Build Your Own teenygrad

Formulate the problem before choosing the machinery

Build Your Own teenygrad begins with a decision problem, not a framework. Construct a lazy buffer, reverse-mode autodiff engine, tensor API, neural primitives, and train a small MLP. Restate that sentence as an observable input, a desired output, and a criterion for preferring one output over another. Identify who or what supplies supervision, whether feedback is immediate or delayed, and whether examples can be considered independent. These choices determine what can be learned and what remains an assumption. The implementation is honest only when those assumptions are visible near the data contract rather than buried in training code.

The raw material becomes a feature representation. Representation decides which distinctions the system can express and which distinctions disappear. List categorical domains, numerical units, missing-value semantics, sequence or spatial axes, masks, player or client perspective, and precision. Then consider invariances: should translation, permutation, rescaling, token position, client identity, or board symmetry change the answer? An architecture that ignores the required invariance wastes data; one that imposes the wrong invariance makes the target impossible to represent.

Finally define the baseline and the abstention point. A baseline can be a constant predictor, random policy, linear rule, naive kernel, synchronous algorithm, or human heuristic. It anchors complexity in evidence. The abstention point describes inputs for which the system lacks support and should decline, defer, or fall back. Together they prevent Build Your Own teenygrad from being judged only by an impressive end-to-end demonstration while basic correctness, calibration, robustness, or operational usefulness remains unknown.

Connect the objective to the behavior you actually want

An objective compresses preferences into a scalar, but no scalar captures every product or scientific goal. For Build Your Own teenygrad, distinguish the training objective from the evaluation metric and the deployment utility. The training objective must provide a usable signal to parameters or state; evaluation must estimate generalization under a controlled protocol; deployment utility includes latency, cost, safety, and the consequence of errors. When these three disagree, optimization can succeed while the system becomes less useful.

Study each term dimensionally and statistically. Ask what happens if one term is multiplied by ten, one class becomes rare, a sequence becomes longer, a client contributes more samples, or rewards are shifted. Determine whether averages are per token, example, client, action, spatial position, or batch. Regularization is not decorative: it encodes a preference over solutions and changes units unless normalized consistently. A correct derivation names the population quantity of interest, its finite-sample estimator, and the approximation introduced by minibatches, replay, sampling, or surrogate losses.

Identifiability is the deeper constraint. Data may not contain enough information to separate competing explanations. Computation graphs, Reverse mode, Lazy execution can improve computation or inductive bias, but they cannot manufacture missing evidence. State causal assumptions, observability limits, support conditions, and equivalence classes of solutions. Use sensitivity analysis and targeted interventions where possible. When identification is impossible, report uncertainty or a set of plausible answers rather than converting an arbitrary modeling choice into unwarranted confidence.

Make mathematical equivalence survive finite precision

Paper algebra assumes exact real numbers; the implementation uses finite precision, bounded memory, and discrete execution order. In Build Your Own teenygrad, audit exponentials, logarithms, divisions, reductions, norms, probabilities, recursive values, and accumulated updates. Rewrite unstable expressions with max subtraction, log-sum-exp, compensated accumulation, safe denominators, or higher-precision reductions. Track where a mathematically harmless reordering changes rounding and where mixed precision needs scaling or master copies.

Shapes are part of the proof. Annotate each intermediate with semantic axes rather than only dimensions: batch, token, head, channel, client, action, expert, feature, row, column, or sample. Broadcasting should be intentional and verified with asymmetric dimensions so an accidental match cannot hide. Record contiguous layout and stride assumptions when performance code depends on them. For every reshape or transpose, write both the precondition and the inverse operation needed during backward, decoding, aggregation, or reconstruction.

Build a numerical ladder: scalar example, tiny vector or matrix example, batched reference, optimized path, then realistic workload. At each rung compare values and invariants before increasing scale. This catches defects while they are still interpretable. The acceptance test should specify absolute and relative error, exceptional values, deterministic modes, and the hardware or library versions used. Numerical stability is not a final cleanup task; it is part of the algorithm’s definition.

Design evidence that can falsify the implementation

Evaluation is an experiment. For Build Your Own teenygrad, specify the unit of analysis, split strategy, temporal boundary, randomization, baseline, metric, and uncertainty before viewing final results. Prevent duplicates, transformed copies, future information, opponent leakage, and shared-client information from crossing the boundary. A single aggregate score can hide subgroup collapse, unstable seeds, poor calibration, tail latency, or rare catastrophic behavior, so pair it with distributions and stratified slices.

Ablations connect outcomes to mechanisms. Remove or replace Computation graphs, Reverse mode, Lazy execution one at a time while controlling data, compute, and evaluation. Compare equal wall-clock or equal resource budgets when efficiency is part of the claim. Repeat stochastic runs and report variation rather than selecting the best seed. Inspect learning curves and intermediate metrics because two systems with the same final score may differ radically in sample efficiency, stability, or cost.

The test suite and the benchmark answer different questions. Unit and property tests prove local contracts; integration tests prove components agree; benchmarks estimate behavior at scale; task evaluation estimates usefulness. Preserve all four. A benchmark that bypasses validation or uses a different code path from production is weak evidence. The strongest release gate reruns the exact packaged implementation with recorded configuration and produces an artifact that another person can inspect.

