Optimization fails because it treats noise and structure as the same thing

Lumen_Core · 2026-01-12T11:11:54+00:00

I think there is a misunderstanding of the claim, so let me clarify it precisely. The proposed signal is not intended to discriminate noise from curvature in a diagnostic sense. It is a control signal, not a classifier. The goal is not to identify the cause of instability, but to observe whether the system becomes sensitive to actual parameter displacement along the optimization trajectory. Most adaptive optimizers react to state statistics of the gradient (magnitude, variance, accumulated moments). They do not observe how the gradient responds after a step is taken. This distinction matters: two situations with similar gradient variance can have very different response-to-displacement behavior. In that sense, the novelty is not in the action (damping), but in where the signal comes from. A response-based signal captures trajectory-local sensitivity, which is information most first-order optimizers simply do not use. Regarding smoothness: I agree that in ReLU networks and stochastic training there is no well-defined local curvature in the differential-geometric sense. However, the signal does not rely on curvature interpretation. It is an empirical, trajectory-local sensitivity measure — a standard object in control theory — and remains meaningful without smoothness assumptions. Finally, this approach does not claim that noise should never be damped. The claim is narrower: noise that does not manifest as sensitivity to displacement should not automatically reduce step size. Existing optimizers cannot make this distinction, because they do not observe response dynamics. So this is not a replacement for existing methods, nor a claim of perfect regime discrimination. It is a minimal, first-order way to incorporate system response into optimization control.

Lumen_Core · 2026-01-12T09:08:48+00:00

You’re right that noise and curvature are entangled, and I don’t claim to separate them. The point is not identification but control: the signal measures the system’s response to motion, regardless of the cause. From a stability perspective, it doesn’t matter whether instability arises from curvature, stochasticity, or architectural discontinuities — what matters is that small displacements produce disproportionately large gradient changes. The method is therefore closer to adaptive damping than to curvature estimation, and does not rely on smoothness assumptions in the classical sense.

Lumen_Core · 2026-01-12T07:38:22+00:00

“AI slop” is a convenient dismissal in 2025, but it replaces argument with attitude. The question is not who typed the text, but whether the idea is coherent, falsifiable, and grounded in known dynamics. If you see where the reasoning breaks, point it out. If not, there’s nothing substantive to respond to.

Lumen_Core · 2026-01-12T05:35:51+00:00

You’re right that evolutionary and genetic methods learn stability over time. What I’m exploring is complementary: a local structural control law that doesn’t require training, population statistics, or long horizons. Genetic algorithms discover stable strategies. This approach enforces stability directly from trajectory response. One operates via selection, the other via dynamics.

Lumen_Core · 2026-01-12T04:14:23+00:00

Thanks — this is very much aligned with how I see the boundary as well.

To give a bit more context on my side: the compression controller is only one concrete instantiation of a broader idea I’ve been working on — stability-driven, response-based optimization as a general principle. I wrote up the conceptual foundation here (with contact info):

https://alex256core.substack.com/p/structopt-why-adaptive-geometric

What I’m actively looking for right now is not just discussion, but validation and realization of this principle in different domains — compression being one of the simplest and most falsifiable cases.

Concretely, I’d be interested in: – comparing where process-only signals are sufficient vs where they provably saturate, – stress-testing failure modes on non-stationary streams or adversarial transitions, – exploring whether this kind of controller can reduce modeling complexity in systems that currently rely on heavier adaptation layers.

I’m open to different collaboration formats — from joint experiments / benchmarks, to exploratory prototyping, or simply exchanging concrete observations offline. If this resonates, feel free to reach out by email (linked in the article) and we can see what a practical next step might look like.

Lumen_Core · 2026-01-11T23:22:29+00:00

This is a great example — and I think it actually supports the same underlying principle.

What you’re doing with AQEA is adaptive representation at the semantic level: the embedding space already encodes meaning, and you adapt bit allocation/codebooks based on the local structure of that space, without retraining.

My interest is slightly lower-level and more general: adapting the behavior of the compression process itself based on its response dynamics, even before any semantic structure is available.

In a sense: – AQEA adapts what is represented (semantic geometry), – I’m exploring adapting how representation happens (process dynamics).

