Belief States Uncovered: Internal Knowledge & Uncertainty in AI Agents

MEMRIQ INFERENCE DIGEST - EDITION

Episode: Belief States Uncovered: Internal Knowledge & Uncertainty in AI Agents

Total Duration:: 36:50

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MORGAN: 00:00

Welcome to the Memriq Inference Digest - Edition, your go-to podcast for deep dives into the latest AI techniques and frameworks. We’re brought to you by Memriq AI, a content studio crafting tools and resources for AI practitioners. Head over to Memriq.ai for more on that.

CASEY: 00:17

Today we’re unpacking a fascinating and foundational concept in AI: belief states—how models represent internal knowledge and uncertainty. When machines operate under incomplete information, belief states become the lens through which they ‘know’ and act.

MORGAN: 00:33

And if you want to dive deeper beyond today’s chat, Keith Bourne’s second edition book is a fantastic resource. It’s packed with diagrams, hands-on code labs, and thorough explanations that complement this topic perfectly, particularly the multiple chapters on advanced agentic memory. Just search Keith Bourne on Amazon.

CASEY: 00:52

We’ll cover everything from classical methods like POMDPs and Bayesian filtering up to cutting-edge approaches like BetaZero and neural implicit belief representations. Plus, we’ll explore real-world use cases and where the field is heading next.

MORGAN: 01:07

Buckle up—this one’s going to challenge how you think about AI decision-making under uncertainty!

JORDAN: 01:14

Imagine this: uncertainty isn’t just noise or a problem to solve; it *is* the agent’s internal state. When an AI can treat its uncertainty like a state itself, it can plan and reason in a whole new way.

MORGAN: 01:26

Wait, so the agent doesn’t just guess the world’s state—it literally operates *on* what it believes about the world?

JORDAN: 01:33

Exactly. Take Partially Observable Markov Decision Processes, or POMDPs. They show us that any partially observable problem can be transformed into a fully observable one if you consider *belief states*—probability distributions over possible world states—as the new state.

CASEY: 01:49

That’s a huge conceptual leap. Instead of needing to know exactly where you are, you plan based on what you *think* is true, right?

JORDAN: 01:58

Spot on. And BetaZero’s 2024 incarnation demonstrates this masterfully. It combines neural networks that implicitly represent belief states with Monte Carlo tree search to plan deeply in uncertain, high-dimensional environments.

MORGAN: 02:12

So, the AI is playing out its own beliefs about the future, not just fixed facts. That’s a paradigm shift in planning under uncertainty.

CASEY: 02:20

But how practical is this outside of board games and simulations?

JORDAN: 02:24

That’s exactly what we’ll explore, Casey. Because this mindset is becoming essential for autonomous vehicles, dialogue systems, robotics, and beyond.

MORGAN: 02:34

Love it. Uncertainty as the *state*—not just a hurdle but the very essence of decision-making. That’s going to stick with me.

CASEY: 02:41

Here’s the heart of it: belief states are mathematical objects encoding an agent’s internal uncertainty—what it knows, suspects, or rules out. They allow principled decision-making under partial information. Key tools include POMDPs, Bayesian filtering methods like Kalman and particle filters, neural networks such as RNNs and Transformers, generative models like VAEs and GANs, logical frameworks like AGM belief revision, and advanced algorithms like BetaZero and I-POMDPs for multi-agent scenarios.

JORDAN: 03:12

Historically, belief states have been around for decades, but early approaches struggled with scalability. Classical POMDP solvers couldn’t handle high-dimensional spaces or complex observations.

CASEY: 03:23

So what’s changed? Why are belief states suddenly more practical?

JORDAN: 03:28

Deep learning played a big role. Neural nets let us implicitly encode beliefs in continuous latent spaces, sidestepping some of the combinatorial complexity.

MORGAN: 03:37

And generative models like VAEs, GANs, and diffusion models?

JORDAN: 03:41

They revolutionized sampling from belief distributions, making it more scalable and flexible. Then there’s BetaZero, which brought belief-space planning into the practical realm for complex tasks by combining learned models with Monte Carlo tree search.

CASEY: 03:57

So it’s the synergy of better function approximators and planning algorithms that cracked open this problem?

