# 75M K-shift offset validation (synth → 75M transfer test)

## Experiment

Two 75M FineWeb-Edu training runs differing **only in `--k-shift-offset`** (1 vs 2).
Both use softmax+K-shift L0 + ALiBi + 1500 steps with default v75 hyperparameters.

CLIs:
```bash
NO_SAVE=1 python train_fineweb_v75.py \
    --k-shift --k-shift-layers 0 --k-shift-offset 2 \
    --max-steps 1500 --eval-interval 250 --eval-iters 8 \
    --tag v76b_75m_kshift_L0_off2

NO_SAVE=1 python train_fineweb_v75.py \
    --k-shift --k-shift-layers 0 --k-shift-offset 1 \
    --max-steps 1500 --eval-interval 250 --eval-iters 8 \
    --tag v76b_75m_kshift_L0_off1_baseline
```

GPU: RTX 5090 on vast.ai. Both runs ~35 min.

## Results

| Step | offset=2 val_bpc | offset=1 val_bpc | Δ (off2 − off1) |
|---|---|---|---|
| 250 | 10.3855 | 10.3779 | +0.008 |
| 500 | 9.6400 | 9.6341 | +0.006 |
| 750 | 9.1074 | 9.1029 | +0.005 |
| 1000 | 8.6848 | 8.7258 | **-0.041** ✅ |
| 1250 | 8.2600 | 8.2717 | **-0.012** ✅ |
| **1500** | **7.9719** | **7.9852** | **-0.013** ✅ |

## Interpretation

**Synth prediction validated at 75M scale**:
- Direction: ✅ offset=2 consistently lower val_bpc from step 1000 onward
- Magnitude: small (-0.013 BPC at step 1500)

The gap emerges around step 1000 (when learning rate exceeds 3e-4 in the
warmup ramp). Before that, both runs are virtually identical — expected
since lr is too small for sign flips to dominate.

**Caveats**:
1. **Both runs are still in warmup** at step 1500 (warmup_steps=2000).
   At full LR (post step 2000), the gap may grow.
2. **ALiBi attenuates the benefit**: synth (no-ALiBi) showed +50pp top-per-head
   IPMR from offset switch; at 75M with ALiBi, val_bpc gap is ~0.013. The
   mechanism (sharper sign-STE attention alignment) is the same, but ALiBi
   limits the absolute distances over which the alignment matters.
3. **Single seed each**. Run-to-run noise typically ~0.02-0.05 BPC at this
   scale. The -0.013 BPC gap is at the edge of noise. Multi-seed runs would
   strengthen the claim.

**Next step to strengthen the result**: train both for 5000+ steps (full LR
post-warmup) to see if the gap widens. Predicted: yes, by 0.05-0.10 BPC
once both runs are at full lr.

## ⚠ 5000-step result — synth prediction REVERSED at 75M

Ran both for 5000 steps (past warmup_steps=2000, full LR cosine to lr_end):

| Step | offset=2 | offset=1 | Δ (off2 - off1) |
|---|---|---|---|
| 500 | 9.6376 | 9.6338 | +0.004 |
| 1000 | 8.6589 | 8.6741 | -0.015 |
| 1500 | 7.9281 | 7.9606 | -0.033 |
| 2000 | 7.6452 | 7.5921 | **+0.053** |
| 2500 | 7.3224 | 7.3297 | -0.007 |
| 3000 | 7.1730 | 7.1523 | +0.021 |
| 3500 | 7.0398 | 7.0338 | +0.006 |
| 4000 | 6.9431 | 6.9256 | +0.018 |
| 4500 | 6.8545 | 6.8384 | +0.016 |
| **5000** | **6.7779** | **6.7639** | **+0.014** |

**At 5000 steps, offset=1 BEATS offset=2 by 0.014 BPC** — synth prediction
*reversed* at this scale. The early offset=2 advantage (steps 1000-1500) is
erased post-warmup; offset=1 then takes a small but consistent lead.

### Honest interpretation

The synth K-shift offset finding **does not transfer cleanly to 75M scale
with ALiBi + natural text**. Likely reasons:

1. **Run-to-run noise**: |Δ| = 0.014 is within val_loss_std (~0.07). Single
   seed each. Multi-seed runs would clarify, but the pattern across the
   trajectory is consistent enough (offset=1 wins steps 2000-5000) that
   noise alone probably can't explain it.

2. **ALiBi attenuation**: ALiBi already provides distance penalty. The
   offset=1 weakness in synth was about "K vectors too smooth at distance 1
   making sign-STE alignment harder for distance-24 attention". With ALiBi,
   the model isn't attending at distance 24+ much anyway, so this weakness
   may not manifest.

3. **Natural text vs synthetic copy task**: synth's fixed-distance pattern
   doesn't match natural text's variable induction distances. Most natural
   induction is at distances 1-15; offset=1 (= prev-token routing,
   Olsson canonical) might be genuinely optimal here.

4. **Training dynamics under cosine LR decay**: synth was constant LR; 75M
   uses cosine decay from 6e-4 to 3e-5. Different optimization trajectory.

### Updated v76 paper recommendation

The synth-derived "switch offset 1 → 2" recommendation **does not improve
val_bpc at 75M scale**. The current v76 K-shift offset=1 (canonical) is
already optimal for natural-text training.

The synth findings remain valid as MECHANISTIC insights (offset=1 has
distinct K-vector smearing at fixed-distance copy), but they don't predict
val_bpc improvements at scale. The mechanism is real but not the right
optimization target for natural text.

**Outstanding**: the placement axis (K-shift L11 vs L0) hasn't been tested
at 75M yet. Synth showed placement was the bigger effect (50pp top-per-head
vs offset's 7pp). Worth testing.

## V76 paper actionable recommendation (post 5000-step result)

**Keep current v76 K-shift offset=1.** The synth-derived "switch offset 1→2"
proposal does not improve val_bpc at 75M scale (offset=1 wins by 0.014 BPC
at 5000 steps).

The synth K-shift offset axis is mechanistically interesting (explains why
sign-STE attention prefers different K shapes) but is **not a useful
optimization knob** for natural-text training under ALiBi.

The broader synth-derived recommendations (try non-L0 placement, drop RWSP
for softmax) remain UNTESTED at 75M — placement test was launched but VM
dropped before completion.

## Statistical caveat (post-hoc analysis)

The 5000-step Δ_val_bpc = +0.014 (off2 worse) has val_loss_std = 0.094 at
step 5000. The observed gap is ~0.15× the std — **not statistically
significant**. Likewise the 1500-step Δ = -0.013 (off2 better) is within
noise. With single seeds and these std values, neither direction can be
claimed at p<0.05 without 4-8 seed averaging.

What this changes:
- The "offset=2 reverses at 75M" claim is overstated — it's "offset=2
  shows no significant difference at 75M". The reversal across train
  steps is consistent with random-walk-around-zero given val_loss_std.
- The synth-derived recommendation isn't refuted; it's unsupported.
- A multi-seed test would clarify, but at 75M scale (~35 min/run on
  vast.ai), 8-seed runs cost ~$15 and ~5 hours — small but not free.

The empirical bottom line stands: **at single-seed 75M, offset=1 vs
offset=2 are indistinguishable**. The current v76 recipe is fine.