Latent Problem Modeling: A Pragmatic Form of Artificial Intelligence

Why Latent Problem Modeling?

Instead of pursuing the broad and often vague ambition of Artificial General Intelligence (AGI)—which aims to emulate the entirety of human cognition—it may be more effective to focus on a more actionable and testable alternative: latent problem modeling.

Latent Problem Modeling can be understood as a form of world modeling, where the "world" is defined not by external physical reality, but by the structure of a given problem: its inputs, outputs, and objectives. By modeling the space of possible problems and solutions, the system constructs an internal model of the world in which it operates.

Latent Problem Modeling does not define intelligence as mimicking humans. Rather, it frames intelligence as the capacity to define a problem, understand the structure that defines it, and discover solutions within that structure. It models the latent structure of objectives, inputs, and outputs that together form a problem instance.

By centering AI research on problem-solving, this approach enables clearer goals, interpretable reasoning, and applicable outcomes. It avoids the pitfalls of anthropomorphism and philosophical abstraction while offering a concrete path for building general-purpose AI.

Latent Problem Modeling thus offers a disciplined and achievable framework for AI—one grounded not in replicating the human mind, but in understanding and solving structured problems.

Defining a Problem as a Triplet \([v, w, x]\)

To support general and systematic problem solving, we require a clear and structured definition of a problem. We propose representing any problem instance as a triplet:

\[[v, w, x]\]

\(v\): the objective to be minimized—quantifying the quality of a solution, such as loss, error, or cost.
\(w\): the output—the solution or action generated by the model.
\(x\): the input—contextual data, conditions, or observed variables describing the instance.

This formulation allows problems to be made machine-readable and learnable. Given various instances of \(x\), a system can learn to produce \(w\) that minimizes \(v\), making the structure suitable for data-driven generalization across domains.

Latent Problem Modeling of Problem Structure

At the heart of Latent Problem Modeling is the idea of learning a joint distribution over \([v, w, x]\) through a latent variable model. This can be formalized as:

\[[v, w, x] = g(z), z \sim \mathbb{D},\]

where:

\(g\) is a learnable function, typically a neural network.
\(z\) is a latent variable sampled from a distribution \(\mathbb{D}\).
The output \([v, w, x]\) forms a complete problem instance.

This generative structure aligns with existing modeling paradigms:

In GANs, \(z\) is random noise and \(g(z)\) produces data samples.
In autoregressive language models, \(z\) captures the random sampling across decoding steps.
In diffusion models, \(z\) encodes the stochastic noise path reversed by \(g\).

By modeling latent variables \(z\) that produce \([v, w, x]\), the model learns the hidden structure of the problem space—a latent problem model that captures how objectives, solutions, and conditions relate.

This goes beyond learning mappings from inputs to outputs. It internalizes the co-dependencies among all elements that define the problem environment.

Latent Problem Modeling can also be seen as a form of world modeling, where the "world" is defined by the structure of a particular problem's solution space. That is, the joint space of objectives, outputs, and inputs \([v, w, x]\) forms the world that the model learns to represent. By capturing this latent structure, the model builds an internal representation of how problems behave—how solutions relate to goals under given conditions. This perspective aligns Latent Problem Modeling with broader trends in AI that emphasize the importance of learning structured world models to enable flexible, generalizable reasoning and behavior.

Solving the Problem by Sampling-Based Inference

Once a latent problem model has been trained, solving a specific problem instance becomes a matter of sampling-based inference. Given a new input \(x\) and a known objective \(v\), the goal is to produce an output \(w\) that minimizes \(v\) under the modeled structure.

The process can be formalized as:

\[[v, w, x] = g(z), z \sim \mathbb{D}.\]

A simple form of sampling-based inference proceeds as follows:

Sample a large number of triplets \([v, w, x′]\) from the model.
Select samples where \(x′\) is most similar to the target input \(x\).
From these, choose samples with the smallest \(v\) values.
Average the corresponding \(w\) values in the final set to produce the solution.

While naive, this method demonstrates how inference can use the learned problem structure to balance relevance to the input and minimization of the objective.

Example: Simulated Motor Control

Consider a simulated motor control task implemented in MATLAB. The goal is to develop an improved controller through latent problem modeling.

Problem definition:

\(v\): the difference between the current and target motor speed.
\(x\): sensor inputs, including phase signals for estimating speed.
\(w\): voltages applied to the motor’s excitation coils.

The process begins with an unoptimized PID-based Field-Oriented Control (FOC) algorithm. This baseline controller is used to collect initial control data \([v, w, x]\), which is used to train the first version of the model.

An iterative refinement process then begins. The model samples candidate outputs \(w\) for new inputs \(x\), and these are evaluated in simulation to gather new training data. Each new generation of the model is trained on data collected from its predecessor's behavior.

Over several epochs, the resulting controller demonstrates improved performance, including lower overshoot and reduced energy cost during motor startup, without manually tuning any control parameters.

This example illustrates how latent problem modeling supports self-improving, data-driven optimization through structural learning.

Applicability and Data Considerations

This triplet formulation \([v, w, x]\) can encompass a wide range of scientific and engineering problems:

Supervised learning tasks, where \(v\) is prediction loss.
Reinforcement learning tasks, where w is an action and \(v\) is negative reward.
Control systems, design optimization, or simulation-based evaluation.

In fact, most modern AI systems fit this paradigm, including large language models (LLMs), which generate \(w\) from \(x\) to minimize language modeling loss \(v\).

This suggests that latent problem modeling is not constrained to a narrow class of tasks, but rather offers a unifying modeling view. If readers encounter examples that do not fit this formulation, feedback is welcomed to explore the framework's boundaries.

Additionally, training data need not include only optimal solutions. Including poor or failed examples can be helpful, allowing the model to learn what not to do, thereby improving its ability to minimize \(v\) effectively.

Comparison with Discriminative Formulations

It is useful to compare latent problem modeling to traditional discriminative approaches, where one might learn:

\[v = g(w, x).\]

Here, the model tries to predict the objective given a solution and an input. While this can be useful for evaluation, it often breaks down due to ambiguity. Multiple plausible objective values \(v\) may correspond to the same \((w, x)\) pair due to hidden variables, noise, or partial observability.

Even with latent variables:

\[v = g(w, x, z), z \sim \mathbb{D}\]

the formulation assumes that a well-defined objective function \(v\) always exists for every problem instance.

In practice, many tasks, such as open-ended creation or exploratory control, may lack an explicit objective. Latent problem modeling avoids this limitation by directly learning the joint distribution over \([v, w, x]\), rather than enforcing a functional dependency.

This joint modeling provides greater flexibility and robustness for real-world problem definitions.

Conclusion: A General Path for Intelligence through Latent Problem Modeling

Latent problem modeling offers a general, interpretable, and practical alternative to traditional approaches to Artificial General Intelligence.

Rather than mimicking human cognition, it aims to understand and model the latent structure of problems—the space of inputs, outputs, and objectives—and to reason within that space to generate solutions.

By embracing structure, generality, and data-driven improvement, this approach provides a coherent foundation for developing intelligent systems capable of adapting across diverse tasks.

As real-world AI applications grow in complexity, modeling the latent structure of problems, rather than minds, may be the key to achieving truly general intelligence.

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