JORDAN: 04:04

Exactly. And with AI adoption growing in robotics, dialogue systems, and autonomous driving, companies are investing heavily in belief state methods to handle real-world uncertainty.

MORGAN: 04:15

So belief states went from theoretical curiosities to practical necessities.

JORDAN: 04:20

That’s right. The timing is perfect for advancing AI agents that operate reliably in noisy, complex environments.

TAYLOR: 04:27

At its core, a belief state captures *everything* the agent knows or suspects about the true environment state at a given moment.

MORGAN: 04:35

So it’s like a probability distribution over possible world states?

TAYLOR: 04:39

Often, yes. In the POMDP framework, the belief state b(s) is updated recursively using the transition model \( P(s'|s,a) \) and observation model \( P(o|s') \). This Bayesian update integrates new observations and actions to refine the belief.

CASEY: 04:54

But belief states aren’t always probabilistic distributions, right?

TAYLOR: 04:58

Correct. Some methods represent beliefs symbolically—as sets of possible worlds, like in AGM belief revision or Kripke structures—capturing logical uncertainty and nested beliefs.

MORGAN: 05:09

So you can have probabilistic, symbolic, or even hybrid belief representations?

TAYLOR: 05:14

Yes, and each has trade-offs. The key insight is that the space of belief states itself forms a Markov decision process, a *belief-MDP.* Planning on this belief space converts the partially observable problem into a fully observable one, preserving the Markov property.

CASEY: 05:31

That’s clever because it lets you use standard MDP planning algorithms over beliefs rather than true states.

TAYLOR: 05:37

Exactly. Architecturally, this raises choices around how to represent beliefs—discrete distributions, continuous latent vectors, logical sets—and how to update them efficiently in real time.

MORGAN: 05:49

And this foundational view underpins everything from classic robotics localization to modern neural planners like BetaZero.

TAYLOR: 05:57

That’s the big picture: belief states bridge what’s unknown and how to act despite uncertainty.

TAYLOR: 06:02

Let’s compare some popular belief state representations and their trade-offs.

CASEY: 06:07

Fire away—what’s on the table?

TAYLOR: 06:09

First, symbolic belief representations, like AGM belief revision frameworks, represent beliefs as logical formulas or sets of possible worlds. They offer great interpretability and can handle nested beliefs—for example, “I believe that you believe X.” But they struggle with probabilistic uncertainty and scale poorly to high-dimensional continuous domains.

CASEY: 06:31

Sounds like they’re great for knowledge bases but less so for noisy sensor data.

TAYLOR: 06:36

Exactly. Next, probabilistic approaches model beliefs as probability distributions—think Bayesian filtering with Kalman or particle filters. These handle noisy observations well and integrate naturally with decision theory but can become computationally expensive in very high dimensions.

MORGAN: 06:54

Particle filters, for instance, can struggle when the state space explodes.

TAYLOR: 06:59

Right. Then we have neural implicit belief representations—RNNs or Transformers trained end-to-end to encode and update belief states in their hidden layers. These scale well with data and complexity and can capture complex temporal dependencies but sacrifice interpretability. The “belief” is implicit, not explicitly a distribution or logical set.

CASEY: 07:20

So you get scalability but at the cost of transparency and sometimes reliability?

TAYLOR: 07:25

Precisely. Lastly, set-valued belief models represent genuine ambiguity by maintaining convex sets of probability distributions, capturing uncertainty that can’t be reduced to a single distribution. These can handle model uncertainty better but are mathematically complex and less explored practically.

MORGAN: 07:44

So, in practice, use symbolic when interpretability and nested beliefs matter, probabilistic for noisy, continuous domains, and neural for large-scale, pattern-rich data?

TAYLOR: 07:54

That’s the nutshell decision framework.

CASEY: 07:56

It’s good to have these clear trade-offs—it helps avoid one-size-fits-all mistakes.

ALEX: 08:02

Let’s get technical and walk through how belief states actually work in practice—starting from Bayesian filtering.

MORGAN: 08:09

So every update folds in how likely the observation is under each possible state?

ALEX: 08:14

Exactly. Kalman filters assume Gaussian distributions and linear dynamics, enabling closed-form updates—great for smooth, continuous systems like tracking position.

