Cognitive Ideation

When David Campbell published “Nonlinear Science from Paradigms to Practicalities” in the Los Alamos Special Issue of 1987, only large mainframes had computing power sufficient for in-depth research. His first sentence honors the work of Stanisław Ulam: “No tribute to the legacy of Stan Ulam would be complete without a discussion of ‘nonlinear science,’ a growing collection of interdisciplinary studies that in the past two decades has excited and challenged researchers from nearly every discipline of the natural sciences, engineering, and mathematics.”

Modern systems based in neural network technologies are nonlinear solutions where the learned weights inside the architecture attempt to approximate a function. Sometimes the function is easily approximated with excellent accuracy and well understood limits. The use of the black box neural network approach requires certain assumptions to be true from the outset, such as the signal magnitude correlates to significance. In chaotic systems, the exact present determines the exact future, whereas the inexact present does not determine the inexact future. And the training set must be a useful representation of the problems being solved. Once any of these assumptions are false, the loss of fidelity and robustness presents in a nonlinear way.

Black box approximation assumes the system is well understood and properly quantized. It also assumes that the distribution is usefully normal. But what if that is simply not the nature of the problem which is being solved?

David Campbell went on to say in The Future of Nonlinear Science:

“At a fundamental level, issues such as the scaling structure of multifractal strange sets, the basis for the ergodic hypothesis, and the hierarchy of equations in pattern-forming systems remain unresolved. On the practical side, deeper understanding of the role of complex configurations in turbulent boundary layers, advanced oil recovery, and high-performance ceramics would provide insight valuable to many forefront technologies. And emerging solutions to problems such as prediction in deterministically chaotic systems or modeling fully developed turbulence have both basic and applied consequences… If, however, one had to choose just one area of clearest future opportunity, one would do well to heed another of Stan Ulam’s well-known bons mots: ‘Ask not what mathematics can do for biology, Ask what biology can do for mathematics.’”

He rightly suggested that most useful and interesting problems are by nature nonlinear.

Gestalt Artificial Intelligence represents a workable technology which addresses “prediction in deterministically chaotic systems.”

Small Momentary Models

Seraphim Technology Company instead decided to look back to symbolic artificial intelligence which had some initial traction from the 1950s through the mid-1980s. All AI techniques have a common flaw at scale. The larger the feature set of an artificial intelligence model, the more washed-out signal becomes, losing both fidelity and contextual alignment. It is easy to understand that sand on a beach is pervasively present, but it is the reefs and rocks which define the beach. Too many small features are likely to become unsubstantial to the interactions of change. They exist but do not define.

In the late 1980s nonconvex designs emerged particularly using neural networks. When data sets are super large they are much harder to achieve fidelity in the model’s application. Gestalt artificial intelligence instead solves problems with small momentary models.

To overcome this problem Seraphim Technology Company shifted to momentary models. By building a model automatically in the moment using only possibilistic context with a feature set which is optimal, we avoid sand in the prediction. Gestalt AI’s input data is in context, aligned to the features of the model and reliably accurate with negligible attrition of fidelity or signal. Where other technologies are going super large, we instead went super small. This naturally avoids model errors since we never keep the model.

Algorithms, Data Structures, and Programs

Niklaus Emil Wirth wrote Algorithms + Data Structures = Programs, winning the 1984 ACM Turing Award. His work implies a clear algebra of computational approaches. The concrete Algorithms in the case of neural networks are hidden through training Data Structures as weights creating an estimation program. However, the Model as Data Structures created is not typically understandable or explainable by human effort when the features grow into several hundreds. Small Large Language Models are usually above hundreds of millions of features, making them impenetrable black-box technologies.

By contrast, Gestalt Artificial Intelligence maximizes the effect of algorithms and selects a small local region of all data to describe and solve a problem. The Program exists for a single moment, making mapping it useless since the context is unique. Also, no data is ever lost. All data exists as symbols in the momentary program. The advantage of this approach is time as both chronology and order are well understood. This means answers that are seasonal or tied to episodic data have high fidelity allowing for competitive ranking against strong structural data. The effect of ranking is contextually appropriate and resists the true but inapplicable solutions.

Momentary models are context aware. The models form based on context and affinity. They are aligned to the query data and can extrapolate reliably. Using a neural network implicitly assumes there actually is a single function to approximate, whereas we make no such assumption. The second assumption is that the aforementioned function is also a good approximation of the Program’s fidelity. Because we don’t assume but learn from a cold start and define a unique model in the moment we avoid assumptions about the system, making this approach superior to global single function solutions. Piecewise solves of the realities of the expressed data are reliably explainable using certificates of proof.

The Gestalt Database

To address the superposition of data in a dynamic system requires a unique technological development: the Gestalt Database. Typical SQL and NoSQL databases are unable to handle data in paracausal superposition. In a dataset that is chaotic, order is not relevant in global terms, only in the path of each action. To address the need for hyperscale the Gestalt Database is built on free-threaded non-locking CRUD rules. This allows tens of thousands of simultaneous changes concurrently. The ability to perform data persistence in ragged fuzzy instances allows classification to work in many simultaneous schemes without information loss.

Superposition in Ideation

Superposition in Ideation is easy to explain… the verb “run” spans meaning from physical to administrative uses all driven by context. The meaning is only deterministic when a context aligns the correct intention of the verb. The same principle exists in most nonlinear systems. Context infers the schema and the integral; the algorithm and the data structure form a program that is deterministic in a specific moment of time.

Gestalt artificial intelligence is a piecewise deterministic solve in a system for which a global algorithm may not exist – which is unsolvable for statistically global techniques.