Contents
  1. Part I — What learning changes
    1. Behavior fitted from examples
      1. Determinism is a separate choice
    2. Examples, features, and targets
      1. Choose the target before the algorithm
      2. Labels are measurements
    3. Parameters and inductive assumptions
      1. Finite data leave choices open
      2. How the developments connect
  2. Part II — From signal to fitted model
    1. Sources of supervision
      1. Targets constructed from observations
    2. Loss and the objective
      1. The penalty changes influence
      2. Optimization can succeed at the wrong task
    3. Parameter updates
      1. Backpropagation computes; the optimizer updates
      2. Fitting is not inference
  3. Part III — Evidence beyond the fitted sample
    1. Generalization to new cases
      1. What each score can support
      2. Rows are not always independent evidence
    2. Validation without leakage
      1. Selection can overfit too
      2. Match the boundary to the claim
      3. Baselines and uncertainty
    3. Underfitting, overfitting, and regularization
      1. Constrain the fit, not the evidence
  4. Part IV — Uncertainty, decisions, and change
    1. Sources of predictive uncertainty
      1. Variation versus limited knowledge
      2. Different intervals answer different questions
    2. From probabilities to actions
      1. The same probability can justify different actions
      2. Rare events produce surprising alert streams
    3. When deployment conditions shift
      1. Different changes require different evidence
      2. The model can change what it sees
  5. Part V — Prediction is not intervention
    1. Association, action, and causal effect
      1. A common cause can reverse the lesson
      2. What intervention evidence requires
      3. Prediction creates feedback
      4. Four claims, four evidence burdens
  6. Check understanding
  7. Open questions
  8. Selected talks
  9. References
  10. Talk library
← All topics

Machine Learning Fundamentals

Machine learning is useful when the behavior you need is easier to demonstrate with examples than to specify as a complete set of rules. A model remains ordinary computation: it receives inputs and produces outputs. What changes is the origin of some of its behavior. Instead of an engineer writing every decision boundary, training selects parameter values that reduce a chosen objective on recorded examples. This exchange creates new engineering obligations. You must define what is predicted, prevent unavailable information from entering the inputs, choose what errors training rewards, and test the resulting behavior on cases that did not influence it. Even then, a model’s probability needs interpretation, deployment conditions can change, and a predictive association does not establish that manipulating an input will improve the outcome.

Part I — What learning changes

Behavior fitted from examples

An explicitly programmed rule gets its decision behavior from authored control flow. A learned predictor gets part of its behavior from parameters fitted to examples. For a request-duration predictor, an engineer might choose the inputs and model family, while fitting determines coefficients that connect request properties to a duration estimate. The resulting model is still a function that software can call.

QuestionAuthored ruleLearned predictor
Where does behavior come from?Conditions written by a programmerParameters fitted from examples
What varies per request?Input valuesInput values
What changes during training?Nothing unless code is editedLearned parameters
What happens during ordinary inference?The rule executesThe fitted function executes
What establishes correctness?Contract and behavioral testsContract checks plus statistical evidence on relevant new cases

Determinism is a separate choice

Learning does not make execution inherently random. A fitted model can return the same output for the same input. Separate three choices: randomness used while fitting, optional sampling used to select a generated output, and nondeterministic numerical implementations. Seeding and deterministic-algorithm settings address different parts of that problem and may still vary across software versions or hardware.

A valid interface is also different from a valid prediction. JSON schema validation can establish that predicted_seconds is a number; it cannot establish that the number is close to the eventual duration. Software Engineering Fundamentals owns the fuller treatment of explicit contracts. Here the important point is that learned behavior adds an empirical correctness question to the usual software questions.

Examples, features, and targets

A learning problem begins by fixing the unit of prediction. One example is one unit about which the model should learn: a service request, an image, a document, or a customer session. Its features are observations available when the prediction must be made. Its label, or target, is the recorded answer training asks the model to predict. A collection used for fitting is the training set.

Choose the target before the algorithm

Predicting a numerical target, such as duration in seconds, is regression. Predicting one category from a set, such as completed, canceled, or timed_out, is classification. Encoding those categories as 0, 1, and 2 does not turn the task into regression; the numbers are identifiers unless their distances have a defined meaning.

Consider an invented request record. At submission time, the system knows the operation type, payload size, service version, and queue depth. Completion duration appears later. Duration can be the target, but using it as an input to predict itself would be leakage. Log-derived setup or execution durations pose the same timing problem: a field can be useful for diagnosis after completion yet invalid as a prediction-time feature.

A target appears after the prediction point

Example

The same request persists, but completion information is introduced only after the model had to predict.

1 / 3 · At submission

The request identity persists; only submission-time fields are available as possible prediction inputs.

In this invented record, the same request acquires completion information only later. The prediction uses submission-time fields; the later observed duration is its target, never a prediction input.
Read the diagram as text
  • Request R-17. The stable request entity.
  • Submission fields. Operation, payload size, service version, and queue depth recorded at prediction time.
  • Duration prediction. A representation derived from the submission fields, not a property already stored on the request.
  • Completion state. A later state of the same request.
  • Observed duration. The target becomes available only after completion.
  • Request R-17Submission fields: has recorded state.
  • Submission fieldsDuration prediction: data input.
  • Request R-17Completion state: later state.
  • Completion stateObserved duration: records target.
  1. At submission. The request identity persists; only submission-time fields are available as possible prediction inputs. Active: Request R-17, Submission fields. New: Request R-17, Submission fields.
  2. Make the prediction. The model derives a duration estimate from the available fields. Active: Request R-17, Submission fields, Duration prediction. New: Duration prediction.
  3. Observe the outcome. Completion adds the target while preserving the original request identity and fields. Active: Request R-17, Submission fields, Duration prediction, Completion state, Observed duration. New: Completion state, Observed duration.
FieldAvailable at submission?Role in duration prediction
request_idYesIdentity; usually not a predictive feature
payload_bytesYesPossible feature
service_versionYesPossible feature
queue_depthYesPossible feature if recorded at the prediction time
completion_durationNoTarget
post-run error traceNoLater diagnostic evidence, not a submission-time feature

Labels are measurements

A recorded target is not automatically the desired truth. It may arrive late, contain measurement error, encode an ambiguous policy choice, or exist only for cases selected by an earlier decision. If a dataset contains only completed requests, it may omit canceled and unfinished requests that future traffic includes. Likewise, an exact label match can be deterministic while the label itself remains disputable or depends on information withheld from the model. Collection, provenance, and labeling practice are developed in Data Quality and Curation.

Parameters and inductive assumptions

Suppose a duration predictor uses payload size xx:

y^=b+wx\hat{y}=b+wx

Here xx changes with each request. The coefficient ww and intercept bb are learned parameters that remain fixed during ordinary prediction. An engineer may instead choose a regularization strength, tree depth, number of layers, or learning rate. Such a setting is a hyperparameter: it governs the candidate functions or the fitting procedure rather than being updated by the ordinary parameter-fitting loop.

Finite data leave choices open

A model family is the set of functions fitting may choose from. Linear regression can choose different lines. A decision tree can choose different feature thresholds and leaf values. A neural network composes parameterized transformations and may learn intermediate features rather than requiring every useful representation to be authored. Embeddings and Representation Learning develops that last idea. Two functions can fit the same observations yet disagree elsewhere. An inductive bias is the preference that makes one continuation easier to select than another.

Historical foundations of fitted behavior

  1. 1805Legendre publishes least squaresSelects unknown parameters by minimizing the sum of squared observational errors.Sources & context

    Contributors: Adrien-Marie Legendre

    What changed: Made parameter selection from imperfect, overdetermined observations explicit. This is a publication milestone, not a sole-invention claim.