CASEY: 08:25

But what about nonlinear or multimodal distributions?

ALEX: 08:28

That’s where particle filters come in. They maintain a set of weighted particles representing hypotheses about the state. After each action and observation, particles are propagated via the transition model and reweighted by observation likelihoods, then resampled to focus on probable states.

MORGAN: 08:46

Efficient but can suffer from particle degeneracy if the number of particles is too low?

ALEX: 08:52

Correct, and computational cost scales with particle count.

CASEY: 08:56

And that’s often unrealistic in high-dimensional sensory domains.

ALEX: 09:00

Right. Neural belief representations sidestep explicit modeling by training RNNs or Transformers end-to-end to encode beliefs in hidden states. The network learns to map observation-action histories to latent belief embeddings, updated via backpropagation through time.

MORGAN: 09:16

So the belief state is implicit in these hidden vectors?

ALEX: 09:20

Exactly. This allows scaling to complex domains like dialogue systems or video games but loses interpretability.

CASEY: 09:27

That’s a powerful combination but sounds computationally intense.

ALEX: 09:32

It is, but it pays off with strong long-horizon planning capabilities in complex POMDP-like settings.

MORGAN: 09:38

Wow, these mechanisms really show how belief states go from theory to practical algorithms.

ALEX: 09:44

And the beauty is how generalizable these belief updates are—from robotics to dialogue to game AI.

ALEX: 09:50

Let’s talk results. BetaZero’s 2024 iteration demonstrated long-horizon planning in high-dimensional, continuous POMDPs where previous methods failed—huge win for scaling belief-space methods.

MORGAN: 10:03

That’s a serious step forward. What about dialogue systems?

ALEX: 10:07

Neural dialogue state trackers using RNNs have shown robust tracking of user intents and slot values across conversations, enabling more natural and accurate interactions.

CASEY: 10:18

And particle filters?

ALEX: 10:19

Still gold standard for sensor fusion and localization tasks in robotics—efficient and interpretable, though limited in scale.

MORGAN: 10:27

So the payoff is better planning, tracking, and decision-making under uncertainty—directly improving real-world AI performance.

ALEX: 10:35

Exactly. But we should be mindful of computational costs and interpretability trade-offs.

CASEY: 10:41

Speaking of trade-offs, let’s be honest about what can go wrong here.

MORGAN: 10:46

Please, do tell!

CASEY: 10:47

Planning in continuous high-dimensional belief spaces is computationally intractable for big problems. Approximations like particle filters or neural embeddings help but introduce bias or lose guarantees.

ALEX: 11:00

And neural implicit beliefs can be poorly calibrated—they might over- or underestimate uncertainty, risking overconfident wrong decisions.

CASEY: 11:08

Model misspecification is another issue. Bayesian updates depend heavily on accurate transition and observation models. If those are off, belief updates degrade quickly.

MORGAN: 11:19

That’s concerning for real-world noisy environments.

CASEY: 11:23

Exactly. Plus, multi-agent recursive beliefs explode combinatorially, limiting practical nesting depth. So modeling “I believe that you believe that I believe...” beyond shallow levels is tough.

ALEX: 11:34

Dialogue systems still grapple with noisy, ambiguous user intents, meaning belief trackers aren’t perfect.

MORGAN: 11:41

So while belief states are powerful, they’re not magic bullets. Critical to understand limitations.

CASEY: 11:47

Absolutely. Transparency about these gotchas helps practitioners set realistic expectations.

SAM: 11:53

Let’s bring this to life with real-world examples.

MORGAN: 11:56

That’s the classic noisy perception problem.

SAM: 11:59

Exactly. Dialogue systems probabilistically track user intents and slot values over time using neural dialogue state trackers, enabling smoother multi-turn conversations.

CASEY: 12:10

And LLMs?

SAM: 12:11

Recent research suggests LLM hidden states implicitly encode belief-like representations, aiding emergent Theory of Mind capabilities—reasoning about other agents’ beliefs and intentions.

MORGAN: 12:23

So belief states underpin AI across vastly different domains from robotics to language.

SAM: 12:29

That’s the power of these representations—they’re everywhere behind the scenes.

