pθ(x) = exp(-Eθ(x)) / Zθ
Zθ = Σx exp(-Eθ(x)).

∇θ L = E_data[∇θ Eθ(x)] − E_model[∇θ Eθ(x)].

F(x) = -log ∫ exp(-E(x,z)) dz

∇x log p(x) = -∇x E(x).

E_data[ 1/2 (∂x log pθ(x))² + ∂²x log pθ(x) ].

E_total(x) = E_A(x) + λ E_B(x).

Advanced Technical Expansion | Normalisation, Sampling, Score Fields and Decision-Safe Energy Models

The first part of this article establishes the core distinction: energy is a compatibility landscape, not a universal confidence number. This expansion develops the consequences. It derives the statistical identities that make EBMs trainable, separates mode finding from probability mass, explains why negative sampling is part of the learned semantics, and turns modern score-based, contrastive, latent and joint-embedding methods into one auditable family without pretending they are the same algorithm.

A. Energy models belong to a larger exponential-family idea

A Gibbs model has the form pθ(x)=exp(-Eθ(x))/Zθ. This is an exponential-family-like representation in which negative energy plays the role of an unnormalised log density. The partition function Zθ converts local scores into globally consistent probabilities.

This viewpoint makes two freedoms visible. First, adding a constant to all energies changes neither probability nor ranking. Second, multiplying all energies by a positive scale changes the sharpness of the distribution unless temperature is adjusted. A representation can therefore preserve ordering while altering probabilistic calibration.

Any downstream system using an energy value should specify which invariances of the number are acceptable. Ranking tasks care mostly about order. Probabilistic tasks care about differences and scale. Cross-model thresholding may require explicit calibration because separate models can choose different gauges and temperatures.

B. The partition function is a global coupling term

For a continuous state, Zθ=∫exp(-Eθ(x))dx. Changing energy in one region changes the normalisation of probability everywhere. This is why likelihood training is global: lowering data energy without compensating elsewhere can increase the partition function and reduce the gain.

The partition function also decides whether the density exists. If E(x) stays bounded as ||x||→∞, the integral over an unbounded space can diverge. A neural scalar function is not automatically a valid negative log density. Tail behaviour is a modelling assumption.

When a method uses energy only as an unnormalised compatibility score, this may be fine. The article or system should then avoid claiming a normalised generative density unless normalisability has been established or the state space is bounded.

C. Differentiate log Z and the negative phase appears

The derivative of the log partition function gives the model expectation that makes maximum-likelihood EBM training difficult. Starting from

Zθ = ∫ exp(-Eθ(x)) dx,

differentiate under suitable regularity conditions:

∇θ log Zθ
= (1/Zθ) ∫ -∇θEθ(x) exp(-Eθ(x)) dx
= -E_{pθ}[∇θEθ(x)].

For data negative log likelihood, the gradient becomes the data expectation minus model expectation. This identity is not merely algebra. It tells us what every approximation is trying to replace: a global average under the model’s current distribution.

Contrastive divergence approximates it with short-run samples. Persistent chains approximate it with longer-lived Markov states. Importance methods reweight samples. Score matching removes the partition function from the objective through derivatives with respect to x. Adversarial approaches replace sampling with learned proposal mechanisms. The methods differ in how they approximate the missing global term.

D. Free energy marginalises hidden explanations instead of choosing one

For observed x and latent z, define a joint energy E(x,z). The marginal probability of x sums or integrates over all z. Its negative log unnormalised probability defines a free energy:

F(x) = -log ∫ exp(-E(x,z)) dz.

The log-sum-exp structure is a soft minimum. If one latent explanation has much lower energy than all others, free energy approaches that minimum. If many explanations have similar energies, their combined mass can dominate even when none is individually best.

This creates a precise warning for interpretability: argmin explanation and marginal evidence are different objects. A system that returns one latent state should not imply the alternatives have negligible posterior mass unless that has been measured.

E. Softmin temperature exposes the transition between choice and uncertainty

Consider F_T(x)=-T log Σ_z exp(-E(x,z)/T) for discrete z. At low temperature, the minimum-energy explanation dominates. At higher temperature, a broader set of explanations contributes. Temperature therefore changes how aggressively the model converts compatibility differences into choice.

The same mathematics appears in softmax classification, entropy-regularised control and probabilistic structured prediction. Reporting temperature or logit scaling is necessary when energy is used as confidence. Two systems can have identical rankings and very different entropy.