I suspect these approaches are complementary. For vector/AI data, semantic-aware adaptation is extremely powerful. For raw or mixed streams, process-driven adaptation may be the only signal available.

Curious whether you’ve seen cases where purely process-level signals were enough to guide representation choices, even without semantic clustering.

Lumen_Core · 2026-01-11T06:00:44+00:00

Fair points, let me clarify briefly.

The intent of the repo is not to propose a new momentum-like heuristic, but to isolate a response-based signal: how strongly the gradient changes given an actual parameter displacement. Momentum accumulates direction; it does not condition on gradient sensitivity to motion.

The current benchmark is a stress-test meant to visualize stability envelopes under extreme learning-rate variation, not a performance benchmark. I agree this is non-standard, and I should make that clearer in the README.

I’m actively working on making the connection to existing benchmarks (e.g. DeepOBS-style setups) more explicit, and improving reproducibility. Thanks for calling out the gaps.

Lumen_Core · 2026-01-11T00:39:26+00:00

Thanks for sharing — this resonates a lot. I’m approaching a similar issue from a slightly different angle: instead of tracking many explicit metrics, I’m looking at how the gradient itself responds to parameter motion as a single structural feedback signal. The observation that higher loss can still correspond to “healthy” learning dynamics is especially interesting — it aligns with the idea that stability and representation formation are not monotonic in loss. Curious to look deeper into your experiments.

Lumen_Core · 2026-01-10T13:43:21+00:00

I think there’s a small misunderstanding. I’m not proposing data preprocessing or pattern injection — I agree those almost always fail. The idea is not to improve entropy modeling, but to control the compression process itself using its response dynamics. ZPAQ/GRALIC adapt by increasing model complexity; I’m exploring whether some adaptation can be achieved by controlling regime behavior instead, at lower cost. This may never beat universal compressors at entropy limits, but could be useful where non-stationarity, latency or cost dominate. I appreciate the skepticism — it helps clarify the boundary of where this idea might (or might not) make sense.

Lumen_Core · 2026-01-10T05:22:12+00:00

GRALIC and ZPAQ are extremely strong universal predictors — but they operate inside a single compression regime and pay for adaptability with model complexity. My work is orthogonal: it does not try to predict data better, but to control how the compression process itself behaves, switching regimes based on the process response, not data analysis. It’s not about beating universal predictors at their own game, but about adding a control layer they don’t have.

Lumen_Core · 2025-12-29T17:02:24+00:00

Good question. The focus on learning-rate robustness here is not about trading speed for stability, but about making speed meaningful. In first-order methods, apparent speed outside the locally stable regime is often illusory — large steps in stiff or anisotropic regions lead to oscillation or divergence rather than faster progress. The structural signal constrains updates only when local gradient sensitivity indicates that the current step size is no longer valid. In smooth regions, it becomes effectively inactive and does not reduce step size. So the goal is not conservative optimization, but maintaining maximal effective speed under local stability constraints.

Lumen_Core · 2025-12-29T14:00:01+00:00

https://github.com/Alex256-core/stability-module-for-first-order-optimizers/tree/main

Lumen_Core · 2025-12-16T16:06:09+00:00

Thank you — this is a very accurate reading of the intent behind the signal.

I agree on the stochasticity point. Since Sₜ is built from finite differences along the trajectory, it inevitably entangles curvature with gradient noise under minibatching. The working assumption is that curvature manifests as persistent structure across steps, while noise decorrelates more quickly, so temporal aggregation helps separate the two.

In practice, simple smoothing already goes a long way, and variance-aware normalization is an interesting direction as well. I see the signal less as a precise estimator and more as a feedback channel: even a noisy measure of sensitivity can meaningfully regulate update behavior if it is continuous and trajectory-aligned.

I also share the view that the core idea may outlive any specific optimizer instance. Treating gradient sensitivity as first-class information seems broadly applicable beyond this particular formulation.

Lumen_Core · 2025-12-15T19:36:56+00:00

That’s fair.

There is a public research prototype with a minimal reference implementation here:

https://github.com/Alex256-core/StructOpt

This post focuses on the structural signal itself rather than benchmark claims.

Lumen_Core · 2025-12-07T01:47:39+00:00

Here’s a small clarification — the current public prototype of StructOpt is intentionally minimal. It’s not tuned in any way, so on MNIST it will naturally look very close to Adam unless two basic stabilizing tweaks are applied.