SAM: 12:34

Let's debate a concrete scenario that many AI practitioners face today: an AI agent-based chatbot that already has a full CoALA memory system in place. How would you incorporate belief states to improve conversations?

MORGAN: 12:47

Hold on—before we dive into belief states, can we level-set on what a CoALA memory system actually includes? Not everyone might be familiar with it. Keith, you're book on RAG and agents covers CoALA agentic memory in-depth, do you want fill us in?

KEITH: 13:02

Happy to break that down. CoALA stands for Cognitive Architecture for Language Agents—it's a framework for building AI agents with human-like memory structures. The three core memory types are episodic, semantic, and procedural. Episodic memory stores specific past interactions—think of it as the agent's autobiographical record of conversations with a particular user, including what was said, when, and in what context. Semantic memory holds general knowledge and learned facts—user preferences, domain expertise, things like "this user prefers concise answers" or "they work in healthcare." Procedural memory captures learned patterns of how to do things—successful conversation flows, when to ask clarifying questions, how to handle certain types of requests. Together, these give an agent persistent, contextual intelligence across sessions. Procedural memory in particular is very powerful, this is where you can set up the agent to start incrementally getting better at whatever it is intended to accomplish, based on goals you can set for it, using self-reflection and essentially autonomously improving itself overtime.

MORGAN: 14:10

So autonomous agents aren't just science fiction any more, this is happening right now in the real world, at real businesses? I feel like I'm in a James Cameron movie!

CASEY: 14:20

Wow Keith, so these CoALA memory driven agents already "remember" past interactions, know things about the user, and have learned behavioral patterns. What's missing that belief states would add?

KEITH: 14:32

Great question. Memory tells you what happened and what you know. Belief states tell you what you think is true right now, with explicit representation of your uncertainty. The agent might remember that a user asked about investment strategies last week, but a belief state would track: "Right now, I'm 70% confident they want retirement advice, 20% they're asking about short-term trading, and 10% this is hypothetical research." That probabilistic reasoning about current context and intent is what's missing.

TAYLOR: 15:04

So belief states add a dynamic uncertainty layer on top of static memory?

KEITH: 15:08

Exactly. Memory is the foundation—belief states are the active inference happening in real-time during a conversation.

SAM: 15:16

Alright, so given this CoALA-equipped chatbot, what approach should we use to add belief states? Let's hear the cases.

CASEY: 15:23

I'll start with symbolic approaches—AGM-style belief revision. I feel like we haven't fully explained AGM for the audience though, so for those unfamiliar, Keith do you want to take this one?

KEITH: 15:35

Sure Casey! I am in full geek mode with this! AGM stands for Alchourrón, Gärdenfors, and Makinson—I hope I said those names right! But these are three researchers who formalized how rational agents should update their beliefs when new information arrives. The framework defines three core operations: expansion, where you add new beliefs to your existing set; contraction, where you remove beliefs that are no longer supported; and revision, where you incorporate new information that might contradict what you previously believed, requiring you to give up some old beliefs to maintain logical consistency. It's essentially a formal logic for how beliefs should change over time while preserving coherence.

CASEY: 16:17

Wow that was geek mode, but very helpful! So in practice, what this means, you'd maintain explicit logical representations of what the agent believes about the user's current state. For example, "User wants X AND User is frustrated AND User prefers detailed explanations." You can do formal belief revision when new information comes in, maintaining logical consistency. The big advantage is interpretability—you can inspect exactly what the agent believes and why.

MORGAN: 16:45

But doesn't that struggle with the messiness of natural language? User intents aren't always clean logical propositions.

CASEY: 16:53

That's the limitation. Symbolic methods work well when you can discretize the belief space into clear categories, but real conversations are ambiguous. "Can you help me with this?" could mean a dozen different things depending on context. Symbolic representations can feel brittle here.

TAYLOR: 17:10

I'll argue for probabilistic POMDP-style methods. You model the conversation as a partially observable process where the true user state—their intent, emotional state, knowledge level, goals—is hidden. The agent maintains a probability distribution over possible user states and updates it with each utterance using Bayesian inference. This naturally handles ambiguity—you don't have to commit to one interpretation, you track likelihoods across possibilities.

