15. Robust, Responsible and Emerging Mathematics for AI

Introduction and Context

Machine-learning systems are often evaluated as if their performance were determined by a single number, such as accuracy or mean squared error. In practice, however, an AI system operates under changing conditions, interacts with people, influences decisions, and may be deliberately attacked. A model can therefore be accurate on an average test set and still be unsafe for deployment. It may fail on minority groups, become poorly calibrated when the population changes, expose private information, or make confident predictions under severe uncertainty.

Mathematics provides the language for analysing these risks. Robustness is studied through perturbation bounds, worst-case optimisation, distributionally robust optimisation, and adversarial risk. Calibration and uncertainty quantification distinguish confidence from correctness. Fairness is expressed through group-conditioned rates and statistical constraints. Differential privacy formalises the effect of an individual record on a released output. Optimal transport gives a principled geometry for comparing probability distributions, while differential geometry and geometric learning extend machine learning beyond flat Euclidean data.

These mathematical tools do not by themselves make an AI system responsible. Responsibility also requires governance: clear purposes, documented assumptions, human oversight, monitoring, auditability, and mechanisms for contesting decisions. The central theme of this chapter is therefore the relationship between mathematical properties and institutional decisions. A small robustness bound, a fairness metric, or a privacy guarantee is meaningful only when its assumptions, scope, and trade-offs are understood.

Learning Objectives

After studying this chapter, students should be able to:

• distinguish ordinary, robust, adversarial, and distribution-shift risk;
• explain calibration, predictive uncertainty, and the difference between aleatoric and epistemic uncertainty;
• analyse common group and individual fairness metrics and their incompatibilities;
• describe the formal definition and practical trade-offs of differential privacy;
• use optimal transport concepts to compare distributions and understand domain adaptation;
• explain the role of geometry in representation learning and manifold-based modelling;
• evaluate mathematical assumptions underlying responsible AI claims;
• design a monitoring and governance framework for a deployed AI system;
• identify limitations, ethical risks, and emerging research directions.

From Average Accuracy to Risk Under Change

Let a predictor be represented by $f_\theta(x)$, with loss $\ell(f_\theta(x),y)$, and let $(X,Y)\sim P$ denote the joint data-generating distribution. The population risk is

$$R_P(\theta)=\mathbb{E}_{(X,Y)\sim P}[\ell(f_\theta(X),Y)].$$

Empirical risk minimisation replaces $P$ with a finite training sample. Its success depends on the assumption that the training and deployment distributions are sufficiently similar. If deployment follows $Q\neq P$, the relevant quantity is $R_Q(\theta)$ rather than $R_P(\theta)$. Distribution shift may affect the input distribution, the conditional label distribution, or both:

• Covariate shift: $P(X)\neq Q(X)$ while $P(Y\mid X)=Q(Y\mid X)$.
• Label shift: $P(Y)\neq Q(Y)$ while $P(X\mid Y)=Q(X\mid Y)$.
• Concept shift: the conditional relationship itself changes, so $P(Y\mid X)\neq Q(Y\mid X)$.

A useful decomposition of deployment error considers sampling variability, model approximation, optimisation error, and shift-induced error. A model may generalise well in the statistical learning sense while still failing because the deployment environment differs structurally from the training environment.

Robustness and Adversarial Risk

A model is robust when its behaviour changes acceptably under relevant perturbations. For an input $x$, an uncertainty or perturbation set $\Delta(x)$ specifies changes considered plausible or threatening. The pointwise robust loss is

$$\ell_{rob}(x,y)=\sup_{\delta\in\Delta(x)}\ell(f_\theta(x+\delta),y).$$

The corresponding robust risk is

$$R_{rob}(\theta)=\mathbb{E}_{(X,Y)\sim P}\left[\sup_{\delta\in\Delta(X)}\ell(f_\theta(X+\delta),Y)\right].$$

For an $\ell_p$ perturbation set, $\Delta(x)=\{\delta:\|\delta\|_p\leq\varepsilon\}$, the parameter $\varepsilon$ determines the threat scale. Small norm does not necessarily mean small semantic change: a tiny pixel perturbation may be imperceptible, whereas a physically meaningful change may require a larger norm.

Adversarial examples are inputs constructed to increase loss or induce a wrong prediction. In gradient-based attacks, a common first-order construction is

$$x'=x+\varepsilon\,\operatorname{sign}(\nabla_x\ell(f_\theta(x),y)).$$

This is useful for stress testing but does not represent every attacker. A robust evaluation should specify the attacker’s information, computational budget, perturbation model, and success criterion. Defensive training can minimise an approximation to robust risk, but often produces a trade-off between clean accuracy and worst-case performance.