Turn the learning artifact into an operable system

Production structure separates pure computation from orchestration, configuration, persistence, and interfaces. Package the core of Build Your Own teenygrad behind typed contracts. Keep data loading, model or state construction, training, evaluation, serialization, and serving independently invocable. Configuration should be validated, versioned, and printable. Random seeds, data identifiers, source commit, dependency lock, hardware, and metric definitions belong in the run record so an apparent regression can be reproduced instead of guessed at.

Capacity planning follows the critical path. Measure sample complexity, arithmetic work, memory, and validation effort across representative input sizes and concurrency. Report warm-up separately, distinguish throughput from latency, and include tail percentiles. Define memory ownership and lifetime so caches, activations, buffers, replay, or optimizer state cannot grow without a bound. Backpressure and admission control are preferable to unpredictable collapse. Where hardware-specific acceleration exists, preserve a portable reference path for correctness and degraded operation.

Observability must explain decisions and failures without exposing sensitive content. Log stable identifiers, shapes, versions, summary statistics, timings, and error categories. Monitor input drift, output distribution, task quality, saturation, retries, and fallback rate. Establish rollback and shadow-evaluation procedures before the first risky change. A production-grade implementation is not merely more abstract than a notebook; it makes dependencies, state, failure, and evidence explicit enough for another engineer to operate safely.

Read claims as reproducible hypotheses

The research surrounding Build Your Own teenygrad improves representations, objectives, algorithms, systems, or evaluation protocols. Classify each paper by which lever it changes. Then identify the comparison budget: data, parameters, tokens, environment steps, hardware, communication, wall-clock time, and tuning effort. A claimed improvement may disappear when budgets are normalized or when the baseline receives equal tuning. Read methods and appendices for details that determine reproducibility, not only the abstract and headline table.

Reproduction begins with the smallest claim. Recreate one table row or ablation before attempting the entire system. Preserve the authors’ preprocessing and metric definitions, then deliberately vary one assumption. Document deviations, failed attempts, and environment details. When a result does not reproduce, distinguish an implementation defect from missing procedural knowledge, stochastic uncertainty, and genuine sensitivity. Negative evidence is useful when it narrows the conditions under which the method works.

Extension should start from a mechanism and a falsifiable prediction. The skills developed here—Autograd, Tensor systems, Framework design—suggest multiple directions, but change one major factor at a time. Predict which metric and intermediate signal should move if the explanation is correct. Use confidence intervals and preregistered stopping rules for expensive experiments where possible. Publish code, configuration, data provenance, and failure cases so the work contributes more than another isolated score.

Maintain a chain of evidence from equation to outcome

A proof ledger for Build Your Own teenygrad links each important claim to the smallest evidence that could disprove it. For a mathematical claim, keep a hand-worked example and a high-precision reference. For a software contract, keep unit and property tests. For an optimization claim, keep profiler traces and equal-budget baselines. For a learning claim, keep per-seed results, confidence intervals, and ablations. For a production claim, keep load tests, failure injection, monitoring queries, and rollback evidence. This structure prevents one successful end-to-end run from being treated as proof of every layer beneath it.

Record evidence beside the versioned artifact it evaluates. A metric without its dataset revision, configuration, dependency lock, hardware, and commit cannot reliably settle a regression. Likewise, a screenshot or generated sample is qualitative evidence, not a distribution. Name the claim, evidence type, acceptance threshold, owner, and date. When the implementation changes, rerun the smallest affected evidence first and then the downstream integration gates. The ledger becomes a map of confidence: it shows what is known, what is assumed, what has become stale, and where another experiment is required.

Use the ledger during review. Ask whether each test would fail for a realistic defect, whether each benchmark measures the packaged code path, whether every aggregate retains inspectable raw values, and whether uncertainty is reported at the correct independent unit. Include counterexamples and failed experiments because they define the boundary of the method. Over time this habit turns Autograd, Tensor systems, Framework design from isolated implementation skills into a reproducible engineering practice that survives new data, new hardware, new collaborators, and changing product constraints.

Prod — from contract to production evidence

Prod is the pipeline boundary at milestone 1 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between shape utilities and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Prod as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Prod depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Prod needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Prod can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Prod changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Shape Utilities. Implement the small helper functions for working with shape tuples and index ordering that the rest of the engine relies on.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

LazyBuffer — from contract to production evidence

LazyBuffer is the pipeline boundary at milestone 4 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between the lazy buffer backend and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat LazyBuffer as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If LazyBuffer depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for LazyBuffer needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how LazyBuffer can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing LazyBuffer changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: The Lazy Buffer Backend. Build the numpy-backed LazyBuffer with constant and random initialization plus elementwise, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Lazybuffer Unary E — from contract to production evidence

Lazybuffer Unary E is the pipeline boundary at milestone 7 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between the lazy buffer backend and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Lazybuffer Unary E as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Lazybuffer Unary E depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Lazybuffer Unary E needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Lazybuffer Unary E can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Lazybuffer Unary E changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: The Lazy Buffer Backend. Build the numpy-backed LazyBuffer with constant and random initialization plus elementwise, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Lazybuffer Reshape — from contract to production evidence