  2. 1958Rosenblatt’s perceptronStudies recognition and generalization in a network whose effective connections change through experience.Sources & context

    Contributors: Frank Rosenblatt, Cornell Aeronautical Laboratory

    What changed: Made experience-dependent classification concrete through reinforcement dynamics that altered later responses.

  3. 1986Rumelhart, Hinton, and Williams on back-propagated errorsUses output errors to train intermediate representations in multilayer networks.Sources & context

    Contributors: David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams

    What changed: Showed how the chain rule could efficiently provide weight sensitivities so hidden units could learn useful features from desired outputs.

Notice the progression from selecting parameters under observational error, to adapting classification connections through experience, to learning intermediate representations from output errors. Spacing is not to scale.

Observed points do not determine one continuation

Example

Two functions fit every observed point yet disagree at an unobserved input.

Two sample-consistent functions

Both candidates agree at x=1, 2, and 4 but differ at the unobserved query x=3.

0123402468Input x (dimensionless)Predicted target (dimensionless)Linear candidateCurved candidateUnobserved query x=3Observed examplesx=3: unobserved64.8
  • 1. Linear candidate
  • 2. Curved candidate
  • 3. Unobserved query x=3
  • 4. Observed examples
Read coordinates and regions as data

X: 04 dimensionless; Y: 08 dimensionless, increasing up. Axes scaled independently; screen angles and distances are not comparable.

Linear candidate (polyline)

(0, 0); (1, 2); (2, 4); (3, 6); (4, 8)

Curved candidate (polyline)

(0, 1); (1, 2); (2, 4); (3, 4.8); (4, 8)

Unobserved query x=3 (polyline)

(3, 0); (3, 6.6)

Observed examples (points)

(1, 2); (2, 4); (4, 8)

x=3: unobserved: (3, 7.25)

6: (3.15, 6.2)

4.8: (3.15, 4.6)

Both candidates fit the three invented observations exactly. At the unobserved x=3, the line predicts 6 and the alternative predicts 4.8. A model family or regularizer favors a continuation; neither is established as correct by these observations.

Architecture, feature representation, regularization, and optimization all contribute to inductive bias. Finite observations do not uniquely determine behavior everywhere; the engineering question is whether the preference fits the intended setting.

The same observations can support different fitted representations. Increasing the range of candidate functions gives fitting more choices, but still leaves the engineer responsible for the objective and the conditions under which predictions will be judged.

How the developments connect

These approaches coexist with earlier statistical methods. Richer representations extend what can be fitted; they do not remove observational error or make the resulting predictor correct outside its assessed setting.

Part II — From signal to fitted model

Sources of supervision

A learning signal tells a fitting procedure how current behavior should change. In supervised learning, each example carries a supplied target: request fields paired with an observed duration, or an image paired with a class. The target need not be perfect, but it is explicitly treated as the answer for that training example.

Targets constructed from observations

In self-supervised learning, the data provide their own constructed targets. BERT, for example, corrupts selected positions in ordinary text and trains the model to recover the original content. The visible text becomes the input and the preserved original values become targets. No person must label every position, but the designer still chooses what to hide, what context is visible, and why recovering it should create reusable behavior.

This is distinct from using a large teacher model to generate labels. Teacher-generated labels are synthetic supervision and may reproduce teacher failures; they are not self-supervised merely because humans did not write them individually. Zeta2’s reported pipeline, for example, checked teacher edit predictions for task-specific violations and attempted repairs before using them as student targets.

Other learning signals encode different structures. Clustering can optimize compactness without supplied category labels. Reinforcement learning uses rewards from interaction rather than demonstrated actions. These signals are not interchangeable: each defines what information rewards a parameter change. Specialized corpus objectives belong in Pretraining and Midtraining; demonstrations, preferences, and rewards are developed in Post-training and Alignment.

Loss and the objective

A loss assigns a numerical penalty to a prediction relative to its target. A training objective aggregates losses across examples and may add weights, constraints, or regularization. The fitting procedure does not understand the prose description of your goal; it receives pressure from this computable quantity.

MAE=1ni=1nyiy^i,MSE=1ni=1n(yiy^i)2\operatorname{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat{y}_i|,\qquad \operatorname{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2

The penalty changes influence

Both objectives prefer small errors, but they apply different pressure. With absolute error, doubling an error doubles its contribution. With squared error, doubling an error quadruples its contribution. A single large duration miss therefore influences mean squared error much more strongly. That may be desirable when large misses dominate an operational budget, or undesirable when rare measurement failures should not control the fit. The objective encodes this choice; its name does not settle it.

How one residual changes the objective

For one duration prediction, the residual is observed duration minus predicted duration, in seconds. A negative residual means the prediction was too high.

Use the arrow keys to change the residual by half a second.

Residual 2 seconds: absolute penalty 2 seconds; squared penalty 4 seconds squared.

One example’s penalty contributions
ResidualAbsolute penalty (s)Squared penalty (s²)
Current: 2 s24
Doubled: 4 s416

Doubling the residual magnitude multiplies the absolute penalty by 2 and the squared penalty by 4. Reversing its sign changes neither penalty.

These are terms for one example, before summing and dividing by the number of examples. MAE has duration units; MSE has squared-duration units. Their raw numeric sizes do not say which objective is better.

Compare a residual with twice its magnitude, then reverse its sign. These are per-example penalty contributions, not the full dataset means.
L=1ni=1n[yilogpi+(1yi)log(1pi)]L=-\frac{1}{n}\sum_{i=1}^{n}\left[y_i\log p_i+(1-y_i)\log(1-p_i)\right]

For binary classification, log loss rewards probability assigned to the recorded class and heavily penalizes confident mistakes. Weighting examples changes which cases dominate the aggregate. Adding λjwj2\lambda\sum_j w_j^2 favors smaller coefficients. These choices affect the selected predictor even when the examples are unchanged.

Optimization can succeed at the wrong task

Training loss remains a proxy. A model can reduce teacher disagreement without becoming more useful, optimize click labels without improving user welfare, or earn a learned preference score without becoming factually correct. Application metrics and decision consequences must therefore be evaluated separately from the quantity optimized during fitting.

Parameter updates

Gradient-based fitting repeats four operations: make predictions, compute the objective, calculate how locally sensitive that objective is to each parameter, and update the parameters. A gradient collects those local sensitivities. It does not identify a symbolic business rule to edit; it says how a small numerical parameter change would affect the current objective.

θt+1=θtη1mi=1mθi(θt)\theta_{t+1}=\theta_t-\eta\,\frac{1}{m}\sum_{i=1}^{m}\nabla_\theta \ell_i(\theta_t)

A minibatch is the subset of training examples used for one parameter update; in the equation, mm is its size. The parameter vector is θ\theta, and η\eta is the learning rate controlling update scale. Small minibatches provide noisier gradient estimates but can make frequent updates; larger ones can use vectorized hardware efficiently. Changing batch size therefore changes both optimization behavior and execution.

Backpropagation computes; the optimizer updates

For composed differentiable operations, backpropagation applies the chain rule efficiently to compute parameter gradients. The optimizer then decides how to use those gradients. Plain stochastic gradient descent subtracts a scaled gradient; Adam and other optimizers transform or accumulate gradient information differently. Backpropagation is therefore not the optimizer and does not itself choose the learning rate.

Training adds a return path that inference omits

Backpropagation computes gradients; the optimizer uses them to create the next parameter state.