Distributionally Robust Optimisation

When the exact deployment distribution is unknown, distributionally robust optimisation considers a set of plausible distributions, called an ambiguity set $\mathcal{U}(P)$:

$$\min_\theta\sup_{Q\in\mathcal{U}(P)}R_Q(\theta).$$

The ambiguity set may be defined by divergence from $P$, moment constraints, or an optimal-transport distance. This formulation is valuable when historical data are not representative and the cost of failure is asymmetric. It also makes assumptions visible: the chosen ambiguity set encodes which distributional changes are regarded as plausible.

Robustness is not identical to fairness or safety. A model may be robust to random noise but systematically wrong for a demographic group. Conversely, improving worst-case group performance may reduce average accuracy. Robust design therefore requires specifying whose risk is being controlled and under which perturbations.

Calibration and Uncertainty Quantification

A classifier produces a probability vector $\hat p(x)$. If it assigns probability 0.8 to a collection of cases, approximately 80 percent of those cases should be correct for the model to be calibrated. Formally, binary calibration requires

$$P(Y=1\mid \hat p(X)=p)=p$$

for relevant values of $p$. Calibration is distinct from discrimination: a model can rank cases correctly while its probabilities are systematically too high or too low.

A reliability diagram compares predicted probabilities with empirical frequencies. Common summary measures include the Brier score,

$$\operatorname{BS}=\frac{1}{n}\sum_{i=1}^{n}(\hat p_i-y_i)^2,$$

and expected calibration error, which averages the absolute difference between mean confidence and empirical accuracy across probability bins. Binning choices affect the estimate, particularly with small samples. Calibration should therefore be assessed with confidence intervals and, where appropriate, recalibrated using methods such as Platt scaling, isotonic regression, or temperature scaling.

Calibration can deteriorate under distribution shift. A model calibrated on a hospital’s patients may not remain calibrated in another hospital with different prevalence, measurement practices, or treatment policies. Groupwise calibration is also important, although simultaneous satisfaction of several fairness and calibration criteria may be mathematically impossible when groups have different base rates and error distributions.

Sources of Predictive Uncertainty

Predictive uncertainty is commonly divided into:

• Aleatoric uncertainty, arising from inherent noise or ambiguity in the data. It may be irreducible even with unlimited training data.
• Epistemic uncertainty, arising from limited data, model uncertainty, or lack of knowledge. It can often be reduced by collecting informative data.

For regression, a heteroscedastic model may predict both a mean $\mu(x)$ and variance $\sigma^2(x)$, using a Gaussian negative log-likelihood such as

$$\mathcal{L}(x,y)=\frac{(y-\mu(x))^2}{2\sigma^2(x)}+\frac{1}{2}\log\sigma^2(x).$$

Prediction intervals should be evaluated for coverage and sharpness. A 90 percent prediction interval is useful only if it contains the true outcome approximately 90 percent of the time under the target population, while remaining as narrow as justified. Conformal prediction constructs distribution-free prediction sets under exchangeability assumptions. Its guarantee concerns marginal coverage; it does not automatically guarantee conditional coverage for every subgroup or future distribution.

Uncertainty estimates can be misused. A model may be confidently wrong outside its training domain, especially when softmax probabilities are interpreted as epistemic uncertainty. Ensembles, Bayesian approximations, conformal methods, and out-of-distribution detectors provide different forms of evidence, not universal solutions.

Fairness as a Mathematical and Social Design Problem

Fairness cannot be reduced to one universally correct metric. Different metrics express different moral and operational commitments. Let $A$ denote a protected attribute, $Y$ the outcome, and $\hat Y$ a prediction.

Demographic parity requires

$$P(\hat Y=1\mid A=a)=P(\hat Y=1\mid A=b).$$

It may be appropriate when equal selection rates are required, but it can ignore genuine differences in outcome prevalence or qualification.

Equal opportunity requires equal true-positive rates:

$$P(\hat Y=1\mid Y=1,A=a)=P(\hat Y=1\mid Y=1,A=b).$$

Equalised odds requires equality of both true-positive and false-positive rates across groups. Predictive parity requires equal positive predictive value, namely

$$P(Y=1\mid \hat Y=1,A=a)=P(Y=1\mid \hat Y=1,A=b).$$

When groups have unequal base rates, nontrivial classifiers generally cannot satisfy equalised odds and predictive parity simultaneously. This is not a software defect; it is a consequence of probability relationships. Consequently, fairness analysis must begin with the decision context, the harms of false positives and false negatives, and the legitimacy of using protected attributes for auditing or adjustment.