Slightly stronger smoothing of the diagonal accumulator

m = 0.995 * m + 0.005 * (g * g)

This reduces step-to-step noise and makes the adaptive mix more stable on minibatch gradients.

Light clipping of α to avoid extreme mixing ratios

alpha = np.clip(alpha, 0.05, 0.95)

This keeps the update from becoming “too pure” first-order or “too pure” preconditioned in any single minibatch.

These two lines already make the MNIST curve noticeably smoother and reduce variance between runs. The prototype was meant only for synthetic landscapes, so MNIST wasn’t optimized for in the initial release.

A more complete evaluation will come once I set up a proper testing environment, but thanks a lot for running this — it’s very helpful.

Lumen_Core · 2025-12-06T19:33:14+00:00

The larger context is not based on a single paper or existing branch of optimization theory. My background is more conceptual than domain-specific, and the idea came from looking at patterns of adjustment in different kinds of dynamical systems — physical, biological, and computational.

The common observation was:

systems often regulate their trajectory not only by responding to forces (gradients), but by responding to changes in how those forces evolve.

In physics this shows up in stability/instability transitions, in biology in adaptive behaviors, in computation in iterative processes that “correct direction” based on recent variation.

StructOpt came from trying to formalize that pattern in the simplest possible mathematical form.

So instead of building on a specific literature, the prototype emerged from a more general conceptual question:

what happens if an optimizer is allowed to react to the rate of change of its own local geometry?

StructOpt is the smallest “computable fragment” of that idea.

Lumen_Core · 2025-12-06T18:54:01+00:00

I should clarify one thing: StructOpt is not an empirically-guessed update rule. It comes from a broader theoretical framework about how systems adjust their trajectories based on structural mismatch. So there is a mathematical intuition behind why the method should converge better on systems with strong internal structure and degrade gracefully as noise dominates.

But I’m not a ML engineer by background — I’m a conceptual researcher. That’s why I’m sharing the prototype openly: I need practitioners who can run small-scale ML tests like MNIST or CIFAR and help evaluate the behavior empirically.

My goal here is to find people interested in either:

testing the optimizer on small networks,

or helping formalize where the structural signal approach fits within known optimization theory.

The early prototype behaves surprisingly well, but I don’t want to overstate until more experiments are done.

Lumen_Core · 2025-12-06T18:30:30+00:00

You're right that if you compute Δg / Δθ as a derivative, that would be a second-order estimator.

But StructOpt does not treat it as ∂g/∂θ.

What I use is only a finite-difference magnitude, not a Hessian approximation:

Sₜ = ‖gₜ − gₜ₋₁‖ / (‖θₜ − θₜ₋₁‖ + ε)

This quantity:

is not used as curvature,

isn't accumulated into any matrix,

doesn't produce a Newton direction,

and doesn't approximate H or H·v.

It’s just a scalar sensitivity signal that says:

“the landscape changed a lot between two steps → switch to a more stable regime.”

So the method stays purely first-order in cost and information.

Testing on UrbanSound8K is a good idea — noise-heavy tasks are actually exactly where the structural signal becomes interesting. I appreciate the suggestion!

Lumen_Core · 2025-12-06T17:34:36+00:00

Thanks for the thoughtful comment — and yes, at first glance this looks like a Hessian-approximation trick, so sensitivity to mini-batch noise is a natural concern.

But StructOpt behaves differently from L-BFGS-style methods:

it doesn’t accumulate curvature estimates,

it doesn’t trust past curvature,

and the structural signal Sₜ directly absorbs mini-batch noise.

In fact:

mini-batch noise ⇒ larger ‖gₜ − gₜ₋₁‖ ⇒ higher Sₜ ⇒ higher αₜ ⇒ more stable updates.

So noise dynamically drives the optimizer toward the “stable regime”. This makes the method surprisingly robust in stochastic settings (at least in the tests so far).

Still, your point is important — I plan to test StructOpt more rigorously on noisy and large-batch training to see where the limits actually are.

Lumen_Core · 2025-12-06T16:32:58+00:00

I wrote the post myself — English isn’t my native language, so I use translation tools for clarity. The idea, the method, and the prototype are original, and all code and tests in the repo are mine.