Calibration should be measured on held-out data. Temperature can correct sharpness without fixing ranking errors or distribution shift.

F. Mode, mean, median and sample answer different receiver questions

The minimum-energy state is a mode under a Gibbs interpretation. A posterior mean can lie between modes and correspond to no plausible state. A median optimises a different loss. A random sample preserves uncertainty but is not necessarily the safest or highest-utility decision.

For multimodal future prediction, one deterministic low-energy future hides alternatives. For image generation, diversity requires exploring multiple modes. For control, the expected-cost optimum may differ from the most probable action. Decision theory sits above the energy landscape.

Do not ask an energy model for “the answer” without specifying the decision rule applied to its landscape.

G. Markov chain Monte Carlo is a family of transition kernels, not one sampler

MCMC constructs a Markov chain whose stationary distribution is the target under suitable conditions. Random-walk Metropolis proposes local moves and accepts them according to density ratios. Langevin methods use energy gradients to propose moves toward higher-probability regions plus noise. Hamiltonian Monte Carlo introduces momentum to travel further through smooth landscapes.

The best method depends on dimension, curvature, differentiability, multimodality and cost of evaluating gradients. A low-dimensional smooth EBM can benefit from gradient-informed proposals. A rugged multimodal landscape can trap all local methods.

Sampler choice is part of training semantics when samples define the negative phase. A model trained against a poorly mixing sampler is shaped partly by the sampler’s blind spots.

H. Detailed balance is useful, but stationarity and mixing are separate questions

Many MCMC kernels are designed to satisfy detailed balance with the target distribution, which implies stationarity. This does not tell us how quickly a finite chain approaches that distribution. A chain can be theoretically correct and practically useless because mixing time is enormous.

Diagnostics should therefore include multiple chains, between-chain variation, autocorrelation, effective sample size, mode visitation and task-specific observables. Acceptance rate is only one statistic.

When EBMs are trained with short chains, the model may adapt to the non-equilibrium distribution the sampler actually produces. This can still yield useful generators or representations, but the result should not be described as exact maximum likelihood.

I. Persistent chains remember the model and can also remember their mistakes

Persistent contrastive divergence maintains Markov-chain states across parameter updates rather than restarting near data every time. In principle this allows chains to wander through the model distribution more fully. In practice, the target distribution is moving because θ changes during training.

Replay buffers can improve diversity and reduce burn-in cost. They can also become stale, overrepresent old modes or fail to discover new regions. Refresh strategies, random restarts and buffer diagnostics matter.

Record how negative states are initialised and updated. Two “same objective” experiments with different replay dynamics can learn very different energy landscapes.

J. Annealed importance sampling estimates ratios by building a path between distributions

Estimating the partition function of a complex EBM can be approached through annealed importance sampling. Start from a tractable base distribution and define intermediate distributions that gradually introduce the target energy. Samples are transported through this sequence while accumulating importance weights.

If adjacent distributions overlap sufficiently and transition kernels mix adequately, AIS can estimate the ratio of normalising constants. If the path changes too rapidly, weights become highly variable and the estimate degrades.

The method is computationally expensive but valuable for evaluation on models where likelihood matters. It reminds us that “intractable normalisation” is not always “impossible to estimate”; it is a resource and variance problem.

K. Importance sampling fails visibly when a few weights carry almost everything

Importance sampling estimates expectations under a target using samples from a proposal and weights proportional to target density divided by proposal density. If the proposal misses important target regions, most weights are near zero and a few dominate.

Effective sample size gives one diagnostic. Inspect maximum weight, weight entropy and repeated estimates. A numerically reported likelihood based on degenerate weights can be far less reliable than its decimal places imply.

Proposal quality is therefore part of evidence. Bridge sampling and annealed paths attempt to reduce mismatch by connecting distributions through overlapping stages.

L. Noise-contrastive estimation turns an unnormalised model into a classification problem

NCE mixes data samples with samples from a known noise distribution. A classifier is trained to decide whether a sample came from data or noise. The optimal log-odds depend on the data density relative to noise density, so an unnormalised model can be fit without summing over the entire state space directly.

The noise distribution must cover the relevant data support. If noise is trivially different, the classification problem is easy but provides little information about fine density structure. The ratio of noise to data samples affects estimator variance.

Modern contrastive learning shares family resemblance with NCE but should not be equated automatically. Some objectives learn representations and pairwise compatibility without intending to recover a normalised data density. The receiver contract decides whether density estimation is actually part of the claim.

