Incremental checkpoints and deduplication

An exact changed-block scheme partitions a serialized logical state into stable regions, writes changed regions, and references unchanged immutable objects. A content-addressed scheme can identify identical encoded bytes, but hashes need a declared algorithm and metadata interpretation. Tensor names, dtype, shape, and region boundaries must remain connected to those bytes. If chunk boundaries change whenever sharding changes, otherwise similar state may deduplicate poorly. Optimizer moments often change densely, so the actual savings depend on the state and workload rather than a universal checkpoint compression ratio.

A gradient log or numerical delta is a different design. Reconstruction may require an ordered base plus records and possibly application computation. Lossy quantization, omitted small updates, or recomputed optimizer state can alter the resumed trajectory unless the recovery contract explicitly allows that approximation. The cited Check-N-Run work studies a particular recommendation-training setting; its workload-specific incremental and quantization results do not establish exact general-purpose recovery for every dense model. Name whether the scheme preserves bytes, logical numerical values, or only an evaluated training-quality criterion.

In a simplified base-plus-delta chain, storage includes the base and every distinct retained delta, plus metadata. A newer generation may reference older unchanged blocks directly rather than require replay of every intermediate generation; another format may require the whole ordered chain. These are different restore costs. Measure read amplification, metadata traversal, reconstruction computation, and failure behavior for the actual representation. Periodic materialized full snapshots can shorten chains at the cost of additional writes and temporarily higher retained storage.

Deduplication also separates logical deletion from physical reclamation. Removing an old generation’s manifest does not authorize deleting all objects it once referenced, because newer generations may share them. Compute reachability from all retained committed manifests, then account for active readers, in-progress writers, and any required recovery grace period. A reference-count update that races publication can lose live data unless updates are transactional or otherwise coordinated. A conservative mark-and-sweep protocol needs a stable root set or an explicit rule for objects created during the sweep.

A shared container file can pack live and dead chunks together. Reclaiming the file requires either proving every chunk dead or compacting live chunks into a new immutable container and publishing replacement references safely. Compaction cannot rewrite an object still referenced by a committed manifest in place. Restore leases or another reader-protection mechanism keep a collector from deleting the only source while a long recovery is reading it. Test interruptions during compaction, publication, and collection, including a retry that sees partially completed work.

The cache lab illustrates reuse but deliberately lacks dependency protection. Reset, set both C=4 and s=4, predict four misses and thirteen hits after seventeen requests, then Step once. Separately Reset, set both C=2 and s=4, predict seventeen misses after seventeen requests, then Step once. Each run begins at sixteen requests, and one Step adds one. The four-address cycle fits only the larger LRU cache. Its eviction decisions are not a checkpoint garbage collector: a rarely accessed object can remain indispensable to a retained generation and must not be deleted merely because LRU would evict it.