  Using finite-state machines to learn patterns, Tsetlin machines (TMs) have
obtained competitive accuracy and learning speed across several benchmarks,
with frugal memory- and energy footprint. A TM represents patterns as
conjunctive clauses in propositional logic (AND-rules), each clause voting for
or against a particular output. While efficient for single-output problems, one
needs a separate TM per output for multi-output problems. Employing multiple
TMs hinders pattern reuse because each TM then operates in a silo. In this
paper, we introduce clause sharing, merging multiple TMs into a single one.
Each clause is related to each output by using a weight. A positive weight
makes the clause vote for output $1$, while a negative weight makes the clause
vote for output $0$. The clauses thus coalesce to produce multiple outputs. The
resulting coalesced Tsetlin Machine (CoTM) simultaneously learns both the
weights and the composition of each clause by employing interacting Stochastic
Searching on the Line (SSL) and Tsetlin Automata (TA) teams. Our empirical
results on MNIST, Fashion-MNIST, and Kuzushiji-MNIST show that CoTM obtains
significantly higher accuracy than TM on $50$- to $1$K-clause configurations,
indicating an ability to repurpose clauses. E.g., accuracy goes from $71.99$%
to $89.66$% on Fashion-MNIST when employing $50$ clauses per class (22 Kb
memory). While TM and CoTM accuracy is similar when using more than $1$K
clauses per class, CoTM reaches peak accuracy $3\times$ faster on MNIST with
$8$K clauses. We further investigate robustness towards imbalanced training
data. Our evaluations on imbalanced versions of IMDb- and CIFAR10 data show
that CoTM is robust towards high degrees of class imbalance. Being able to
share clauses, we believe CoTM will enable new TM application domains that
involve multiple outputs, such as learning language models and auto-encoding.