M. Negative sampling creates a local universe of alternatives

Every contrastive batch implicitly defines a candidate universe. If the positive is compared only against random unrelated negatives, the energy need only separate those cases. It can ignore distinctions never challenged by the batch.

Hard-negative mining expands the local universe toward confusable states. But mining from the current model can create feedback loops: the model repeatedly focuses on its own mistakes, potentially amplifying annotation errors or rare pathologies.

Document negative provenance. A compatibility score is best understood as “low relative to the negatives and objective that shaped it”, not as an absolute semantic distance independent of training context.

N. InfoNCE-like objectives can be read as relative-energy objectives without becoming full EBMs

In many contrastive objectives, a similarity score between a query and candidates is exponentiated and normalised over the candidate set. Defining energy as negative similarity gives a finite Gibbs distribution within the batch or sampled candidate set.

This does not automatically define a density over all possible inputs. It defines relative compatibility within the sampling process. Temperature shapes the softness of competition. Batch composition changes the denominator and therefore the learning signal.

This local-normalisation perspective is useful because it connects metric learning and EBMs while preserving the boundary between conditional contrast and global density modelling.

O. Score matching removes Z by differentiating with respect to the state, not the parameters

The reason score matching avoids the partition function is structural. log pθ(x)=-Eθ(x)-log Zθ. The partition function depends on θ but not x, so ∇_x log Zθ=0. State derivatives see only the energy surface.

Hyvärinen’s objective compares model and data score fields. Integration by parts replaces the unknown data score with divergence and squared-norm terms involving the model. Boundary conditions matter: surface terms must vanish or be handled appropriately.

This is why generalized score matching is needed for constrained supports such as non-negative data. The mathematics of the boundary is part of the estimator, not a technical footnote.

P. Stein identities offer another route to checking score fields

Stein’s identity relates expectations of score functions and derivatives of test functions under suitable conditions. It provides discrepancy measures that can compare a model score with data samples without knowing the normalising constant.

Kernel Stein discrepancies and related tools can diagnose whether a score-based model matches a target distribution under a chosen function class. As always, finite-sample power and kernel choice determine which discrepancies are visible.

The broader principle is recurring: unnormalised models can be evaluated through local differential identities, but each identity has assumptions and a sensitivity profile.

Q. Denoising score matching changes the target to the score of a corrupted distribution

Add Gaussian noise with known variance to clean data. The corrupted distribution is smoother and has full support under common conditions. A model can learn the score of this noised distribution from pairs of clean and noisy samples.

At large noise, the score field captures coarse global structure. At small noise, it captures fine detail but becomes harder to estimate near a thin data manifold. Training across noise scales creates a hierarchy of score fields.

Generation then uses a schedule that moves from high-noise easy structure toward low-noise detailed structure. This connects representation scale, density estimation and sampling in a way a single fixed energy landscape may not.

R. Diffusion and score models share mathematics without requiring one naming convention

Many diffusion parameterisations learn noise, clean data, velocity-like variables or scores under related transformations. Conversions depend on the forward corruption schedule. The model may never expose an explicit scalar energy E(x).

Calling every diffusion model an EBM can obscure these implementation differences. A better hierarchy is: both can model distributions through local information related to log-density gradients, while explicit-energy models and direct score parameterisations expose different objects and training procedures.

The public claim should name the learned object: scalar energy, score vector field, denoiser, noise predictor or compatibility function.

S. Integrability asks whether a learned vector field really comes from one scalar energy

An explicit energy automatically produces a conservative score field -∇E. A separately parameterised vector field is not guaranteed to be the gradient of any global scalar. In a simply connected smooth domain, a necessary local condition is symmetry of appropriate cross-partials: curl-like components should vanish.

Direct score training can work without ever constructing a scalar energy, so non-integrability may or may not matter to the receiver. If energy composition or global potential interpretation is required, it matters greatly.

Test loop integrals or Jacobian antisymmetry in controlled settings. “Score model” and “energy model” are close relatives, not always identical data structures.

T. Structured energies make constraints visible but inference can become the bottleneck

Suppose E(y|x) decomposes into unary terms for individual labels and pairwise terms for neighbouring labels. This explicit structure can encode smoothness, compatibility or grammar. But finding the minimum-energy y can be combinatorial.

Some structures permit exact dynamic programming or message passing. Others require approximate search, relaxations or learned inference networks. Training must account for the inference procedure actually used at deployment.