Fairness also includes individual, causal, and intersectional perspectives. Individual fairness asks whether similar individuals receive similar treatment, but requires a defensible similarity metric. Causal fairness examines whether a decision is influenced through prohibited causal pathways. Intersectional analysis considers combinations of attributes that may be invisible in aggregate group statistics.

A mathematically responsible fairness workflow includes subgroup performance, calibration, error analysis, data-quality assessment, uncertainty intervals, and consultation with affected communities. Fairness metrics should not be optimised mechanically while ignoring the meaning of labels, unequal access to services, or the possibility that the decision itself is harmful.

Privacy, Differential Privacy, and Statistical Disclosure

Removing names from a dataset does not guarantee privacy. Linkage attacks can combine quasi-identifiers with external information, and a model may memorise rare training examples. Privacy is therefore a property of data collection, computation, release, and access control.

Differential privacy provides a formal guarantee. Two datasets $D$ and $D'$ are neighbouring if they differ in one individual’s record. A randomised mechanism $M$ is $(\varepsilon,\delta)$-differentially private if, for every measurable output set $S$,

$$P(M(D)\in S)\leq e^\varepsilon P(M(D')\in S)+\delta.$$

The parameter $\varepsilon$ controls the privacy-loss scale, while $\delta$ permits a small probability of failure. Smaller values generally provide stronger privacy but may reduce statistical utility.

For a query $q$ with global sensitivity

$$\Delta q=\max_{D\sim D'}\|q(D)-q(D')\|,$$

the Laplace mechanism releases $q(D)+Z$, where noise coordinates follow a Laplace distribution with scale $\Delta q/\varepsilon$. The Gaussian mechanism is commonly used for approximate differential privacy. Privacy composes: multiple analyses consume a cumulative privacy budget, although advanced composition and privacy accountants can provide tighter bounds than simple addition.

In machine learning, differentially private stochastic gradient descent clips each individual contribution and adds calibrated noise to aggregate gradients. Clipping limits sensitivity; noise provides privacy. The resulting model may experience lower utility, particularly for small datasets, complex models, or rare subgroups. Privacy protection can also interact with fairness because noise may disproportionately affect groups with fewer observations.

Differential privacy does not guarantee that a model is fair, accurate, secure against every attack, or ethically justified. It protects participation-level information under its formal assumptions. Governance must still address consent, purpose limitation, retention, access, and the legitimacy of collecting the data.

Optimal Transport and the Geometry of Distribution Shift

Optimal transport compares probability distributions by asking how much cost is required to transform one into another. Given distributions $\mu$ and $\nu$ and a transport plan $\pi$ with these marginals, the Wasserstein-$p$ distance is

$$W_p(\mu,\nu)=\left(\inf_{\pi\in\Pi(\mu,\nu)}\int d(x,y)^p\,d\pi(x,y)\right)^{1/p}.$$

Unlike divergences that may become uninformative when supports do not overlap, Wasserstein distance uses the geometry of the underlying space. For empirical distributions, the transport plan can be interpreted as a soft matching between observations.

Applications include domain adaptation, generative modelling, dataset comparison, imbalanced learning, and distributionally robust optimisation. A domain adaptation method may seek a representation in which source and target distributions have small transport distance while preserving label information. However, aligning marginal distributions can be dangerous if class-conditional distributions differ. A model may appear domain-invariant while mixing semantically different classes.

The Kantorovich formulation is computationally expensive for large datasets. Entropic regularisation adds an entropy term to the transport objective, enabling efficient approximations such as Sinkhorn iterations. Regularisation improves computational speed but changes the distance and may blur the transport plan. The choice of ground metric is equally important: Euclidean distance in raw pixels may not correspond to perceptual or semantic similarity.

Geometric Learning

Many data objects do not naturally lie in a vector space. Rotations, graphs, meshes, molecular structures, and probability distributions have constraints or symmetries. Differential geometry models a smooth manifold locally through tangent spaces, metrics, geodesics, and curvature. A geodesic is a shortest path under the manifold metric, and curvature describes how the space deviates from flat Euclidean geometry.