Features and fitted parameters produce predictions in both modes. Training additionally compares predictions with targets, computes gradients from the loss, and applies an optimizer update. Ordinary inference stops at the prediction.
Read the diagram as text
  • Features. Inputs available for the current examples.
  • Parameters θₜ. The parameter values used by the current forward pass.
  • Forward model. The authored parameterized computation.
  • Predictions. Ordinary inference stops here. Training continues to the loss comparison.
  • Targets. Recorded answers supplied during supervised training.
  • Batch loss. The objective evaluated from predictions and targets.
  • Backpropagation. Computes the gradient of the loss with respect to θₜ.
  • Optimizer. Training only: combines θₜ and gradients with its update rule and learning rate to produce θₜ₊₁.
  • Parameters θₜ₊₁. The distinct parameter state produced for the next training iteration.
  • FeaturesForward model: input.
  • Parameters θₜForward model: current values.
  • Forward modelPredictions: forward computation.
  • PredictionsBatch loss: training only: predicted values.
  • TargetsBatch loss: recorded answers.
  • Batch lossBackpropagation: differentiate.
  • BackpropagationOptimizer: gradient.
  • Parameters θₜOptimizer: previous state.
  • OptimizerParameters θₜ₊₁: update.

Illustrative pseudocode

Python-like pseudocode
for batch in training_data:
    predictions = model(batch.features, parameters)
    loss = objective(predictions, batch.targets)
    gradients = backward(loss, parameters)
    parameters = optimizer_step(parameters, gradients)

# Ordinary inference performs only the forward model call.

A large learning rate can cross a low-loss region and land on a worse point; a smaller rate can move toward it more cautiously. But lower training loss is only evidence about the fitted examples. Generalization remains a separate question. Also, not every learner uses gradients: decision trees greedily choose discrete feature splits according to an impurity or loss criterion.

Fitting is not inference

Robbins and Monro’s 1951 stochastic-approximation method established a recursive way to update an estimate from noisy observations under stated conditions. It is a useful historical foundation for noisy iterative updates, but it did not itself describe modern minibatches, neural networks, or backpropagation. During inference, fitted parameters normally remain unchanged. Examples placed in a prompt can still alter a response through the current input; that is the distinct mechanism developed in Prompting and In-Context Learning.

Part III — Evidence beyond the fitted sample

Generalization to new cases

Generalization is useful performance on new cases from the intended setting. Training error averages loss over observed examples. Population error is the expected loss over the underlying distribution of cases the system will encounter. The former is directly computable from the fitted sample; the latter is the quantity deployment usually cares about.

R^(f)=1ni=1n(f(xi),yi),R(f)=E(X,Y)P[(f(X),Y)]\widehat{R}(f)=\frac{1}{n}\sum_{i=1}^{n}\ell(f(x_i),y_i),\qquad R(f)=\mathbb{E}_{(X,Y)\sim P}[\ell(f(X),Y)]

Minimizing R^\widehat{R} is empirical risk minimization. It does not guarantee a small RR. Confidence comes from the combination of an appropriate inductive bias, sufficient coverage, representative sampling, and measurements on genuinely new cases. Interpolation within well-covered conditions and extrapolation beyond observed conditions make different demands on those assumptions.

What each score can support

EvidenceWhat it measuresWhat it does not establish
Training errorFit on examples used for learningPerformance on unseen cases
Random held-out rowsPerformance on similar held-out recordsGeneralization to new entities if related records cross the split
Held-out projectsPerformance on projects absent from fittingFuture performance after conditions change
Earlier-to-later splitForecast performance across the represented time boundaryStability beyond that period

Rows are not always independent evidence

Random shuffling does not create independence. A thousand builds from one repository may contain less evidence about a new repository than a hundred builds from a hundred repositories. Group-aware splitting keeps dependent observations together when the claim concerns new entities; chronological splitting answers a different question about future observations.

Validation without leakage

Split names describe responsibilities. The training set fits model parameters and fitted preprocessing. The validation set guides choices such as model family, hyperparameters, features, and stopping point. The test set is held aside until those choices are frozen, then estimates the selected system’s performance.

Selection can overfit too

Repeatedly changing the system after reading test results makes the test set part of development, even when its rows never enter a gradient calculation. Adaptive selection depends on the reused data through the reported scores. Specialized reusable-holdout procedures exist under explicit query and sampling conditions, but ordinary final-test claims require fresh, independently sampled cases after adaptive development.

Data leakage occurs when fitting or selection uses information that would be unavailable in the intended prediction setting. Common paths include scaling features with statistics computed from all records, selecting features before splitting, placing records from the same entity on both sides of a split, or using observations from the future. A pipeline can ensure that fitted transformations are learned within each training fold, but it cannot prove that the raw fields were genuinely available at prediction time.

Three data boundaries, three responsibilities

The test estimate remains independent only when the complete system is frozen before test outcomes are read.

Training data fit preprocessing and parameters; validation results guide choices; the frozen pipeline is assessed on untouched test data. All-data preprocessing, test-driven revision, future information, and related records crossing a claim-relevant group boundary violate this separation. A pipeline does not establish raw-field timing or group independence by itself.
Read the diagram as text
  • Training data. Contains only information permitted inside the fitting boundary.
  • Fitted candidate. Preprocessing state and model parameters are learned from training data.
  • Validation assessment. Evaluate the fitted candidate on validation data; results guide selection, not ordinary parameter fitting.
  • Development choice. Validation results guide model family, features, hyperparameters, and stopping.
  • Frozen pipeline. The selected preprocessing and predictor after development decisions are complete.
  • Untouched test assessment. Evaluate the frozen pipeline on untouched test cases matching the final population or time claim.
  • Final estimate. Performance of the frozen pipeline on the represented population or time boundary.
  • Boundary rules. Fit preprocessing inside training; keep claim-relevant groups together; exclude future information; obtain fresh cases after test-driven revisions.
  • Training dataFitted candidate: fits state.
  • Fitted candidateValidation assessment: evaluated for selection.
  • Validation assessmentDevelopment choice: selection results.
  • Development choiceFrozen pipeline: freezes complete system.
  • Frozen pipelineUntouched test assessment: one final assessment.
  • Untouched test assessmentFinal estimate: scored outcomes.
  • Boundary rulesTraining data: constrains fitting sample.
  • Boundary rulesUntouched test assessment: constrains assessment sample.

Match the boundary to the claim

Intended claimUseful boundaryReason
New independent cases from the same populationRandom holdout or cross-validationEstimates variation across independently sampled cases
New customers, repositories, or patientsGroup-aware splitPrevents related records from appearing in fitting and evaluation
Future requestsChronological splitPrevents later information from influencing earlier forecasts
Final performance after model selectionUntouched test setSeparates selection from assessment

Baselines and uncertainty

Always compare against a simple baseline. A regression baseline might predict the training-set mean for every request; a classifier might always predict the most frequent training class. Beating it does not prove deployment value, but failing to beat it reveals that the learned features have not justified their complexity. Evaluation proportions also have sampling uncertainty, especially with small samples or rare failures. These foundations lead into the broader system-level methods in Evals and Benchmarks.

Underfitting, overfitting, and regularization

Underfitting means the fitted system has not captured useful structure available for the task. Overfitting means improving fit increasingly reflects sample-specific patterns that do not transfer. High training error can result from an unsuitable model family or unsuccessful optimization. Low training error combined with worse validation performance suggests a generalization gap, but only after leakage and validation mismatch have been ruled out.

Constrain the fit, not the evidence

Regularization changes which fitted solutions are favored. An L2 penalty discourages large coefficients; early stopping selects a training point using validation performance. These are different interventions, and neither repairs invalid labels, future leakage, or an evaluation population that does not match deployment.

ObservationPlausible limitationNext controlled comparison
Training and validation performance are both poorLimited fit, weak features, or optimization failureTry a more suitable representation, model family, or verified optimization change
Training improves while validation worsensPossible overfitting or selection biasCheck leakage, then compare regularization, earlier stopping, or simpler choices
Validation improves as independent training examples increaseEvidence that representative data helpCollect more examples from the same intended population
Both curves remain poor as sample size growsPersistent task, feature, label, or family limitationRevisit the prediction contract rather than merely adding rows

Training-step curves and sample-size learning curves answer different questions. The former vary continued optimization with a fixed dataset. The latter vary how many training examples are available. More parameters do not imply a universal U-shaped generalization curve, and more data from the same biased source may simply reinforce the same shortcut.