An exact energy with approximate inference is a different system from an approximate energy with exact inference. Error budgets should separate model error from search error.

U. Latent-variable EBMs can represent multiple explanations and can hide them behind one free-energy number

Latent variables increase flexibility because several hidden configurations can explain one observation. They also make interpretation harder. A low free energy can arise from one extremely good latent state or from many moderately good states.

When the hidden state is meaningful—pose, object assignment, parse tree, future trajectory—inspect the posterior over z rather than only the marginal free energy. Multimodality can be operationally important.

Posterior collapse has an energy analogue: the model can ignore a latent variable if other terms explain data well enough. Track mutual information or usage statistics for latent state.

V. Compositional energies need a common scale and compatible semantics

Adding energies is attractive because independent constraints can be combined without retraining one monolithic model. But energy units are learned. If one module outputs values in a range of hundreds and another in tenths, the first dominates irrespective of semantic importance.

Calibrate scales through temperature, validation objectives or probabilistic interpretation. Check gradient direction as well as scalar magnitude: two energies can pull the state in conflicting directions.

Composition also assumes the factors can be multiplied like experts without double-counting shared evidence. Two modules trained on overlapping signals can produce overconfident products. Independence assumptions should be treated as assumptions.

W. Mixture and product answer different uncertainty stories

A product-of-experts says states should satisfy several constraints simultaneously. A mixture says there are alternative explanatory components and a state can be supported by any one of them. Products sharpen intersections; mixtures preserve multiple modes.

Confusing these operations can erase uncertainty. If two plausible future modes should remain alternatives, adding their energies as if both must be satisfied can favour an implausible compromise or reject both.

Write composition semantics before combining models: AND, OR, weighted preference, hard constraint or fallback. The algebra follows the intended logic.

X. Classifier energy needs gauge-aware OOD calibration

Softmax classification is unchanged if a function c(x) is added to every logit. Any OOD score built from absolute logits or energies can change under that transformation even though class probabilities stay identical. Training conventions usually fix a practical gauge implicitly, but the freedom matters conceptually.

OOD calibration should therefore be empirical on the deployed model, not inferred from softmax semantics. Compare energy score with maximum softmax probability, entropy and dedicated OOD baselines across several shift types.

Thresholds should be version-specific. Retraining can move energy distributions while preserving classification accuracy.

Y. Out-of-distribution is a family of hypotheses, not one negative class

Near-OOD samples differ subtly from training data. Far-OOD samples may be unrelated. Covariate shift changes inputs while preserving label semantics. Concept shift changes the mapping itself. Adversarial inputs target the model. Open-set recognition introduces new classes.

One scalar energy can rank these families differently. A detector tuned on random noise may fail on unseen but semantically similar classes. A detector tuned on class novelty may flag harmless sensor changes.

Build an OOD matrix with operationally relevant shifts and report per-shift detection. “OOD accuracy” without a shift definition is too broad to guide decisions.

Z. Energy margins should be evaluated, not just positive/negative ordering

If positives have energy 0.9 and negatives 1.0, ranking is correct but fragile. A tiny perturbation can reverse the order. Larger margins can improve robustness but can also encourage overly confident separation and distort geometry.

Plot the distribution of positive-negative energy gaps by subgroup and difficulty. Evaluate perturbation sensitivity. For retrieval, measure ranking metrics. For decisions, map margins to empirical error rates rather than assuming a universal threshold.

Compatibility is useful because it is relative. The magnitude of the relation still needs evidence.

AA. Energy geometry can reveal adversarial directions

The gradient ∇_xE(x) shows a local direction of increasing energy; -∇E points toward locally lower energy. An adversary can exploit gradients to find small input changes that lower the energy of an incorrect state or raise the energy of the correct one.

Robustness tests should therefore include constrained perturbations. Compare energy changes under random and adversarial directions. Inspect Hessian or local Lipschitz measures where practical. Flatness near data can improve tolerance and can also blur distinctions.

A smooth landscape is not automatically a correct landscape. Robustness and discrimination remain a trade-off.

AB. Replay-buffer diversity is a representation-health metric for training negatives

If a replay buffer collapses to a few modes, the model’s negative phase becomes narrow. Track pairwise diversity, clustering, nearest-data distance and age of samples. Visual inspection alone can miss duplicate or near-duplicate negatives.

Refresh a fraction from noise or data perturbations, compare short-run and persistent negatives, and measure how training changes if the buffer is reinitialised. If the model’s apparent performance depends heavily on one buffer trajectory, reproducibility is weak.

