Bloom Filter

A Bloom filter represents a set using a fixed-size bit array and k independent hash functions. When inserting an element, each hash function sets a corresponding bit to 1. To query membership, the same hash functions are computed—if all bits are 1, the element is probably in the set. This structure achieves sub-linear space complexity relative to the number of elements stored, typically requiring only 8-10 bits per element for a 1% false positive rate, compared to storing full keys which may consume hundreds of bytes each.

The probability of a false positive—where the filter incorrectly reports an element as present—is a tunable parameter determined by:

• m: The size of the bit array
• k: The number of hash functions
• n: The number of inserted elements

The optimal number of hash functions is k = (m/n) * ln(2). For example, a filter with m/n = 10 bits per element and k = 7 hash functions yields approximately a 1% false positive rate. Critically, false negatives are impossible—if the filter says an element is absent, it is definitively absent.

In sovereign inference caching, a Bloom filter acts as a lightweight gatekeeper before querying the main semantic cache or vector database. When a new embedding arrives:

• The Bloom filter is checked first to determine if the key might exist in the cache
• If the filter returns negative, the expensive cache lookup is entirely skipped, saving memory bandwidth and compute cycles
• If the filter returns positive, the full cache is queried to confirm the hit

This pattern is especially valuable when the cache miss penalty is high, such as when the origin model is a self-hosted LLM running on scarce GPU resources.

A standard Bloom filter does not support element deletion. Because multiple elements may set the same bit, clearing a bit to remove one element could introduce false negatives for other elements that share that bit. For use cases requiring deletion, variants such as Counting Bloom Filters replace each bit with a small counter, incrementing on insertion and decrementing on deletion. However, this increases memory overhead by a factor of 3-4x depending on counter width.

Bloom filters representing sets with the same bit array size and hash functions can be combined:

• Union: A bitwise OR of two filters produces a filter representing the combined set, useful for merging cache shard membership queries
• Intersection: A bitwise AND approximates the intersection, though it may introduce additional false positives

These properties enable distributed cache architectures where each sovereign node maintains a local Bloom filter that can be aggregated for global membership queries without centralizing the actual cached data.

When the number of elements to insert is unknown in advance, a Scalable Bloom Filter dynamically allocates additional filter layers as the fill ratio exceeds a threshold. Each new layer has a tighter false positive probability (e.g., halving at each level), ensuring the overall false positive rate remains bounded. This is critical for long-running sovereign inference caches where the working set grows over time and static sizing would lead to degraded accuracy.

A caching layer that stores responses based on the semantic meaning of a query rather than exact keyword matching. It uses embeddings to serve previously computed LLM outputs for similar requests.

• Reduces latency by avoiding redundant inference
• Relies on probabilistic structures like Bloom Filters for rapid key existence checks
• Essential for sovereign environments where external API calls must be minimized

The deterministic algorithm that decides which entries to remove when a cache reaches its memory capacity. The policy balances hit rate against resource constraints.

• LRU (Least Recently Used): Discards the oldest-accessed item first
• LFU (Least Frequently Used): Removes items with the lowest access count
• TTL-Based: Evicts entries after a pre-defined expiration duration
• Bloom Filters help avoid re-caching items known to be absent

A cascading failure scenario where a popular cache entry expires, causing a flood of concurrent requests to simultaneously hit the origin model or database. This overwhelms backend resources.

• Bloom Filters can mitigate stampedes by quickly rejecting duplicate in-flight requests
• Often addressed with probabilistic early expiration and request coalescing
• A primary threat to sovereign inference infrastructure stability

A distributed hashing scheme that minimizes key remapping when cache nodes are added or removed. This is essential for maintaining high hit rates in elastic cache clusters.

• Only K/n keys are remapped on node changes (where K is total keys, n is nodes)
• Prevents mass cache invalidation during sovereign cluster scaling
• Often used alongside Bloom Filters in distributed cache architectures