Part IV — Uncertainty, decisions, and change

Sources of predictive uncertainty

A point prediction gives one estimated outcome. A predictive distribution assigns probabilities across possible outcomes, while a prediction interval describes a range intended to contain a future observation at a stated long-run rate under its assumptions. These are richer claims than a single duration estimate.

Variation versus limited knowledge

Aleatoric uncertainty is unresolved outcome variation given the available information. Two requests with the same recorded features may still take different times because relevant causes were not observed or because outcomes genuinely vary. Epistemic uncertainty is limited knowledge about the predictive relationship, often exposed where examples are sparse or the model family is inadequate. The distinction is relative to the information and model: adding an informative feature can explain variation that previously looked irreducible.

More representative examples can reduce uncertainty about the fitted relationship without making each future outcome predictable. Conversely, richer observations may reduce outcome ambiguity while leaving the relationship poorly estimated in a new region. Some internal uncertainty decompositions are not uniquely identified by the same predictive distribution, so named components should not be treated as directly observed quantities in every model.

Different intervals answer different questions

OutputQuestion
Point predictionWhat single estimate does the model produce?
Prediction intervalWhere might one new outcome fall?
Confidence interval for a meanHow uncertain is the estimated average response?

A number between zero and one is not automatically a validated probability. Token log probabilities describe the model’s generation distribution, not calibrated factual confidence. A generated confidence statement and agreement among several similar models require their own evaluation. Calibration can also deteriorate under shift even when it looked acceptable on the original validation population.

From probabilities to actions

A probabilistic classifier is calibrated in an evaluated population when cases assigned probability near pp experience the outcome about a fraction pp of the time. Calibration is a frequency property across comparable cases, not a guarantee for one case. It also differs from discrimination, the ability to rank higher-risk cases above lower-risk ones. Predicting the population base rate for everyone can be calibrated while ranking nobody.

An action requires consequences as well as probabilities. If a false positive costs CFPC_{FP}, a false negative costs CFNC_{FN}, and correct decisions have zero cost, choosing the positive action minimizes expected cost when:

pCFPCFP+CFNp\geq \frac{C_{FP}}{C_{FP}+C_{FN}}

The same probability can justify different actions

Predicted timeout probabilityFalse alarm costMissed-timeout costResult
0.30LowHighIntervene at a relatively low threshold
0.30HighLowDo not intervene at that threshold
0.30ModerateModerate, with useful human review availableDefer if the review path has acceptable capacity and delay

Rare events produce surprising alert streams

Base rates matter. In a constructed set of 10,000 cases containing 100 real events, detecting 80% yields 80 true alerts. A 1% false-positive rate among 9,900 non-events adds 99 false alerts. Only 80 of 179 alerts are real even though 1% sounds small. This arithmetic is not a measured deployment result; it exposes why event prevalence and the denominator must accompany an alert rate.

Abstention adds a reject or defer action. Coverage is the fraction accepted automatically; selective risk is error among accepted cases. Raising a threshold helps only when the score meaningfully orders mistakes, and lower coverage transfers work elsewhere. Evaluate that downstream path rather than treating abstention as free safety. In bug-review systems, long lists of invalid reports illustrate the operational cost of a prediction stream whose report volume overwhelms human triage.

When deployment conditions shift

Distribution shift means that development or evaluation conditions differ from use conditions. The phrase is broad; diagnosing the changed relationship matters. Under covariate shift, input frequencies P(X)P(X) change while P(YX)P(Y\mid X) is assumed stable. Under label shift, outcome prevalence P(Y)P(Y) changes while P(XY)P(X\mid Y) is assumed stable. Under concept shift, the relationship P(YX)P(Y\mid X) itself changes.

Different changes require different evidence

Suppose large requests become more common but the duration relationship for each request size remains unchanged. That is compatible with covariate shift. If a service migration makes requests of the same size take different times, the conditional relationship has changed. The first problem may call for reweighting or evaluation on the new mix under strong assumptions; the second requires new labels and renewed validation of the predictive relationship.

A shortcut is a decision rule that works under ordinary development conditions but fails under a targeted change. Data, architecture, and training choices influence which shortcut a model finds. Held-out success drawn from the same shortcut-supporting conditions therefore does not prove that the intended rule was learned.

Detecting changed inputs and establishing degraded predictions are separate tasks. One study reported a controlled image shift that a detector noticed without harming the tested classifier. Conversely, an input-only test does not directly test a changed input–outcome relationship. Performance monitoring needs fresh outcomes, not merely feature drift alarms.

The model can change what it sees

Sequential systems add feedback. In imitation learning, a policy’s early mistake can move it into states absent from expert demonstrations; later decisions then face a new, policy-induced distribution. DAgger addresses this setting by executing the learned policy and collecting expert actions for states it actually encounters. The mechanism illustrates why deployment behavior can change future inputs. Longer-term update, retention, and forgetting strategies belong in Continual Learning.

Part V — Prediction is not intervention

Association, action, and causal effect

Prediction estimates an outcome under patterns represented in observed data. A causal effect compares outcomes under alternative interventions. The difference matters whenever a model output is used to choose an action: a variable can predict an outcome without being a useful lever for changing it.

A common cause can reverse the lesson

Imagine autoscaling records in which high load causes operators to add replicas and also increases latency. Replica count may therefore be positively associated with latency even if adding a replica under comparable load reduces latency. Load is a confounder because it influences both the observed action and the outcome. A predictor can learn the association accurately and still answer the intervention question incorrectly.

Load confounds the observed replica–latency relationship

Example

Ordinary scaling records combine a load-driven association with the effect of changing replica count.

The arrows are an assumed causal structure for this invented example. Observed association mixes the load-driven path with the replica effect. Under randomized assignment, replace the load-to-replica selection mechanism with random assignment; retain load → latency and replica count → latency. This supports an average-effect comparison under the experimental conditions, not both outcomes for one request.
Read the diagram as text
  • Operational load. A common cause of the scaling decision and latency.
  • Replica count. The action whose effect is being studied.
  • Latency. The outcome affected by load and potentially by replica count.
  • Operational loadReplica count: ordinary scaling responds to load.
  • Operational loadLatency: load affects outcome.
  • Replica countLatency: possible action effect.

Editing the replica-count feature and rescoring a predictive model is not automatically a causal experiment. Feature attribution assigns parts of a prediction to inputs under a reference construction; it does not establish the real-world effect of changing the corresponding quantity. Causal reasoning needs a specified intervention and assumptions about how outcomes would be generated under it.

What intervention evidence requires

Random assignment makes action selection independent of potential outcomes in expectation, allowing differences between assigned groups to estimate an average effect under the experiment’s conditions. It does not reveal both possible outcomes for one request. Observational adjustment instead needs assumptions such as consistency, conditional exchangeability, and positivity: the action must be well specified, measured covariates must remove action–outcome confounding, and each relevant group must have support for the actions being compared.

Prediction creates feedback

Acting on predictions can also change later data. Prices, traffic, reviewer decisions, and alerts can alter the inputs and labels collected for the next model. An interface that encourages reviewers to approve model suggestions can feed model-influenced decisions back as apparent truth; an independent judgment step can reveal disagreements, though it does not guarantee correct labels.

Four claims, four evidence burdens

ClaimEvidence needed
The model forecasts accuratelyIndependent, representative outcomes scored with a defined metric
The forecast supports a useful decisionValidated probabilities or rankings plus consequences, capacity, and alternatives
The action changes the outcomeRandomized evidence or observational identification with defensible causal assumptions
The complete system helps in operationEnd-to-end evaluation of outcomes, side effects, adoption, and changed conditions

Open questions

  1. How can useful epistemic uncertainty be estimated when several internal uncertainty representations produce the same predictive distribution? Progress would require methods whose uncertainty distinctions are identifiable, empirically connected to future errors, and validated after realistic distribution changes.

