pineconedad/undertrained-tokens-0.6B-6B-benchmark

Technical Challenge: Blind Spots of Frontier Models

Question 1: Critical Blind Spot, Bias, or Capability Gap

While investigating under-trained ("glitch") tokens for my undergraduate thesis, I encountered a mechanistic anomaly that standard LLM benchmarks and existing token-detection papers overlook: "under-trained" tokens are not uniformly unlearned across model families and embedding architectures.

Standard benchmarks (like MMLU or GSM8K) only probe high-frequency vocabulary paths, while prior glitch-token studies treat all low-norm tokens as a single broken category that the model failed to learn. Through systematic weight-space ablations, I found that low-norm tokens actually split into two distinct regimes:

1. Magnitude Starvation ("Quietly Learned" Directions): In untied Qwen models, the model successfully aligns the token's output vector direction ($\cos\theta$) during pre-training, but its L2 norm ($\Vert{}W_{\text{out}}[t]\Vert{}$) remains crushed in the bottom 2.4th percentile of the vocabulary. Because logit projection is a dot product ($\text{logit}t = \Vert{}\tilde{h}\Vert{} \cdot \Vert{}W{\text{out}}[t]\Vert{} \cdot \cos(\tilde{h}, W_{\text{out}}[t])$), a token with a valid semantic direction but a crushed norm is capped at roughly 55% of a healthy token's logit and loses the softmax competition.
2. Directional Collapse / Tied-Weight Interference: In other model families or architectures where input and output embeddings are tied ($W_{\text{in}} \equiv W_{\text{out}}$), low-norm rows either fail to learn a usable direction or suffer interference between reading and writing gradients.

Crucially, in my thesis census of 782 repairable tokens in Qwen2.5, 93.0% (727/782) belong to non-Latin scripts (38.1% Korean Hangul, 17.5% CJK, 10.5% Arabic, 7.3% Hebrew, 2.9% Cyrillic). What looks like a low-level weight-norm quirk is in practice a deterministic multilingual reliability failure.

Question 2: Systematic Evaluation on Hugging Face Models (0.6B to 6B)

To test how output-row rescaling generalizes across small frontier models (0.6B to 6B parameters) and across untied vs. tied embedding tables, this repository curates a stratified multi-model benchmark (data/eval_cohort_100_per_model.csv) derived from an 81-model Magikarp detector dictionary (data/model_manifest.json).

We evaluate models across four architectural cells:

• Qwen Untied Anchor: Qwen/Qwen1.5-4B (4.0B, tie_word_embeddings=False)
• Qwen Tied Counterpart: Qwen/Qwen2.5-3B (3.09B, tie_word_embeddings=True)
• Non-Qwen Untied Comparators: microsoft/Phi-3-mini-128k-instruct (3.8B) and microsoft/phi-2 (2.7B)
• Non-Qwen Tied Comparators: google/gemma-2b (2.5B) and LGAI-EXAONE/EXAONE-3.5-2.4B-Instruct (2.4B)

For each model, our Colab notebook (notebooks/evaluate_scaling.ipynb) measures:

1. Healthy Vocabulary Reference ($r$): The median L2 norm of healthy rows in lm_head.weight (computed in float32).
2. Baseline Reproduction Rate: Exact-match token reproduction on held-out prompts assembled via exact token-ID splicing.
3. Surgical Output-Row Rescaling: Scaling each broken token's output row to the healthy median norm ($W_{\text{out}}[t] \leftarrow r \cdot \frac{W_{\text{out}}[t]}{\Vert{}W_{\text{out}}[t]\Vert{}}$) while keeping its direction unchanged ($\cos = 1.0000$), testing both native tied scaling and decoupled lm_head scaling.
4. Cost Controls: Rare-token intrusion rate (false emissions in unrelated contexts) and collateral perplexity.

Question 3: Proposing a Path Forward

To fix magnitude starvation at its root without full retraining or high intrusion costs, I propose three concrete mechanisms:

1. Analytical Post-Training Scale Calibration (Pareto Tuning): Setting all low-norm output rows straight to $1.0\times$ the healthy median norm repairs 85.0% of broken tokens in Qwen2.5-7B, but raises rare-token intrusion 64-fold. Because lm_head is the final linear operation, scaling row $t$ by $s$ multiplies $\text{logit}_t$ by $s$ while leaving all other logits unchanged ($P_s(t) = \frac{e^{s \cdot \text{logit}_t}}{e^{s \cdot \text{logit}t} + \sum{j \neq t} e^{\text{logit}_j}}$). We can sweep $s \in (0, 1]$ analytically from a single forward pass to pick the exact per-token scale factor $s^$ that maximizes echo recovery while bounding intrusion near baseline.*
2. Frequency-Scaled Weight Decay on Embedding Tables: During AdamW pre-training, standard decoupled weight decay shrinks every row of $W_{\text{in}}$ and $W_{\text{out}}$ at every step, even when rare non-Latin tokens do not appear in the batch. Scaling the weight-decay multiplier on embedding rows by their empirical batch occurrence frequency prevents pre-training from crushing the norm of rare tokens after they align their direction.
3. Decoupling Unembedding Norms in Small Checkpoints: Small models (under 4B) routinely tie $W_{\text{in}}$ and $W_{\text{out}}$ to save parameters, even though initial layer normalization removes input magnitude while output softmax remains strictly norm-sensitive. Adding a single learnable scalar vector $\mathbf{g} \in \mathbb{R}^{V}$ on the unembedding head ($\text{logit}_t = g_t (\tilde{h} \cdot W[t])$) adds only 0.15M parameters for a 150k vocabulary while decoupling output audibility from input representation.