Key findings: TST alone improved validation loss by ~0.073 nats over the base (no-TST, no-MTP)
model. MTP=1 alone improved by ~0.011 nats. Combining TST with MTP=1 achieved the best result
in the series at 2.204673 nats — a total improvement of ~0.083 nats over the base.
TST+MTP=2 did not improve over TST+MTP=1, suggesting diminishing returns beyond one MTP head
at this scale.
Validation loss is next-token cross-entropy in nats, evaluated on a held-out Wikipedia Markdown
validation set using the same 16,000-token BPE vocabulary. Lower is better.
Research artifact. These checkpoints are screening-scale models (3,000 steps, ~100M parameters)
released for research and ablation comparison. They are not intended as production models.
Why 3,000 steps? After dozens of prior experiments running 15,000+ steps, it was
consistently observed that the winning model was already ahead of competing runs within the
first 2,000 steps. Running to 3,000 steps provides a clear signal while keeping turnaround
fast enough to run many conditions in parallel.
Why ~100M parameters? After many experiments at 200M–500M parameters, the model that
won at larger scale consistently also won at ~100M. Screening at ~100M is therefore a
reliable and efficient proxy: top candidates from this series will be scaled further.
What might change at scale? At ~100M parameters and 3,000 steps, the model has
limited capacity to predict far into the future — which likely explains why MTP=1 was optimal
and MTP=2 did not help. A small model trained on relatively little data cannot reliably
leverage the signal from heads that predict multiple steps ahead; the additional auxiliary
loss may add noise rather than useful gradient. At larger model sizes and longer training
runs, the optimal MTP depth is expected to increase as the model gains the capacity to
make accurate multi-step predictions. Similarly, the optimal TST bag size (s=6 here) may
shift with scale — larger models may benefit from larger or smaller bags depending on how
effectively they can decompress the superposition signal during recovery.
Further research is needed to determine how these findings scale across model size,
training budget, and TST bag size.
About This Model
Base training (no TST) with two Multi-Token Prediction (MTP) heads. Despite the additional head, this model performs slightly worse than MTP=1 (AOMTS-Base-100M-3k-1MTP-v1, 2.276289 nats), suggesting diminishing or negative returns from a second MTP head in the base (no-TST) setting.
Architecture
Parameter
Value
Vocabulary size
16,000
Hidden dimension (d_model)
512
Layers
12
Attention heads
8
KV heads
8
Head dimension
64
FFN hidden dimension
4,800
FFN variant
SwiGLU
Max sequence length
2,048
RoPE θ
10,000
Normalization
RMSNorm
Tied embeddings
Yes
Total parameters: 135,348,736
Embeddings (tied tok_emb / lm_head): 8,192,000
Non-embedding, non-MTP (transformer blocks): 109,261,312 (identical across all AOMTS runs)
MTP heads (2 × 8,947,712): 17,895,424
MTP parameters are auxiliary training heads. They are not used during standard language modeling evaluation and do not affect validation loss — the val loss reported here is computed from the main head only. The non-embedding, non-MTP parameter count (109,261,312) is identical across all runs in this series.
Training
Setting
Value
Total steps
3,000
Batch size
16 sequences
Gradient accumulation
2
Effective batch size
32 sequences / 65,536 model-context tokens per step
Total raw tokens seen
196,608,000
Sequence length
2,048
LR schedule
WSD — 150 warmup steps, stable LR, then linear decay over the last 300 steps (final 10 % of training) to 0.0
MTP depth: 2 additional prediction heads
MTP loss weight: 0.1
Parameters per MTP head: 8,947,712
Total MTP parameters: 17,895,424
During standard (phase 2 / non-TST) training, each MTP head (d = 1 … 2)
predicts the token at position i+1+d given the hidden state at position i.
The MTP auxiliary loss is added to the main CE loss with weight 0.1.
Token Superposition Training (TST)
Token Superposition Training is not used in this model.
¹ s = bag size: the number of raw tokens averaged into each compressed embedding position during TST phase 1.
² Optim Reset = phase 2 restarted the optimizer state and LR schedule from scratch rather than carrying them over from phase 1. Models without this flag use a unified schedule across both phases.
References
Peng, B., Gigant, E., Quesnelle, J. (Nous Research, 2025). Token Superposition Training for Language Model Pretraining.arXiv:2605.06546