  2. How should adaptive development reuse valuable failures without converting every benchmark into training data? The challenge is preserving regression tests while obtaining an honest estimate of performance on the intended population. Progress would combine versioned development sets, fresh independent cases, and reusable-holdout methods whose sampling and query-budget assumptions are actually enforced.

  3. How can teams measure the causal benefit of model-guided actions when deployment changes who receives an action and which outcomes become observable? Progress would require explicit intervention definitions, support for credible comparisons, measurement of feedback effects, and evaluation beyond predictive accuracy.

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References

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A synthesis of selected conference talks and technical references. Citations link to the source material; they do not imply that every talk on this subject is included.

  1. Dive into Deep Learning: Generalization in Deep Learning

    Inductive biases are assumptions or preferences favoring solutions with particular properties. Optimizing training loss and obtaining useful predictions on new examples are different problems. The chapter explains that neural networks can fit arbitrary training labels and that generalization need not worsen monotonically as model complexity increases; double-descent behavior is one counterexample to a universal single U-shaped complexity curve.

  2. PyTorch Quickstart: forward computation, training, and loading

    Tensors hold shaped numerical data: a batch has dimensions for examples and features, while parameter tensors hold learned weights and biases. Forward computation applies the network's layers to input tensors using those parameters, producing prediction scores. Training additionally compares predictions with targets through a loss, calls backward() to compute parameter gradients, and calls optimizer.step() to update parameters; zero_grad() clears accumulated gradients. Loading recreates the architecture and restores its state dictionary. The example then predicts using eval() and no_grad(), without loss-driven parameter updates. Computing a loss for evaluation does not itself train the model.

  3. PyTorch 2.9: Reproducibility

    PyTorch distinguishes random-number use from nondeterministic implementations. Seeding can reproduce a random-number sequence within a controlled environment, while deterministic-algorithm settings select deterministic alternatives or reject known nondeterministic operations. Identical seeds still do not guarantee identical results across releases, platforms, or CPU and GPU execution. Deterministic operations may also be slower.

  4. Google: Supervised learning foundations

    Features are input values x; a label y is the target recorded for an example. Parameters θ are learned numbers defining a model fθ. Training repeatedly compares predictions with labels using a loss and adjusts these numbers to improve agreement. Inference evaluates the trained function on a new input without needing its label. Generalization means performing well on examples outside training; evaluation therefore compares predictions against withheld labels. Programmer-oriented illustration: training fits w and b in f(x)=wx+b from examples, whereas an authored rule such as if x>c executes a programmer-specified condition. Both execute code at inference, but the origin of their decision behavior differs.

  5. Dive into Deep Learning: Linear Regression

    Linear regression predicts y_hat=b+sum_j(w_j*x_j). Each dataset row supplies features, while weights and bias are shared fitted parameters. Observed targets can differ from predictions because measurements contain noise. Squared loss penalizes each residual quadratically; averaging these losses produces the empirical training objective. Doubling a residual quadruples its squared contribution. Ordinary least squares also admits analytic fitting, so training need not always use iterative gradient updates. Learning rate and batch size are hyperparameters rather than values updated by the ordinary fitting loop.

  6. Scikit-learn: scoring rules and baseline estimators

    Evaluation tools accept an explicit scoring rule; classification accuracy is sum_i 1[prediction_i=target_i]/n. Dummy estimators provide sanity-check baselines such as always selecting the training set's most frequent class. Accuracy can conceal poor minority-class performance, motivating metrics such as balanced accuracy. Methodological inference for technical tasks: define the correctness criterion and baseline before selection, evaluate candidates on the same validation cases, and apply the frozen criterion to the final test set. A syntax check, exact-answer comparison, and executable task test measure different properties.

  7. scikit-learn: Preprocessing data

    One-hot encoding represents a categorical feature using one binary column per category: the matching column is 1 and the others are 0. Unlike arbitrary integer codes, this does not impose a numeric ordering among categories. Standardization transforms each nonconstant feature as z_j=(x_j-mu_j)/s_j, using the mean and standard deviation fitted on training examples and retained for later inputs. Combining this transformation with the squared-Euclidean objective in reused note web-ml-kmeans-objective-and-assumptions gives distance squared sum_j((x_j-x'_j)/s_j)^2. Thus centering cancels in pairwise differences, while relative scaling changes each feature's contribution and can change cluster assignments.

  8. TravisTorrent: Data Format

    Each TravisTorrent row represents a build job and combines repository information, Travis API fields, and build-log analysis. The schema distinguishes build and job identifiers, API-reported build status and full build duration, and log-derived setup, test, and build-command durations. It also records project identity and repository attributes. These distinctions support explicitly choosing the prediction unit and duration target before constructing a learning dataset.

  9. scikit-learn: Common pitfalls and recommended practices

    Preprocessing transformations learned during training must also be applied to later inputs. Fit transformation state on training data, then use transform on held-out or production data without refitting. Leakage occurs when model construction uses information unavailable at prediction time, including test-derived preprocessing statistics. Pipelines combine transformations with estimators and fit them on the appropriate training subset during cross-validation. The documentation demonstrates that selecting features before splitting can produce misleading performance even with randomly assigned targets.

  10. The Selective Labels Problem: Evaluating Algorithmic Predictions in the Presence of Unobservables

    Observed outcomes can depend on earlier human decisions, so the labeled sample need not represent the people on whom a replacement model would act. This paper studies bail decisions: a release outcome is observed only for defendants released. Evaluating on that selected subset can misstate performance for a new decision policy. The same structural concern applies to underwriting when repayment outcomes are observed only for granted loans; that financial example is an inference from the mechanism, not an experiment in this paper.

  11. Stop Burning Tokens: Why self-improvement needs domain expertise first - Annabell Schäfer, Langfuse

    Deterministic scoring can conceal ambiguity in the labels being treated as ground truth.

  12. L2 regularization and generalization

    L2 regularization penalizes sum_j(w_j^2); training minimizes predictive loss plus lambda times that penalty. Combining this documented penalty with binary log loss gives a beginner objective J(w,b)=-(1/N)*sum_i[y_i*log(p_i)+(1-y_i)*log(1-p_i)]+lambda*sum_j(w_j^2), with p_i=sigmoid(b+w·x_i). Here the intercept is deliberately left unpenalized. Overfitting means fitting training-specific patterns that fail to generalize to unseen examples. Increasing lambda discourages large weights but excessive shrinkage can impair predictions; lambda=0 removes the penalty. Select its strength using validation performance. Early stopping instead halts training when validation loss starts worsening.

  13. scikit-learn: Decision Trees

    Decision trees learn rules from features and produce piecewise-constant predictions. Training recursively partitions examples using a feature and threshold, grouping similar target values. Candidate splits are evaluated using a task-dependent loss or impurity measure. This contrasts with a single weighted linear relationship and illustrates fitting through discrete split selection rather than gradient descent. The documented CART implementation constructs binary trees.

  14. Rumelhart, Hinton and Williams: Learning Representations by Back-Propagating Errors

    The 1986 paper addresses how intermediate units can learn useful features when training examples specify only desired outputs. A forward pass computes activations; a backward pass applies the chain rule to calculate how each weight affects output error. Those derivatives support gradient-based weight updates. Its demonstrations include learning mirror symmetry and representations of family relationships. Unlike fixed feature analyzers, the intermediate representations change through training.

  15. Geirhos et al.: Shortcut Learning in Deep Neural Networks

    Geirhos and colleagues define shortcuts as decision rules that perform well under standard testing conditions but fail under more challenging conditions. Their toy classification example permits shape-, size- and location-based rules to succeed on training and same-distribution test examples; systematically changing size or location distinguishes those rules. They identify architecture, data and training choices as sources of inductive bias that affect which rule is learned.

