Paul Kirkland presents What World Models Forget: The Case for Algebraic Cognitive Maps
On 2026-06-09 10:00:00 at G205, Karlovo náměstí 13, Praha 2
TOPIC: Event-based vision and neuromorphic algos.
Modern semantic SLAM systems and learned world models have made major progress,
but persistent, compact, and queryable spatial memory remains difficult. Memory
is often bounded by a context window, stored in an explicit map that must be
searched or traversed, or embedded in a learned representation whose uncertainty
is hard to interpret. The issue is not only memory size, but representation:
these systems often have indices and associations, but limited algebra for
manipulating memory.
We present a cognitive-map substrate based on Vector Symbolic Architectures and
Spatial Semantic Pointers. Object identity, learned semantic features, and
continuous world-coordinate position are bound into a single high-dimensional
representation using SLAM-derived pose estimates. This enables spatial contents
and relations to be queried algebraically, such as retrieving likely objects at
a location or approximating “what is to the left of the table?” through
spatial shifts and associative recall.
A key feature of the approach is that uncertainty is built into the
representation rather than added only after inference. VSA memory has
predictable capacity limits: retrieval error can be analysed in terms of
dimensionality-driven crosstalk noise, while SSP geometry introduces a spatial
kernel bias that determines how sharply locations can be resolved. This provides
a compact algebraic memory layer for SLAM and learned world models, aimed at
persistent spatial reasoning in SWaP-constrained robotic and neuromorphic
systems where predictable behaviour and low compute cost are critical.
Modern semantic SLAM systems and learned world models have made major progress,
but persistent, compact, and queryable spatial memory remains difficult. Memory
is often bounded by a context window, stored in an explicit map that must be
searched or traversed, or embedded in a learned representation whose uncertainty
is hard to interpret. The issue is not only memory size, but representation:
these systems often have indices and associations, but limited algebra for
manipulating memory.
We present a cognitive-map substrate based on Vector Symbolic Architectures and
Spatial Semantic Pointers. Object identity, learned semantic features, and
continuous world-coordinate position are bound into a single high-dimensional
representation using SLAM-derived pose estimates. This enables spatial contents
and relations to be queried algebraically, such as retrieving likely objects at
a location or approximating “what is to the left of the table?” through
spatial shifts and associative recall.
A key feature of the approach is that uncertainty is built into the
representation rather than added only after inference. VSA memory has
predictable capacity limits: retrieval error can be analysed in terms of
dimensionality-driven crosstalk noise, while SSP geometry introduces a spatial
kernel bias that determines how sharply locations can be resolved. This provides
a compact algebraic memory layer for SLAM and learned world models, aimed at
persistent spatial reasoning in SWaP-constrained robotic and neuromorphic
systems where predictable behaviour and low compute cost are critical.