Established
The inverse-tan family itself is useful: a learned global λ already gives a strong and interpretable stabilization baseline.
Active research project
Frequency-Localized Stabilization for State Space Models
Topo_S4 studies whether S4-like models become unusually sensitive near the Nyquist boundary and whether persistent-homology-guided spectral control can stabilize those regions without erasing useful high-frequency structure.
S4 / S4D / S4ND
Persistent Homology
Inverse-tan normalization
Flattened CIFAR-10
Pathfinder
PH-peak residual boost
Research question
The central question is not just whether high-frequency sensitivity exists in S4-like models, but whether a topology-aware controller can decide when attenuation helps and when it should back off toward identity.
ω(Ω) = (2 / Δ) tan(Ω / 2), dω/dΩ = (1 / Δ) sec²(Ω / 2)
Current issue
The latest sample-wise follow-up suggests the present PH / spectrum controllers are not making rich local decisions; they drift toward near-boundary scalar solutions.
Design implication
The next controller should act locally in frequency, not through another single global or near-global Δλ.
Method snapshot
Current main filter
The active line uses a PH-guided inverse-tan spectral normalizer with an exact identity fallback when λ = 0.
Wλ(Ω) = β + (1 - β) / (1 + λ tan²(Ω / 2))
This keeps the intervention interpretable: increasing λ primarily suppresses near-Nyquist components.
Next controller shape
The next experiment keeps the stable global inverse-tan low-pass and adds a frequency-local residual release around PH peaks instead of another scalar Δλ head.
W(ω; x) = Winv(ω; λg) + (1 - Winv(ω; λg)) BPH(ω; x)
The aim is to preserve stability while reopening narrow bands that the PH signal says are structurally meaningful.
This week’s progress
This week I consolidated the latest sample-wise follow-up runs and used them to narrow the next design step. On flattened CIFAR-10, the global inverse-tan baseline E1 remained stable at 86.44 best dev and 85.63 test@best-dev. The PH-MLP controller E5 finished at 86.54/85.63, while the spectrum-MLP controller E6 reached 86.56/85.69 at best dev and ended at 86.34/85.83. So the clean-accuracy gap between global and sample-wise control is still small. More importantly, E5’s shuffled-PH evaluation matched the non-shuffled result at the final checkpoint, which weakens the claim that the current PH head is using meaningful sample-specific structure. Pathfinder showed the same pattern. The raw baseline E0 reached 93.36/93.36 and E1 reached 93.27/93.11, while the uploaded E5 log stayed below them even in its strongest visible region. The controller traces are the key signal: CIFAR E5 ended with λ=0.1769 against base λ=2.1769, E6 with 0.2658 against 2.2658, and Pathfinder E5 pushed the other way toward the upper bound. This suggests that the current sample-wise Δλ heads are collapsing toward clamp limits instead of learning useful local frequency decisions. The main conclusion this week is therefore not that PH guidance failed, but that the scalar Δλ bottleneck is too restrictive. The next experiment is a PH-peak residual boost mask on top of the stable inverse-tan global filter.
Current empirical picture
Milestone already established: RGB CIFAR
These runs remain the strongest completed clean + robustness evidence for the inverse-tan line and define the current confirmed baseline story.
| Dataset | Exp | Best dev | Test@best-dev | Best test | Final test | Corruption mean | Severity-5 mean |
|---|---|---|---|---|---|---|---|
| CIFAR-10 RGB | E0 | 91.32 | 90.86 | 91.42 | 91.41 | 74.36 | 60.30 |
| CIFAR-10 RGB | E1 | 91.42 | 91.38 | 91.43 | 91.36 | 77.15 | 64.29 |
| CIFAR-10 RGB | E4 | 91.66 | 91.30 | 91.40 | 91.36 | 75.57 | 61.63 |
| CIFAR-100 RGB | E0 | 71.50 | 71.99 | 72.10 | 72.08 | 50.71 | 37.03 |
| CIFAR-100 RGB | E1 | 71.42 | 72.51 | 72.56 | 72.55 | 51.79 | 38.17 |
Interpretation: E1 remains the strongest confirmed RGB clean + robustness baseline. The RGB implementation still uses a single inverse-tan profile shared across channels for each sample.
Latest sample-wise follow-up: flattened CIFAR-10 and Pathfinder
The newest runs sharpen the bottleneck: the sample-wise heads are competitive but still look much more like saturated scalar controllers than like meaningful local frequency selectors.
| Dataset | Exp | Best dev | Test@best-dev | Final / visible final | Controller note |
|---|---|---|---|---|---|
| Flattened CIFAR-10 | E0 | 86.72 | 85.34 | 85.52 | Raw baseline. |
| Flattened CIFAR-10 | E1 | 86.44 | 85.63 | 85.85 | Stable global λ baseline. |
| Flattened CIFAR-10 | E5 (PH-MLP) | 86.54 | 85.63 | 85.63 | Final shuffled-PH matched the non-shuffled result; λ ≈ 0.1769 vs base λ ≈ 2.1769. |
| Flattened CIFAR-10 | E6 (Spectrum-MLP) | 86.56 | 85.69 | 85.83 | Best clean score among current sample-wise runs, but λ still collapsed far below base λ. |
| Pathfinder | E0 | 93.36 | 93.36 | 93.40 | Strong raw baseline. |
| Pathfinder | E1 | 93.27 | 93.11 | 93.19 | Stable global λ baseline. |
| Pathfinder | E5 (PH-MLP) | 92.18* | 92.25* | 92.16* | Visible log stays below E0 / E1 and pushes toward the upper λ bound. |
* Pathfinder E5 is shown from the uploaded visible log region, which runs through epoch 197.
Interpretation
Inverse-tan remains useful
The global-λ line is still the cleanest confirmed stabilization story, especially on the completed RGB CIFAR evaluation.
PH is not disproved
The latest follow-up does not show that topology is useless; it shows that the current controller parameterization is too narrow.
Local release is the next move
A PH-peak residual boost is a better match to the failure mode than another scalar Δλ or another near-global controller.
Roadmap
- Implement PH-peak residual boosting. Keep the stable global inverse-tan filter and add narrow PH-guided release bands.
- Rerun flattened CIFAR-10 and Pathfinder with multi-seed tracking. Report clean accuracy together with λ, base λ, pass ratio, and shuffled-PH controls.
- Move beyond flattened images. Test native 1D and 2D settings where “high frequency” is less entangled with flattening artifacts.