  16. Legendre: Nouvelles méthodes pour la détermination des orbites des comètes

    Adrien-Marie Legendre's 1805 work presents the “method of least squares” for overdetermined observational equations: choose unknown quantities so the sum of squared errors is minimized. Its appendix derives the resulting equations and shows that, when estimating one quantity from repeated observations, minimizing squared deviations yields their arithmetic mean. Legendre applies the method to astronomical and meridian measurements.

  17. Rosenblatt: The Perceptron—A Probabilistic Model for Information Storage and Organization in the Brain

    Rosenblatt's 1958 paper at Cornell Aeronautical Laboratory investigated recognition and generalization through a network whose effective signal strengths change with experience. Its simplified perceptron combines sensory inputs, association units and competing responses. Reinforcing active association units makes the corresponding response more likely on subsequent presentations. The paper analyzes several reinforcement dynamics rather than describing a single universal learning rule.

  18. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

    BERT constructs prediction targets from ordinary text: selected token positions are corrupted, and training predicts the original tokens using cross-entropy. The original text supplies the answers without separate human annotation for each prediction. This is a concrete example of self-supervised target construction, distinct from grouping observations into clusters. The paper subsequently fine-tunes pretrained parameters for downstream tasks.

  19. How We Built Zeta2: Training an Edit Prediction Model in Production — Ben Kunkle, Zed

    Zeta2's distillation pipeline checks frontier-model predictions for task-specific failures and repairs flagged outputs before using them as student targets.

  20. scikit-learn: Clustering

    K-means divides observations into a chosen number of groups represented by centroids, the groups' mean feature vectors. It seeks to minimize within-cluster squared Euclidean distances. Its objective favors compact, isotropic groups and can behave poorly for elongated or irregularly shaped clusters. This provides an explicit learning objective without externally supplied category targets.

  21. Reinforcement Learning: An Introduction — second-edition draft

    Reinforcement learning improves a policy using rewards from interaction rather than labels specifying demonstrated actions. The objective is expected return: G_t = sum_k gamma^k R_(t+k+1), with gamma controlling discounting. In a finite episode with only terminal reward R_T, this reduces to gamma^(T-t-1)R_T: the outcome evaluates a trajectory without identifying which earlier decisions helped. Temporal credit assignment propagates that information to earlier choices. Monte Carlo methods update from completed returns; TD prediction uses V(s) <- V(s) + alpha[r + gamma V(s') - V(s)], bootstrapping from the next state's estimate. Policy improvement then favors actions with higher expected return; prediction updates alone do not change the policy.

  22. scikit-learn: Mean absolute error

    For residuals e_i=y_i−ŷ_i, mean absolute error is MAE=(1/n)Σ|e_i|, whereas mean squared error is MSE=(1/n)Σe_i². MAE therefore penalizes residual magnitude linearly: doubling an error doubles its contribution. MSE uses a quadratic penalty: doubling an error quadruples its contribution, so large residuals exert relatively greater influence.

  23. Logistic regression: binary log loss

    For N examples with binary labels y_i and predictions p_i, mean log loss is L=-(1/N)*sum_i[y_i*log(p_i)+(1-y_i)*log(1-p_i)]. A positive example contributes -log(p_i); a negative contributes -log(1-p_i). Confident incorrect predictions receive large penalties. Training adjusts parameters to reduce this loss, with regularization limiting overfitting. Mathematical application: when labels encode clicks, the objective rewards predicting those labels, not independently measured utility. Replacing labels or weighting examples changes the training objective and can change the interpretation of the output.

  24. Training language models to follow instructions with human feedback

    The training loop separates demonstrations, ranked responses, and fresh policy rollouts. A scalar reward model learns preferences via -log sigmoid(r(x,y_w)-r(x,y_l)); the absolute score is less meaningful than the difference for the same prompt. PPO then generates responses and optimizes their learned reward with a per-token penalty for departure from the supervised reference. In expectation the log-probability-ratio penalty gives KL(pi_theta || pi_ref). A learned value function estimates expected return for advantage estimation. The paper also mixes pretraining gradients into some RL runs to reduce regressions on retained NLP tasks. It partitions prompts by user identity, rather than randomly splitting near-related prompts across sets.

  25. Weak supervision needs evaluation beyond supervisor agreement

    Oversight becomes difficult when an evaluator cannot reliably judge behavior available to a stronger model: matching its labels can reproduce its mistakes. The paper trains a weak model on ground-truth labels, obtains its predictions on held-out examples, and trains a stronger student on those weak labels. It compares ground-truth test performance with both the weak supervisor and a strong model trained directly on ground truth. Performance gap recovered is PGR=(student-weak)/(strong_ceiling-weak), requiring a nonzero denominator. PGR=0 means no improvement over the supervisor; PGR=1 matches the experimental ceiling. Independent correctness scores and agreement on supervisor-wrong examples distinguish useful generalization from imitation. Experiments show task-dependent generalization and overfitting to weak labels; an auxiliary confidence loss improves some NLP results.

  26. Minibatch Stochastic Gradient Descent — Dive into Deep Learning

    Training evaluates a loss on a batch, differentiates it with respect to model parameters, and updates those parameters. In minibatch SGD, the update subtracts the learning rate times the mean example gradient: theta_next = theta - eta * mean_i gradient_theta loss_i. A gradient indicates local sensitivity of the chosen loss, not a symbolic edit to a particular rule. Minibatches trade statistical noise against efficient vectorized computation; changing batch size changes both optimization and execution behavior.

  27. PyTorch: Optimizing Model Parameters

    Supervised examples pair inputs x with target labels y. A parameterized function fθ predicts from x; a loss measures disagreement with y. Training repeatedly computes predictions, loss, gradients and parameter updates. For ordinary gradient descent, θ ← θ − η∇θL, where η is the learning rate and L is the batch loss. PyTorch implements this through backward() and optimizer.step(), clearing accumulated gradients between updates. Ordinary inference evaluates fθ on new inputs without an optimizer update. The example uses model.eval() for evaluation behavior and no_grad() to avoid constructing gradients.

  28. Training an LLM from Scratch, Locally

    Use a short low-rate warm-up, increase to a peak, and then reduce the learning rate with cosine decay.

  29. Robbins and Monro: A Stochastic Approximation Method

    Herbert Robbins and Sutton Monro's September 1951 paper studies finding a value x where an unknown expected response M(x) equals a target a when experiments return noisy observations Y(x). Their recursive procedure chooses successive experimental levels and updates the estimate using the latest response and a positive step-size sequence. Under stated monotonicity, boundedness and step-size conditions, they prove convergence in probability.

  30. Language Models are Few-Shot Learners

    Few-shot inference supplies demonstrations as input conditioning while keeping model weights fixed; fine-tuning changes pretrained weights through training. Examples consume bounded context and influence subsequent predictions without becoming parameter updates. Separately, benchmark contamination means evaluation material overlaps training data, weakening claims of generalization to unseen examples. GPT-3's study compares original scores with subsets lacking detected n-gram overlap, but acknowledges false positives and possible distribution differences between clean and original subsets. Conceptually, contamination concerns exposure to evaluation data; optimizing a proxy concerns objective mismatch, while biased reviewer labels concern measurement. Those problems can occur independently.

  31. Dive into Deep Learning: generalization in classification

    For a fixed classifier f, empirical error on n labeled examples is sum_i 1[f(x_i) != y_i]/n. Population error is the expectation of that disagreement over the underlying data distribution. A fresh representative test set estimates population error; fitting or memorizing training examples does not establish performance on unseen examples. Consequently, a deterministic predictor can repeatedly return the same incorrect answer: repeatability constrains computation, not agreement with the target. This last statement is an inference from the fixed-classifier definition, not a measured claim about a particular LLM.