The buffer is part of the learned system state and should be included in continuation checkpoints.

AC. Adversarial negative generators replace one sampling problem with a two-player learning problem

One way to avoid expensive MCMC is to train a generator or proposal network to produce challenging negative samples. The energy model learns to distinguish data from generated negatives; the generator learns to find low-energy regions or fool the energy.

This can improve scalability, as explored in recent adversarial EBM work. But generator mode collapse, game instability and support mismatch become new failure modes. The proposal can ignore regions the energy then never learns to raise.

Evaluate generator coverage independently. Adversarial efficiency does not remove the need to ask which parts of the state space were actually contrasted.

AD. Energy model fusion creates a policy-combination problem

Energy-based fusion can combine preferences or competencies from several models. For decisions, one model may score task success, another safety margin, another style or resource use. Combining them creates a new policy landscape.

Calibration, conflicting minima and missing constraints become central. If one energy was never trained on states proposed by another, extrapolated scores can be meaningless. Fusion needs cross-model validation on the composed state distribution.

Recent decision-fusion work such as EMFuse should therefore be read as a method with an evaluation boundary, not a generic permission to add arbitrary model scores together.

AE. JEPA-style latent energy needs an anti-collapse story and a target-space story

If context representation c is used to predict target representation t, a simple energy might be a distance between predicted and target embeddings. Low energy says the latent structures match. But if all targets collapse to the same vector, prediction becomes trivial.

The method therefore needs a mechanism that keeps target representations informative. It also needs a reason the target space preserves semantics rather than nuisance detail. The energy is only as meaningful as the representation on which it is defined.

This links JEPA, collapse prevention and representation design. Compatibility learning cannot escape the question of what deserves to be compatible.

AF. A low latent prediction energy does not imply a good world model

A world model must represent how state changes under actions and uncertainty. Predicting a nearby latent target can succeed through correlations that fail under intervention. The model can learn a compatibility landscape without causal transition semantics.

Test action-conditioned rollouts, counterfactual interventions and long-horizon compounding. Separate observation prediction from controllable dynamics. If several futures are possible, preserve multiple low-energy trajectories rather than averaging them into one latent point.

Energy provides a flexible objective for world-state compatibility; causality and control still require their own evidence.

AG. Physical energy and learned energy should never be conflated silently

In physics, energy has units, conservation relationships and operational measurement. In machine learning, “energy” is often any scalar where lower means more compatible. The analogy is mathematically productive and semantically dangerous.

If a learned molecular potential is trained to approximate physical energy, units and derivatives matter. If a text-image model uses an arbitrary compatibility energy, joules have nothing to do with it. A public explanation should say which meaning applies.

The safest phrase is “energy score” or “learned energy” when the scalar has no physical unit.

AH. The energy evidence card

• Variables: what state or pair does the energy score?
• Semantics: ranking, negative log density, constraint, distance, physical potential or compatibility.
• Gauge: which shifts or scales leave the relevant decision unchanged?
• Normalisation: exact, estimated, local candidate normalisation or none.
• Training rule: likelihood, contrastive, NCE, score matching, adversarial or predictive.
• Negatives: how alternatives were sampled.
• Sampler: MCMC/proposal details and mixing diagnostics if used.
• Latents: marginalisation versus argmin and multimodality.
• Calibration: how energy maps to error probability or threshold decisions.
• Composition: AND/product, OR/mixture, weighted preference or hard constraint.
• OOD scope: which shift families were tested.
• Robustness: margins, perturbations and adversarial response.
• Authority: which decisions remain outside the learned score.
• Versioning: whether thresholds remain valid after retraining.

AI. Worked laboratory: exact four-state likelihood gradient

Define four states with energies linear in θ. Compute Z, exact probabilities and the negative log likelihood for a chosen empirical data distribution. Differentiate analytically and with automatic differentiation. Verify that the result equals the difference between data and model expectations of the energy gradient.

Then perturb θ and use finite differences. This triangulates the sign and implementation. A neural EBM should not be trusted before this tiny reference case passes.

AJ. Worked laboratory: mode versus mass in a simple discrete model

Create one state with energy zero and one hundred states with energy one. The single minimum-energy state has the best individual score, but the hundred slightly worse states can carry more total probability mass depending on temperature.

This demonstrates why MAP explanation is not posterior mass. The effect grows with the number of alternatives. Latent combinatorics matter.