Graph neural networks provide a related form of geometric learning. A graph $G=(V,E)$ can be processed by message passing, for example

$$h_v^{(k+1)}=\phi\left(h_v^{(k)},\operatorname{AGG}_{u\in\mathcal{N}(v)}\psi(h_v^{(k)},h_u^{(k)},e_{uv})\right).$$

The aggregation function should respect relevant symmetries, such as permutation invariance to node ordering. In physical and scientific applications, equivariance is often more appropriate: transforming the input should transform the output predictably. Geometric deep learning therefore links architecture design to group actions and conservation principles.

The geometric viewpoint can improve sample efficiency and interpretability when the selected structure reflects the domain. It can also mislead when the assumed geometry is wrong. A representation that removes sensitive information may also remove legitimate signal; a graph built from correlations may encode spurious relationships; and manifold assumptions can fail near boundaries or under noisy measurements.

A Governance Framework for Mathematical Responsibility

A responsible AI system should be treated as a socio-technical process rather than a model alone. A practical governance cycle has five connected stages.

First, define the purpose, affected stakeholders, decision authority, and unacceptable harms. Second, document data provenance, sampling, labels, missingness, and protected attributes. Third, evaluate performance using stratified robustness, calibration, uncertainty, privacy, and fairness analyses. Fourth, validate the system in realistic operational conditions, including human workflow, distribution shift, and adversarial testing. Fifth, monitor after deployment and establish thresholds for investigation, rollback, retraining, or suspension.

Useful artefacts include model cards, data sheets, risk registers, audit logs, impact assessments, and incident reports. Quantitative thresholds should be linked to actions. For example, an increase in calibration error may trigger recalibration, while a severe subgroup disparity may require stopping automated decisions until the cause is understood.

Governance must also address contestability. Individuals should receive an understandable explanation of the decision, a route for correction, and access to human review where appropriate. Explanations should not be confused with causal proof: feature importance can describe model behaviour without showing that changing a feature would change the outcome.

Illustrative Case Study: A Hospital Readmission Model

Background

Consider an illustrative regional health network developing a model to identify patients at high risk of readmission within 30 days. The model uses clinical records, medication history, previous admissions, and demographic information. Its stated purpose is to allocate additional discharge planning and follow-up support, not to deny treatment.

Situation and Problem

Initial validation reports an area under the ROC curve of 0.84. After deployment, clinicians observe that risk scores are higher at one hospital than another. The model is also less calibrated for a minority population and performs poorly for patients with sparse records. Privacy officers are concerned that rare diagnoses may be memorised.

Analysis

The team first separates discrimination from calibration. Although ranking performance remains reasonable, reliability analysis shows that a predicted risk of 0.4 corresponds to substantially different observed frequencies across hospitals. This indicates site-related distribution shift. Missingness is not random: sparse records often reflect limited access rather than low clinical risk.

The team evaluates groupwise false-negative and false-positive rates, but does not select a single fairness metric without considering the intervention. Because the purpose is to offer support, false negatives may be more harmful than false positives, provided resources are available. Equal opportunity is therefore examined alongside calibration and resource capacity.

A perturbation analysis tests sensitivity to plausible coding changes and missing values. An uncertainty model flags cases outside the training population. Privacy analysis identifies small cells and evaluates whether differentially private training can provide acceptable utility.

Approach and Strategy

The network adopts a staged solution. It recalibrates scores separately using carefully validated site information, while retaining a common risk model only where transportability is justified. It introduces a missingness indicator and investigates whether the feature represents access barriers. High-uncertainty cases are routed to clinician review rather than automatically classified as low risk.

The team reports subgroup metrics with confidence intervals, conducts an impact assessment with patients and clinicians, and limits access to individual-level scores. A privacy-preserving training experiment uses gradient clipping and noise, with an explicit privacy budget recorded in the model documentation. Monitoring tracks calibration, subgroup error rates, prevalence changes, and intervention outcomes.

Outcome

The resulting system has slightly lower headline discrimination but better calibration across sites and fewer missed high-risk cases in groups previously under-served. It is not declared universally fair or robust. Instead, its approval is conditional on continued monitoring, periodic review, and a clear rule that the score supplements rather than replaces clinical judgement.

Learning Points

The case demonstrates that a single accuracy statistic cannot establish readiness. Calibration is operationally important when scores allocate scarce support. Missing data may encode structural inequality. Privacy, fairness, uncertainty, and robustness interact rather than forming independent checkboxes. Finally, governance converts mathematical evidence into accountable action.