  32. NIST/SEMATECH e-Handbook: How do we Use the Model Beyond the Data Domain?

    Interpolation predicts within the domain covered by observed inputs; extrapolation predicts outside it. Good fit at observed points does not guarantee good predictions farther away. Extending a fitted relationship beyond observations assumes that its form remains useful there; an empirical equation does not automatically incorporate the underlying engineering mechanism. NIST recommends additional confirmatory observations for both kinds of prediction. Applied to a constructed single-input build-size example, more frequent large projects within the historical size range remain within the interpolation domain, whereas sizes beyond that range require extrapolation.

  33. scikit-learn: Cross-validation for grouped and time-series data

    Groups of dependent observations violate ordinary independent-sample assumptions. Group-aware splitting keeps selected groups out of training when assessing them. Time-series splitting instead trains on earlier folds and evaluates later observations. These address different dependencies: holding out an entity and forecasting its future are different evaluation questions.

  34. Google ML Crash Course: Dividing Datasets

    Training data fits model parameters; validation data guides model and hyperparameter choices; a held-out test set evaluates the selected system. Repeatedly modifying the system in response to test results indirectly fits that test set even without gradient updates on its examples. Validation sets can also become overused. Test data should be sufficiently large, representative of deployment and free of training duplicates. Engineering application: prevent related records or future information from leaking across splits when deployment requires generalization across entities or time.

  35. Generalization in Adaptive Data Analysis and Holdout Reuse

    Selecting later analyses using earlier results makes the selection depend on the reused dataset. Aggregate scores can therefore influence selection even when individual test cases remain hidden; ordinary fixed-analysis guarantees no longer follow automatically. Engineering application: after using evaluation failures or scores to revise a coding agent, retain useful failures for regression testing but evaluate the revised configuration on fresh, independently sampled untouched cases for an ordinary holdout claim. Reuse is possible under specialized safeguards: Thresholdout compares training and holdout averages using noisy thresholds, releases controlled answers and stops when its overfitting budget is exhausted.

  36. Cawley and Talbot: On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation

    Cawley and Talbot show that optimizing hyperparameters against a finite-sample model-selection criterion can overfit that criterion, even though those choices are not ordinary fitted parameters. Their experiments demonstrate optimistic performance estimates when model selection is conducted outside the resampling process. They argue that selection must be treated as part of fitting and repeated independently within each evaluation trial, as in nested cross-validation.

  37. Cross-validation and held-out evaluation

    Testing on data used to fit or repeatedly tune a system can overestimate generalization. The documentation separates training, validation for selection, and an untouched final test set; cross-validation does not eliminate the need for final held-out evaluation. Applied to model judges, tune rubrics and examples on calibration data, freeze the judge, then measure agreement with independent human labels on unseen examples. Applied to context policies, select retrieval and compression settings on development tasks and evaluate the selected policy on held-out tasks. Repeatedly changing settings after seeing test results converts that test set into development data.

  38. scikit-learn: DummyRegressor

    DummyRegressor with strategy='mean' learns the mean of the training targets and returns that constant for every prediction. Its predictions disregard input features. This supplies a concrete regression baseline against which a feature-dependent predictor can be assessed; median and specified-quantile strategies provide alternative constant predictions.

  39. NIST: Confidence Intervals for a Proportion

    An observed proportion estimates a population rate with sampling uncertainty. NIST's published example finds four defective items among twenty, an observed rate of 20%; its displayed exact-binomial bounds for a 90% interval are approximately 7.1% and 40.1%. Applied to independent pass/fail evaluations, such an interval concerns the underlying error rate, not an interval of possible outcomes for one case. Small samples or few failures make simple normal approximations unreliable.

  40. Dive into Deep Learning: Model Selection, Underfitting, and Overfitting

    The chapter contrasts insufficiently expressive models with models that fit training examples much better than validation examples. Its polynomial example varies model complexity and dataset size. Increasing polynomial degree enlarges the available function family and cannot increase the best achievable training fit error, but does not ensure better predictions. A fair-coin example shows how a finite sample's majority class can look more predictable than the underlying process actually is.

  41. Hoerl and Kennard: Ridge Regression—Biased Estimation for Nonorthogonal Problems

    Hoerl and Kennard's February 1970 paper addresses unstable least-squares coefficients when predictors are strongly related. Ridge estimation introduces a positive adjustment that shortens the coefficient vector, accepting bias to reduce sensitivity to the observed sample. Their analysis separates squared bias from parameter-estimation variance and establishes conditions under which their sum is smaller than for ordinary least squares. Regularization therefore has statistical roots in stabilizing estimation, rather than originating as a neural-network remedy.

  42. scikit-learn: Validation Curves—Plotting Scores to Evaluate Models

    A sample-size learning curve compares training and validation scores while varying the number of training examples. A validation curve instead varies a hyperparameter. These answer different questions: whether additional examples might help, versus how a modeling choice changes fit and generalization. In the documentation's examples, some models retain low training and validation scores as data grows, whereas others show a gap that additional examples can reduce.

  43. NIST: How Can I Predict the Value and Estimate the Uncertainty of a Single Response?

    A point prediction supplies one estimated outcome. A prediction interval describes uncertainty about a new observation, whereas a confidence interval for the mean response concerns the estimated average at specified inputs. In NIST's regression setting, prediction uncertainty includes both uncertainty in the estimated mean and variation of the new observation. Increasing the training sample can narrow uncertainty about the mean while leaving substantial uncertainty about an individual outcome. Nominal interval coverage is a repeated-sampling property under the construction's assumptions.

  44. Hüllermeier and Waegeman: Aleatoric and Epistemic Uncertainty in Machine Learning

    Aleatoric uncertainty is unresolved outcome variation given the available inputs; epistemic uncertainty is limited knowledge about the predictive relationship. Even knowing the outcome distribution can leave an individual outcome uncertain. Additional examples can reduce uncertainty about the fitted relationship without removing that variation. The distinction depends on the information and model available: adding an informative feature can resolve variation that previously appeared irreducible. Uncertainty about a particular future outcome also differs from uncertainty about the model's average risk.

  45. Jürgens et al.: Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?

    Different internal uncertainty representations can produce the same predictive distribution. For the paper's unregularized inner-loss objectives with Dirichlet or normal-inverse-gamma representations, multiple parameter settings yield identical outcome predictions but different reported epistemic uncertainty. Thus, fitting observed outcomes alone need not uniquely determine a decomposition into uncertainty sources.

  46. AI Engineering 201: Inference

    Log probabilities expose information about generation that text-only responses conceal, but proprietary APIs can restrict that visibility.

  47. Guo et al.: On Calibration of Modern Neural Networks

    Confidence calibration asks whether predictions assigned a probability of correctness p are correct with frequency p. For example, predictions assigned 0.8 confidence should be correct about 80% of the time, rather than every prediction being individually guaranteed. Reliability diagrams compare observed accuracy and average confidence within probability bins. The paper demonstrates that a classifier can have better accuracy yet worse calibration: its CIFAR-100 ResNet is more accurate than its LeNet comparison but substantially overconfident.

  48. Ovadia et al.: Can You Trust Your Model's Uncertainty?

    The study evaluates uncertainty on original test data, shifted inputs and entirely different datasets. Its experiments show that calibration obtained on an ordinary validation distribution need not persist after shift. On rotated or translated MNIST, methods with similar accuracy can differ in probability quality and confidently wrong predictions. CIFAR-10 and ImageNet corruption experiments also show worsening accuracy and calibration as corruption increases.

  49. Hébert-Johnson et al.: Multicalibration—Calibration for the Computationally-Identifiable Masses

    Assigning everyone in a population its average outcome probability can satisfy population-level calibration while ignoring substantial differences within that population. Consequently, aggregate calibration does not establish useful individual discrimination or calibration within every subgroup. The paper motivates checking calibration across specified, potentially overlapping subpopulations rather than relying only on a pooled result.