AK. Worked laboratory: two-well MCMC and false reassurance from acceptance rate

Use an energy with two separated quadratic wells. Run random-walk Metropolis with a very small proposal standard deviation. Acceptance can be high while the chain remains in one well. Increase proposal size: mode jumps become possible but rejection grows. Run several chains from different wells and compare.

Compute autocorrelation and effective sample size for an indicator of which well the chain occupies. The exercise converts “mixing” from a vague concern into a measurable property.

AL. Worked laboratory: score field of a Gaussian mixture

For a one-dimensional Gaussian mixture, calculate the density and its derivative exactly, then compute ∂x log p(x). Plot the score. It points toward nearby high-density regions but passes through zero at modes and also at some stationary structures depending on the mixture.

Integrate the score numerically up to a constant and recover log density in one dimension. This shows the relationship between local field and global energy where integrability is guaranteed.

AM. Worked laboratory: product versus mixture of two constraints

Define two one-dimensional Gaussian preferences centred at -2 and +2. A mixture has two modes, representing alternatives. A product has one mode near the overlap, representing simultaneous satisfaction. Plot both. The algebra makes “OR” versus “AND” visible.

Then change the variance or energy scale of one expert and observe dominance. Composition requires calibration because multiplication amplifies confidence.

AN. Worked laboratory: OOD thresholds across several shift families

Train a simple classifier on two classes and derive an energy score from logits. Create near-OOD points between classes, far-OOD points far from both, label-shifted points and adversarial perturbations. Plot score distributions for each.

A threshold chosen on far-OOD may perform poorly on near-OOD. Report AUROC and operating points separately. The experiment shows why “OOD” must be typed by shift.

AO. Worked laboratory: local energy margin versus perturbation robustness

Construct positive and negative candidates with known energy gaps. Add bounded perturbations to inputs and measure how often rankings flip. Compare models with similar ranking accuracy but different margins and gradient norms.

This reveals that a clean ranking on static examples is not the same as a stable compatibility boundary.

AP. Decision safety: energy should enter a bounded control stack

A learned energy can rank actions, plans or outputs. It should not silently become the final authority for irreversible or safety-critical execution. Hard constraints, permissions, legal rules, resource limits and human confirmation can sit outside the learned landscape.

The control stack can treat energy as one proposal signal. Candidate generation produces alternatives; the EBM ranks compatibility; a constraint solver rejects inadmissible states; uncertainty checks detect unsupported regions; an authority layer approves or denies execution.

This design preserves the value of flexible learned preferences without asking one scalar to carry responsibilities it was never trained to represent.

AQ. Versioning and calibration drift

Retraining an EBM can shift the entire energy distribution while preserving task accuracy. A threshold of 3.2 that once separated familiar and unfamiliar data may become meaningless. Negative sampling changes can also change margin scale.

Version thresholds with the model. Recalibrate after architecture, data, temperature or objective changes. Store score histograms on reference datasets as regression artefacts.

An energy interface is a protocol. Protocols need compatibility tests.

AR. Final audit: when does an energy claim deserve release?

1. The scored variables and candidate universe are explicit.
2. Low energy has a stated semantic meaning.
3. Gauge and temperature freedoms are understood.
4. Normalisation claims match the estimator actually used.
5. Positive and negative phases or their substitutes are documented.
6. Negative sampling covers the distinctions claimed.
7. Sampler mixing is tested when model samples matter.
8. Latent alternatives are marginalised or exposed according to the receiver job.
9. Score fields are not mislabelled as calibrated probabilities.
10. OOD thresholds are tested across named shift families.
11. Composed energies have calibrated scales and explicit AND/OR semantics.
12. Representation collapse is checked.
13. JEPA-style compatibility is not overclaimed as pixel generation or causal world modelling.
14. Decision authority remains bounded by hard constraints and permissions.
15. Thresholds and calibration are versioned across retraining.

Energy-based representation learning is powerful because it can separate the question “how well do these pieces fit?” from the much harder demand to enumerate every possible world. That flexibility is the source of its breadth and the source of its interpretive risk. A low energy can mean high relative compatibility, a high unnormalised density, a small learned distance, a satisfied constraint or a good latent prediction depending on the system. The mature discipline is to preserve that flexibility while naming the meaning precisely. The landscape is useful when its valleys correspond to the distinctions the receiver needs, its unexplored regions are visible, and its scalar score never quietly acquires authority beyond its evidence.