Improve Bounded Evidence Performance
If we don't allow evidence to grow infinitely, memory fades. Develop mechanisms to deal with this, including using nodes with more neuron-like integration properties.
In the current evidence-based learning module, evidence grows infinitely as Monty compares each hypothesis’s predictions with the observed features at every matching step.
Hypotheses accumulate evidence proportional to their similarity to the observed features, which produces unbounded scores.
Unbounded accumulation of evidence is undesirable for several reasons.
The Challenges and Expected Improvements
A Temporal Bias Limits Improved Hypotheses
First, unbounded accumulation introduces a strong temporal bias.
Hypotheses that are initialized earlier in an episode have more opportunities to accumulate evidence and can dominate the hypothesis space simply due to their age.
This behavior becomes problematic when new hypotheses are sampled later in time.
Newly sampled hypotheses are disadvantaged and may fail to out-compete existing ones, even if they are more consistent with recent observations.
A concrete outcome that we could measure for is that the most likely hypothesis (MLH) that Monty infers approaches the "theoretical limit" (see TheoreticalLimitLMLoggingMixin), i.e. the error associated with the best hypothesis that Monty has initialized. Unbound evidence currently means that an older, "good enough" hypothesis will often remain the MLH even where the theoretical limit is lower following sampling of new hypotheses.
Evidence Interpretation and Hyperparameter Tuning are Challenging
A second issue is that, when resampling of hypotheses is allowed, unbounded evidence values become difficult to interpret and reason about.
As evidence grows arbitrarily large, the absolute magnitude of a score becomes less meaningful, and comparisons depend increasingly on the hypotheses age values rather than consistency with recent observations.
Bounded scores are easier to work with as they allow downstream components to rely on known numerical ranges, simplifying threshold selection and enabling more stable decision rules for deleting and resampling hypotheses.
Potential Solutions
Bounding evidence through methods such as exponential moving averages, weighted averages (e.g. past and present weight summing to 1), or normalization by hypothesis age can keep scores within a bounded range.
However, these techniques compress historical information and cause memory to fade over time.
Monty loses the influence of important past features, such as a mug handle, as a result, recognition can become less accurate in long sequences.
A promising direction is to pair bounded evidence with saliency-driven saccades or other attention mechanisms, which we now have a working version of - currently this combination remains untested.
If the system consistently revisits the key discriminative features that are important for recognition, and does so efficiently, then those features remain present in recent history.
A Biological Connection and Other Benefits
It is worth highlighting that this Future Work item bears some interesting parallels to Monty more closely modeling the brain. In particular, neurons in the brain can be well described by the leaky integrate-and-fire (LIF) model. LIF neurons gradually accumulate incoming spikes, up to a limit at which they spike and reset their membrane potential. At the same time, they constantly lose current (hence "leaky") towards a resting membrane potential. We believe something like a "Cumulative Moving Average neuron" (CMA neuron) could well approximate the dynamics we are interested in (evidence upper-bounded and temporal decay) that are captured in LIF neurons.
The above biological framing may help us develop other useful properties. For example, "spiking" in CMA neurons (i.e., reaching a particular threshold) could be a basis for communicating representations further up in the hierarchy or via voting, including informing associative learning between LMs. At the same time, hypotheses in Monty can be thought of as "neuron instances" - unlike biological brains that must use a fixed capacity of physical neurons, we have the benefit that we can initialize new neural instances as required. This affords trading off computational intensity for parallelization and faster inference speed, and could enable a new kind of neuron that borrows from the strengths of silicon and biological systems.
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Updated 26 days ago