Limitations, Risks, and Common Errors

Several recurring mistakes weaken responsible AI analysis. First, researchers may report average performance without defining the deployment population or estimating uncertainty. Second, robustness may be tested only against convenient attacks, producing false confidence. Third, fairness may be treated as a leaderboard in which one metric is maximised without examining the decision’s purpose. Fourth, calibration may be assessed on an overly small sample or assumed to transfer automatically across groups.

Differential privacy can be misunderstood as anonymisation, while privacy budgets may be spent without tracking composition. Optimal transport can create misleading conclusions when the ground metric lacks semantic validity. Geometric models may encode inappropriate invariances. Conformal intervals may be presented as guarantees under distribution shift even though their assumptions concern exchangeability.

There are also organisational risks. Documentation may be completed after deployment, affected communities may not participate in problem definition, and monitoring may collect metrics without assigning responsibility for action. Human oversight can become symbolic if reviewers lack time, authority, or information. A responsible system must therefore connect mathematical diagnostics to institutional decisions and resources.

Current Developments and Emerging Directions

Research is increasingly focused on uncertainty under distribution shift, test-time adaptation, and methods that detect when guarantees no longer apply. Selective prediction allows a model to abstain when confidence or data support is inadequate. Conformal methods are being extended to structured outputs, online settings, and distribution-shifted environments, though guarantees require careful qualification.

Optimal transport is being combined with causal modelling, robust optimisation, and generative learning. Geometric methods are expanding toward equivariant architectures for physical sciences, robotics, and molecular design. Privacy research includes federated learning, secure aggregation, and tighter privacy accounting, while recognising that distributed computation does not automatically solve governance or inference risks.

There is also growing interest in foundation-model evaluation, data governance, algorithmic auditing, and formal verification of neural networks. Formal certificates can establish robustness within specified perturbation sets, but scalability and realistic threat modelling remain challenges. The broader direction is toward measurable claims with explicit assumptions, rather than broad labels such as “trustworthy” unsupported by evidence.

Best Practices for Advanced AI Projects

A strong project should begin by defining the threat model, target population, decision consequences, and acceptable failure modes. It should report performance with uncertainty intervals and subgroup breakdowns, test calibration separately from discrimination, and evaluate realistic forms of shift. Privacy mechanisms and budgets should be selected before sensitive data are released, not added as an afterthought.

Teams should compare several fairness metrics, explain why a particular criterion is relevant, and document unavoidable trade-offs. They should use domain-appropriate distances in transport and geometry-based methods, validate invariances with experts, and treat abstention or human review as legitimate design options. Finally, every metric should have an owner, a monitoring frequency, and a pre-agreed response.

Chapter Summary

Responsible AI requires analysis beyond average predictive accuracy. Robustness examines performance under perturbations and distributional change; adversarial risk formalises worst-case behaviour within a threat model. Calibration and uncertainty quantification assess whether predictions and intervals deserve confidence. Fairness metrics such as demographic parity, equal opportunity, equalised odds, and predictive parity express different commitments and may be incompatible under unequal base rates. Differential privacy limits the influence of any one record through a formal probabilistic guarantee, but introduces utility and composition trade-offs. Optimal transport supplies a geometry for comparing distributions, while geometric learning exploits structure, symmetry, and manifolds. Mathematical governance connects these tools to documentation, monitoring, human oversight, contestability, and organisational accountability.

Key Terms

Robustness: The ability of a model to maintain acceptable behaviour under specified perturbations or changes.

Adversarial risk: Expected loss when an attacker selects a perturbation from a defined threat set.

Distribution shift: A change between training and deployment data-generating distributions.

Covariate shift: Change in the input distribution while the conditional outcome mechanism remains stable.

Calibration: Agreement between predicted probabilities or intervals and observed frequencies.

Aleatoric uncertainty: Uncertainty caused by inherent randomness or noise in observations.

Epistemic uncertainty: Uncertainty caused by limited knowledge, data, or model specification.

Conformal prediction: A framework producing prediction sets or intervals with coverage guarantees under exchangeability.

Demographic parity: Equality of prediction or selection rates across protected groups.

Equal opportunity: Equality of true-positive rates across groups.

Equalised odds: Equality of both true-positive and false-positive rates across groups.

Predictive parity: Equality of positive predictive values across groups.

Differential privacy: A guarantee limiting how much one individual can affect a mechanism’s output.

Sensitivity: Maximum change in a query’s output between neighbouring datasets.

Privacy budget: A quantitative accounting of privacy loss across analyses.