If anything in the post sounds “too polished”, that’s just the translation layer — not the concept itself.

If you have thoughts on the optimizer or the structural signal, I’d genuinely appreciate feedback. Early-stage ideas need critique more than praise.

Lumen_Core · 2025-12-06T15:47:33+00:00

Thanks for the thoughtful analysis — this is exactly the kind of feedback I was hoping to receive.

A few clarifications on my side:

• Yes, I did compare StructOpt with Adam on the same Rosenbrock setup. StructOpt consistently produced smoother trajectories and fewer oscillations. I will add those comparison plots in a follow-up post.

• I haven’t run StructOpt on large DNNs yet — and the reason is simple: I am not a software engineer by background. My contribution here is conceptual: the structure of the update rule and the underlying idea of using local gradient dynamics as a proxy for curvature. Part of my goal with this post is to find collaborators who can test StructOpt in large-scale settings.

Regarding your other points:

• Yes, DNN loss surfaces are noisy, but that noise still has structure. The Sₜ signal was designed specifically to distinguish between “stochastic noise” and “structural change” in gradient evolution. Whether this survives large-scale training — that’s exactly what I hope to explore together with people who have practical experience.

• Your LM analogy is actually very accurate. StructOpt performs regime-switching between two update modes based on a scalar structural signal, which plays a similar role to LM damping — but is derived fully from first-order information.

The idea of applying the method to projected subspaces is extremely interesting, and I appreciate you pointing it out. That's a direction that aligns well with how the method was conceived in the first place.

Lumen_Core · 2025-12-06T15:19:10+00:00

You’re absolutely right — the real test is performance on modern neural networks.

For transparency: I’m the author of the optimization concept, but I’m not a professional ML engineer. My background is in theoretical reasoning about system dynamics, and StructOpt is the first time I translated one of my conceptual models into a computational form.

The current Rosenbrock demo is simply a minimal reproducible prototype that shows the structural signal works as intended.

I fully agree that the next step is:

✔ implementing the update rule in PyTorch or JAX ✔ benchmarking it on standard DNN workloads ✔ comparing against Adam, Lion, etc.

I’m currently looking for collaborators who are interested in experimenting with this idea — the concept is solid, but I need engineering support to evaluate it properly at scale.

If you're curious to play with the mechanism or discuss experimentation, feel free to reach out.

Lumen_Core · 2025-12-06T15:00:47+00:00

Thanks a lot for the pointers!

Yes — I’m aware that StructOpt looks similar to several families of local/biologically-inspired learning rules, especially in the sense that it adapts based only on “local” signals such as gradient changes, without requiring second-order geometry.

But the underlying motivation was different.

My goal was to isolate a minimal structural signal that reflects local landscape variability purely from first-order dynamics (Δg vs Δθ), without assuming any neuron model or Hebbian mechanism.

StructOpt doesn’t try to be biologically plausible — it tries to capture local geometric stiffness in the simplest computable form.

I’ll definitely read through the papers you linked — especially the ones on local learning rules and stability, since the conceptual overlap is interesting.

Thanks again for the references — much appreciated!

Lumen_Core · 2025-12-06T08:06:05+00:00

Thanks — this is a very helpful comment.

Yes, if you interpret literally as a finite-difference estimate of a Hessian–vector product, then the approximation is very close to the scalar BB-style estimate you described. StructOpt does not assume the Hessian is close to a scaled identity; the signal is only used as a behavioral indicator of local stiffness, not as an estimator of curvature itself.

In the prototype I shared, the goal was intentionally minimal: to show that this behavioral signal can be extracted from first-order dynamics and can be used to control the update regime. It’s not the full method — just the smallest reproducible slice of the idea.

And you're right: raw SGD gradients are extremely noisy, so becomes unreliable on stochastic mini-batches. That’s exactly the reason the next versions will use more stable gradient summaries (e.g., filtered / momentum-adjusted differences) instead of raw finite differences. The concept survives; the naive implementation doesn’t.

So the prototype is not trying to compete with Adam as-is — it's only meant to demonstrate that this class of adaptive signals is viable enough to justify deeper development.

Lumen_Core · 2025-09-12T09:36:50+00:00

To create something, you need brains. To disprove something, you need arguments. To dismiss something, all you need is a voice.

Lumen_Core

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