  50. Elkan: The Foundations of Cost-Sensitive Learning

    A decision should minimize expected consequences, using probabilities and a consistently defined cost matrix. The most probable class need not produce the best action. For binary decisions with zero cost for correct decisions, false-positive cost C_FP and false-negative cost C_FN, choose positive when C_FP(1-p) is no greater than C_FN p. Rearranging gives the threshold p >= C_FP/(C_FP+C_FN). This is an algebraic specialization of the paper's decision rule, not an empirical result.

  51. Axelsson: The Base-Rate Fallacy and the Difficulty of Intrusion Detection

    The fraction of alerts that correspond to real events depends jointly on event prevalence, detection rate and false-positive rate. A small false-positive rate can produce many false alarms when non-events dominate. Constructed illustration: among 10,000 cases with 100 events, 80% event detection yields 80 true alerts and 20 misses; a 1% false-positive rate among 9,900 non-events adds 99 false alerts. Only 80 of 179 alerts are then true. These counts illustrate the paper's probability relationship.

  52. Geifman and El-Yaniv: Selective classification and risk control

    A selective classifier combines prediction f(x) with acceptance g(x)∈{0,1}; g=0 means abstain. Coverage is φ=P(g(X)=1). With positive coverage, selective risk is R=E[loss(f(X),Y)g(X)]/φ, the error among accepted predictions. Raising a confidence threshold rejects more inputs; error falls only if the score usefully orders mistakes. The paper's SGR procedure uses labeled examples and binomial upper bounds, adjusted for its threshold search, to bound accepted-set error with a specified failure probability δ. A target error is supported only when the returned bound meets that target.

  53. Agents reported thousands of bugs, how many were real? - Ian Butler and Nick Gregory

    An agent can find a real defect yet be impractical to use when it surrounds that finding with many false alarms.

  54. Dive into Deep Learning: environment and distribution shift

    Distribution shift occurs when deployment data follow a different distribution from training data. Covariate shift changes P(X) while retaining P(Y|X); label shift changes P(Y) while retaining P(X|Y). Such assumptions describe different failure and correction conditions. Performance estimated on the source distribution need not transfer to the target distribution. Unlike sampling randomness, which changes token choices for given scores, distribution shift changes which inputs and targets the predictor encounters. That comparison is a synthesis with the generation documentation.

  55. Dive into Deep Learning: Concept Shift

    Concept shift can change the conditional relationship P(Y|X), rather than only the frequency of inputs. The textbook illustrates this through changing category definitions and geographical differences in names for the same objects.

  56. Rabanser, Günnemann and Lipton: Failing Loudly

    Detecting changed input distributions and establishing degraded predictions are different tasks. The paper reports a COIL-100 rotation-angle split where detected shift did not harm the tested classifier. Directly measuring target error requires target labels; the authors investigate labeling selected anomalous examples as a heuristic. Their input-distribution test does not test the input-outcome relationship. Consequently, a change confined to that relationship could escape an input-only test; this last statement follows from the test's defined null hypothesis.

  57. Ross, Gordon and Bagnell: A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning

    Ross, Gordon and Bagnell show why sequential prediction differs from ordinary fixed-input supervised learning: a policy's action changes the observations it encounters later. Training only on expert-encountered states can therefore leave a learned policy unprepared for states caused by its own mistakes. DAgger iteratively executes a policy, obtains expert actions for encountered states and aggregates those examples so training better covers the policy-induced state distribution.

  58. Agents are Robots Too: What Self-Driving Taught Me About Building Agents — Jesse Hu, Abundant

    Departures from human-demonstration trajectories can put an agent into unfamiliar states and compound its errors; the talk connects this to DAgger and out-of-distribution behavior.

  59. Hernán and Robins: Causal Inference—What If

    A causal effect compares outcomes under alternative interventions. A counterfactual outcome describes what would occur under a specified action. Shared causes of action and outcome create confounding: their observed association includes a path other than the action's effect.

  60. When observational action records identify causal effects

    For action A, pre-action covariates L and potential outcome Y^a, standard adjustment identifies E[Y^a]=sum_l E[Y|A=a,L=l]P(L=l) under consistency, conditional exchangeability and positivity. Consistency links observed outcomes to a sufficiently specified intervention. Exchangeability requires Y^a independent of A given L: measured covariates adequately remove action-outcome confounding. Positivity requires P(A=a|L=l)>0 wherever the target population has support. Unmeasured common causes can invalidate exchangeability; actions never taken in relevant states leave their effects unidentified by this adjustment. Predictive accuracy on observed actions does not repair either failure.

  61. Feature attribution is not a real-world intervention effect

    Attribution methods distribute a prediction's difference from a reference value among input features. Results depend on how omitted features are averaged: conditioning on observed features preserves statistical associations, whereas intervening on model inputs and averaging other inputs marginally asks a different question. The paper shows that conditional attribution can assign relevance to a correlated feature the predictor does not use. Its intervention concerns inputs to a computational predictor, explicitly distinguished from causal relations among real-world variables. Therefore, changing a feature's attribution or changing that input in software does not establish how an intervention on the corresponding real-world quantity changes the actual outcome.

  62. Holland: Statistics and Causal Inference

    A unit's causal effect compares its potential outcomes under two specified treatments, but only the outcome under the received treatment is observed. Population averages offer a statistical route around this missing comparison. Random assignment makes treatment assignment independent of potential outcomes, allowing differences in observed group averages to estimate the average effect. Without that independence, the observed association need not equal the causal effect. An average effect also need not describe the effect on a particular unit.

  63. Perdomo et al.: Performative Prediction

    When predictions guide actions, deploying a predictor can change the distribution of future inputs and outcomes. The paper formalizes this by making the data distribution depend on the deployed model. Traffic predictions influencing traffic patterns are one motivating example. Fitting the historical distribution is then different from performing well on the distribution produced by acting on the model. Repeated retraining is not automatically a solution; convergence requires additional conditions.

  64. Build AI Systems for Discernment, Not Approval - Angel Ortmann Lee, Duolingo

    The human-AI interaction loop is cyclical: interfaces that encourage rubber-stamping can turn model-influenced approvals into misleading evaluation and training labels.

  65. Rolling-origin forecast evaluation

    Time-series cross-validation moves the forecast origin forward. At each origin T, the training set contains only earlier observations, and forecasts are scored against subsequent observations. Repeating this produces an out-of-sample error series; multi-step evaluation scores the horizon actually needed rather than only one-step predictions. Engineering consequence: preprocessing, model fitting and model selection must respect each origin's information boundary. Using a future observation anywhere in constructing its forecast defeats the chronological split.

  66. How Autoresearch Is Changing ML Research — Zhengyao Jiang, Weco AI

    In the reported fraud-detection experiment, separating test-data access from training preprocessing removed observed leakage that had inflated scores under a shared API.

  67. Beyond Static Intelligence: Evaluating Continual Learning

    Repeated SQL question answering can test whether retained schema knowledge reduces exploration, while simulated migrations test whether the agent discards obsolete knowledge.

  68. How LLMs work for Web Devs: GPT in 600 lines of Vanilla JS

    The MLP combines weighted inputs and biases with activation functions, connecting successive neuron layers through dense transformations.

  69. How LLMs work for Web Devs: GPT in 600 lines of Vanilla JS

    The foggy-mountain analogy presents optimization as using local slope information to seek parameter settings with lower prediction error.

  70. Stop Burning Tokens: Why self-improvement needs domain expertise first - Annabell Schäfer, Langfuse

    Use separate fit, validation, and untouched test datasets, with distinct roles in the optimization loop.

  71. Build AI Systems for Discernment, Not Approval - Angel Ortmann Lee, Duolingo

    The When Machines Mislead case study inserted fake copy-typing alerts into legitimate historical exam sessions and found that skilled proctors accepted half of those alerts.