Elamur Groupantsalgorithm-forward-backward-tests
The groupant beside algorithms/src/forward_backward/tests.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | syntax.json |
| descriptant | present | descriptant |
| invariant | partial | model |
| tests | existing checks referenced | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
independent_oracle | independent_oracle | partial source derived model | independent_oracle |
boundary_partition | boundary_partition | partial source derived model | boundary_partition |
compiled_mutation | compiled_mutation | partial source derived model | compiled_mutation |
Model text
descriptant
forward_backward checks
Original std-only implementation and fixtures; source citations appear in module documentation.
Independent finite oracle and boundary tests for forward_backward. Production: n1..64,T0..4096; normalized finite initial/transition rows and time-major emissions in[0,1]. Shape then values then row normalization. Alpha log-sum-exp over incoming paths; beta log-sum-exp over outgoing paths. exp(alpha+beta-logZ), normalized per posterior row. Empty returns logZ0/no rows; zero evidence returns None.
Epoch 2026-10-30: independent tiny-domain oracle, repeated debug/release and compiled production mutation. No timing or end-to-end Mova claims.
model
Invariants and state
Independent finite oracle and boundary tests for forward_backward. Production: n1..64,T0..4096; normalized finite initial/transition rows and time-major emissions in[0,1]. Shape then values then row normalization. Alpha log-sum-exp over incoming paths; beta log-sum-exp over outgoing paths. exp(alpha+beta-logZ), normalized per posterior row. Empty returns logZ0/no rows; zero evidence returns None.
All-pass excludes represented oracle mismatches and rejected boundary violations in these finite fixtures only. Production excluded-output relation: Negative or nonnormalized posterior rows are excluded by the real model; represented rows are normalized by their computed sum. Impossible evidence excludes a posterior. Validation errors take precedence over empty-sequence success.
O(Tnn) arithmetic, O(T*n+n) space; log-sum-exp allocates a temporary bounded n-vector per recurrence.
All allocations follow standard Rust process policy, not fallible allocation APIs. No callbacks or external effects. f64 roundoff and underflow remain explicit limitations.
approximant
Forward and cost approximant
Independent finite oracle and boundary tests for forward_backward. Production: n1..64,T0..4096; normalized finite initial/transition rows and time-major emissions in[0,1]. Shape then values then row normalization. Alpha log-sum-exp over incoming paths; beta log-sum-exp over outgoing paths. exp(alpha+beta-logZ), normalized per posterior row. Empty returns logZ0/no rows; zero evidence returns None.
O(Tnn) arithmetic, O(T*n+n) space; log-sum-exp allocates a temporary bounded n-vector per recurrence.
No executable cheaper surrogate or supported generic 1/2/5/10% profile is claimed. Residuals and floating estimates are not solution-error certificates.
models
behavior_complement
All-pass excludes represented oracle mismatches and rejected boundary violations in these finite fixtures only. Production excluded-output relation: Negative or nonnormalized posterior rows are excluded by the real model; represented rows are normalized by their computed sum. Impossible evidence excludes a posterior. Validation errors take precedence over empty-sequence success.
reverse_reconstruction
All-pass observations admit implementations differing on unsampled inputs. This finite test fiber does not uniquely identify source or prove universality. Production fiber: Posterior and likelihood admit many hidden models, e.g. a one-state model with different emission factorizations sharing the same product. Observed marginals do not recover joint state paths or transitions uniquely.
independent_oracle
Tiny path enumeration, analytical rank-one matrices or independent weighted moments reconstruct expectations without calling the production recurrence; scope is finite.
boundary_partition
Shape, zero/empty, invalid finite values, ties or budget boundaries are explicitly asserted. Numeric tolerance is fixture-specific.
compiled_mutation
A compiled changed production recurrence must fail the named oracle assertion. Restoration plus positive rerun checks that the gate can distinguish this wrong behavior.
tests
Validation
Run cargo test -p mova-algorithms forward_backward::tests. Evidence in $MOVA_DATA/runs/octopus-wave26-probability-2026-10-30: repeated profiles, mutation logs and restored positive runs. Three named tests per module. See receipt.json for evidence hashes. No allocator fault injection, timing or full-school measurement.
prospective
Probability batch prospective math
Written before implementation. All code original, std-only. Bounded allocations use standard Vec; allocator failure follows Rust process policy, no callbacks or RNG.
Alias: Walker (1977), An efficient method for generating discrete random variables with general distributions; Vose (1991), A linear algorithm for generating random numbers with a given distribution. n 1..4096, finite nonnegative weights, positive maximum. Scale by maximum then total to avoid overflow. Small/large work lists conserve total scaled mass. Column uniform and coin uniform [0,1) produce the specified categorical distribution in real arithmetic; caller explicitly supplies coordinates. O(n) build/storage, O(1) draw. No probabilistic draw generation or numeric percentage guarantee.
HMM: Rabiner (1989), A tutorial on hidden Markov models and selected applications in speech recognition; Viterbi (1967), Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. n1..64, T0..4096; finite probabilities in [0,1], initial/transition rows sum to one within 1e-10. Emissions time-major likelihoods in [0,1], need not sum across states. Validate structure then numeric values before empty sequence. Empty log likelihood0/path empty. Viterbi log max-plus recurrence, predecessor ties lowest index and terminal ties lowest index (not global lexicographic). No positive path =>None. Forward/backward log-sum-exp, posterior proportional exp(alpha+beta-logZ); per-row normalization corrects rounding. O(Tn²) time/O(Tn) space. Tiny exhaustive state-sequence enumeration is independent oracle. Log scales avoid direct-product underflow; no general floating error bound.
Sinkhorn: Sinkhorn and Knopp (1967), Concerning nonnegative matrices and doubly stochastic matrices. Positive matrix entries and marginals restricted [1e-100,1e100], dims1..64, equal marginal totals within tolerance1e-12 relative. Alternate row and column multiplication to target marginals; residual max absolute marginal discrepancy. Budget0..10000, finite tolerance>0. Stop on residual<=tolerance or budget; overflow/underflow to zero explicit arithmetic error. O(iterationsrc) time/O(rc) space. Residual is feasibility evidence, not solution distance/optimality guarantee. Scale-invariant input fibers and budget status explicit.
Weighted covariance: West (1979), Updating mean and variance estimates: an improved method; Chan, Golub, LeVeque (1983), Algorithms for computing the sample variance. dimension1..64; finite coordinates |x|<=1e100, weights[0,1e100]. Population covariance M2/W, not unbiased sample covariance. Zero weight validates coordinates then does nothing. Merge dimensions must match, empty neutral. Merge W=A+B; delta=muB-muA; mu=muA+deltaB/W; M2=M2A+M2B+delta outer deltaA*(B/W). Atomic error updates, finite intermediates required. O(d²) push/merge/storage. Independent batch weighted centered moments oracle, partition merge equivalence within tolerance. No order-bitwise identity or universal covariance error certificate.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/forward_backward/tests.rs.groupant/