Lazybuffer Reshape is the pipeline boundary at milestone 10 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between the lazy buffer backend and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Lazybuffer Reshape as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Lazybuffer Reshape depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Lazybuffer Reshape needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Lazybuffer Reshape can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Lazybuffer Reshape changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: The Lazy Buffer Backend. Build the numpy-backed LazyBuffer with constant and random initialization plus elementwise, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Function — from contract to production evidence

Function is the pipeline boundary at milestone 13 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Function as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Function depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Function needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Function can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Function changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Relu — from contract to production evidence

Relu is the pipeline boundary at milestone 17 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Relu as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Relu depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Relu needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Relu can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Relu changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Sqrt — from contract to production evidence

Sqrt is the pipeline boundary at milestone 20 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Sqrt as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Sqrt depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Sqrt needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Sqrt can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Sqrt changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Sub — from contract to production evidence

Sub is the pipeline boundary at milestone 23 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Sub as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Sub depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Sub needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Sub can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Sub changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Sum Function Forward — from contract to production evidence

Sum Function Forward is the transformation at milestone 26 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Sum Function Forward as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Sum Function Forward depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Sum Function Forward needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Sum Function Forward can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Sum Function Forward changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Reshape — from contract to production evidence

Reshape is the pipeline boundary at milestone 30 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Reshape as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Reshape depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Reshape needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Reshape can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Reshape changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Permute Function Forward Backward — from contract to production evidence

Permute Function Forward Backward is the learning update at milestone 33 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between autograd functions and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Permute Function Forward Backward as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Permute Function Forward Backward depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Permute Function Forward Backward needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Permute Function Forward Backward can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Permute Function Forward Backward changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Autograd Functions. Define the differentiable Function base class and implement forward and backward passes for all unary, binary, reduce, and movement operations.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Tensor Creation Helpers — from contract to production evidence

Tensor Creation Helpers is the pipeline boundary at milestone 36 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between the tensor api and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Tensor Creation Helpers as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Tensor Creation Helpers depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Tensor Creation Helpers needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Tensor Creation Helpers can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Tensor Creation Helpers changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: The Tensor API. Create the Tensor wrapper, creation helpers, topological backward pass, and method bindings for every supported operation.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Tensor Backward — from contract to production evidence

Tensor Backward is the learning update at milestone 39 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between the tensor api and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Tensor Backward as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Tensor Backward depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Tensor Backward needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Tensor Backward can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Tensor Backward changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: The Tensor API. Create the Tensor wrapper, creation helpers, topological backward pass, and method bindings for every supported operation.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Bind Binary Tensor Methods — from contract to production evidence

Bind Binary Tensor Methods is the pipeline boundary at milestone 42 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between the tensor api and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Bind Binary Tensor Methods as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Bind Binary Tensor Methods depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Bind Binary Tensor Methods needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Bind Binary Tensor Methods can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Bind Binary Tensor Methods changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: The Tensor API. Create the Tensor wrapper, creation helpers, topological backward pass, and method bindings for every supported operation.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Tensor Transpose — from contract to production evidence

Tensor Transpose is the pipeline boundary at milestone 46 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between functional and composite ops and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Tensor Transpose as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Tensor Transpose depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Tensor Transpose needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Tensor Transpose can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Tensor Transpose changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Functional and Composite Ops. Compose primitives into higher-level operations like mean, matmul, softmax, log_softmax, and cross entropy.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Tensor Log Softmax — from contract to production evidence

Tensor Log Softmax is the transformation at milestone 49 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between functional and composite ops and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Tensor Log Softmax as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Tensor Log Softmax depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Tensor Log Softmax needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Tensor Log Softmax can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Tensor Log Softmax changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Functional and Composite Ops. Compose primitives into higher-level operations like mean, matmul, softmax, log_softmax, and cross entropy.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

MLP — from contract to production evidence

MLP is the pipeline boundary at milestone 52 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between neural network modules and optimizer and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat MLP as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If MLP depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for MLP needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how MLP can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing MLP changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Neural Network Modules and Optimizer. Implement Linear layers, an MLP, and the SGD optimizer with gradient zeroing.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Make Toy Digit Dataset — from contract to production evidence

Make Toy Digit Dataset is the construction at milestone 55 of Build Your Own teenygrad. Its purpose is not merely to make the next function run. It establishes a contract between training and evaluation and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Computation graphs, Reverse mode, Lazy execution—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Make Toy Digit Dataset as a mapping from available information to a new feature representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Make Toy Digit Dataset depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Make Toy Digit Dataset needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against hand calculations, unit tests, controlled baselines, and held-out metrics. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Make Toy Digit Dataset can look plausible while being wrong. Inspect leakage, numerical instability, overfitting, shape errors, and misleading aggregate metrics. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Make Toy Digit Dataset changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure sample complexity, arithmetic work, memory, and validation effort. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Training and Evaluation. Generate a toy dataset, train the MLP end to end, and evaluate its accuracy on a held-out split.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.