Optimal transport: A framework for minimally costly transformation between probability distributions.

Wasserstein distance: A transport-based distance measuring the cost of moving one distribution to another.

Geometric learning: Machine learning that incorporates manifolds, graphs, symmetries, or other geometric structure.

Distributionally robust optimisation: Optimisation against the worst distribution in a specified ambiguity set.

Contestability: The ability of affected people to question, correct, or appeal an AI-assisted decision.

Review Questions

Short Answer Questions

1. Distinguish covariate shift from concept shift.

2. What does calibration mean for a binary classifier?

3. Differentiate aleatoric and epistemic uncertainty.

4. State the central idea of differential privacy.

5. Why is the ground metric important in optimal transport?

Long Answer Questions

1. Explain robust risk and distributionally robust optimisation, including their assumptions and trade-offs.

2. Compare demographic parity, equal opportunity, equalised odds, and predictive parity.

3. Explain how differential privacy works through sensitivity, noise, and composition.

4. Discuss calibration, prediction intervals, and uncertainty under distribution shift.

5. Explain how geometric learning uses manifolds, graphs, and symmetry.

Analytical / Application Questions

1. A model has equal accuracy across two groups but different calibration and false-negative rates. Analyse why accuracy alone is insufficient and propose an evaluation plan.

2. Design a privacy and monitoring strategy for a model trained on a small medical dataset, considering utility, subgroup effects, and privacy-budget composition.

3. A domain-adaptation system aligns source and target feature distributions but performance falls for one class. Use optimal-transport reasoning to diagnose the problem and suggest safeguards.

22. Multiple Choice Questions with Answers

Question 1

Which expression best represents robust risk for a perturbation set Δ(X)?

A. The loss evaluated only on the training sample

B. The expected maximum loss over allowed perturbations

C. The average prediction probability across groups

D. The minimum loss over all possible distributions

Correct Answer: B. The expected maximum loss over allowed perturbations

Question 2

A classifier assigns probability 0.8 to many cases, but only 60% are positive. What property is primarily violated?

A. Calibration

B. Permutation invariance

C. Differential privacy

D. Demographic parity

Correct Answer: A. Calibration

Question 3

Which uncertainty is most directly associated with limited training data and lack of model knowledge?

A. Aleatoric uncertainty

B. Epistemic uncertainty

C. Measurement precision

D. Label prevalence

Correct Answer: B. Epistemic uncertainty

Question 4

Why can equalised odds and predictive parity be incompatible?

A. They require identical model parameters

B. They are defined only for regression

C. Unequal group base rates can prevent simultaneous satisfaction by a nontrivial classifier

D. Neither metric uses group membership

Correct Answer: C. Unequal group base rates can prevent simultaneous satisfaction by a nontrivial classifier

Question 5

In differential privacy, query sensitivity measures:

A. The number of model layers

B. The maximum output change between neighbouring datasets

C. The fraction of correctly classified examples

D. The distance between two neural-network embeddings

Correct Answer: B. The maximum output change between neighbouring datasets

Question 6

What is the main role of the privacy parameter ε?

A. It controls the scale of privacy loss

B. It specifies the model’s learning rate

C. It guarantees equal accuracy across groups

D. It measures transport cost

Correct Answer: A. It controls the scale of privacy loss

Question 7

Optimal transport compares distributions primarily by:

A. Counting only identical samples

B. Measuring the minimum cost of transforming one distribution into another

C. Maximising classification accuracy without labels

D. Removing all geometric information

Correct Answer: B. Measuring the minimum cost of transforming one distribution into another

Question 8

A hospital model is well calibrated at one site but not another. The most plausible initial explanation is:

A. The model has no loss function

B. The deployment distribution differs from the training distribution

C. Differential privacy always causes miscalibration

D. Equalised odds guarantees site invariance

Correct Answer: B. The deployment distribution differs from the training distribution

Question 9

In geometric learning, permutation invariance in a graph model means that:

A. Changing node ordering should not change the graph-level output

B. All nodes must have identical features

C. Edges must be removed before learning

D. The model must use Euclidean coordinates only

Correct Answer: A. Changing node ordering should not change the graph-level output

Question 10

Which governance response is most appropriate when a model is highly uncertain for an out-of-domain case?

A. Increase confidence artificially

B. Automatically approve the prediction

C. Route the case to abstention or human review according to policy

D. Delete all training data

Correct Answer: C. Route the case to abstention or human review according to policy