_dim\nfrom 32 to 64:\nroughly doubled model parameters;\nroughly doubled estimated training compute;\nreduced training throughput;\nproduced progressively smaller improvements in loss.\nThat makes 48 dimensions look like a reasonable efficiency point in this particular setup.\nIt captured most of the benefit from increasing width, achieved the highest matched top-1 accuracy, and avoided the full runtime and compute cost of the 64-dimensional model.\nWhat I learned\nThis experiment produced three main observations:\nWider models achieved lower validation loss.\nDiverse training data improved broad generalization.\nWidth helped more consistently across topic clusters after diverse training, even though the aggregate interaction was weak.\nMy takeaway is narrower than my original hypothesis:\nWider representations helped, and diverse training helped—but they did not strongly amplify each other in the overall validation result.\nThe more interesting effect appeared at the topic level.\nThe low-diversity model behaved more like a specialist. The high-diversity model behaved more like a generalist. Additional width improved that generalist across a broader range of topics.\nAs with my previous experiments, these findings are specific to my model, clustering method, dataset, learning rate, and training budget.\nBut they offered a useful reminder:\nAggregate metrics can hide where an architectural change is actually helping.\nReferences\nVaswani, A. et al. (2017).\nAttention Is All You Need\nLan, Z. et al. (2019).\nALBERT: A Lite BERT for Self-supervised Learning of Language Representations\nKaplan, J. et al. (2020).\nScaling Laws for Neural Language Models\nHoffmann, J. et al. (2022).\nTraining Compute-Optimal Large Language Models\nGao, L. et al. (2020).\nThe Pile: An 800GB Dataset of Diverse Text for Language Modeling\nXie, S. M. et al. 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