ALEX: 17:37

The math is elegant, but POMDPs get computationally expensive fast. How many possible user states are you tracking? Intent alone could have hundreds of categories, then multiply by emotional states, context factors, conversation phase...

TAYLOR: 17:52

Fair point. You need careful state space design and approximation methods. But the principled handling of uncertainty is worth it—you can make decisions that explicitly account for "I'm not sure what they want, so I should ask a clarifying question" versus "I'm confident, so I'll proceed."

ALEX: 18:10

Let me make the case for neural implicit belief representations. You train the system end-to-end to encode belief states in learned embeddings—maybe in transformer hidden states or a dedicated belief encoder network. The model learns from data what belief representations are useful for predicting user needs and generating good responses. No hand-crafted state spaces, no explicit probability calculations—the network figures out what to track.

MORGAN: 18:37

That's appealing for scalability. But doesn't it become a black box? How do you know what the agent believes?

ALEX: 18:43

That's the trade-off. You lose interpretability but gain flexibility and the ability to capture subtle patterns humans might not think to model explicitly. With enough training data, these representations can be surprisingly sophisticated.

SAM: 18:58

Keith, you've built production memory systems. What's your take on the right approach here?

KEITH: 19:03

I've thought about this a lot, and I don't think it's a single-approach answer—it's a hybrid architecture, but with clear principles about what goes where. Here's how I'd structure it. First, the CoALA memory system remains your foundation. Episodic memory feeds belief state updates—recent conversation turns are your observations. Semantic memory provides priors—if you know this user typically asks about topic X, that informs your initial belief distribution. Procedural memory tells you how to act on beliefs—when confidence is low, trigger a clarifying question pattern.

MORGAN: 19:38

So memory and belief states are tightly integrated, not separate systems?

KEITH: 19:43

Exactly. Now for the belief representation itself, I'd advocate for a two-layer approach. The first layer is an explicit probabilistic tracker for high-stakes variables—user intent category, confidence level, conversation phase, detected sentiment. These are things you need to inspect, log, and potentially explain. Use lightweight Bayesian updates here—nothing fancy, just proper probability propagation based on observed signals.

CASEY: 20:09

So you get the interpretability of probabilistic methods for the things that matter most?

KEITH: 20:14

Right. The second layer is a neural belief embedding that captures everything else—the subtle contextual factors, nuanced patterns, things you can't easily discretize. This feeds into your response generation but doesn't need to be fully interpretable. You're essentially using the neural network as a learned prior and pattern detector, while the explicit tracker handles actionable uncertainty.

TAYLOR: 20:39

How do these two layers interact?

KEITH: 20:41

The neural embedding influences the explicit tracker's updates—it can provide likelihood signals that shift probabilities. And the explicit tracker constrains the neural system—if you're highly confident about intent, that gates certain response strategies. Think of it as System 1 and System 2 in dual-process psychology. The neural layer is fast, intuitive pattern matching. The explicit layer is slower, deliberate reasoning about uncertainty.

ALEX: 21:08

What about the computational cost? Running both systems in real-time during conversation seems heavy.

KEITH: 21:14

You batch and cache intelligently. The neural embedding updates with each turn anyway—that's just your transformer doing its thing. The explicit tracker is lightweight math. The key is you're not doing full POMDP planning over thousands of states—you're tracking maybe a dozen key variables with simple updates. The neural system handles the complexity, the explicit system handles the interpretability.

SAM: 21:39

What about calibration? Neural systems can be overconfident.

KEITH: 21:43

Critical point. This is where the two-layer approach really pays off. You can calibrate the explicit tracker against ground truth—did the user actually want what we thought they wanted? That's measurable. When the neural confidence signals consistently mismatch reality, you detect it and adjust. The explicit layer acts as a sanity check on the implicit layer.

MORGAN: 22:05

So you get the best of both worlds—neural flexibility with probabilistic rigor?

KEITH: 22:10

That's the goal. And here's the practical kicker—this integrates naturally with any agent architecture using a graph-based state. Your belief state becomes part of the agent state that flows through your graph. Memory retrieval is conditioned on belief—if confidence is low, maybe you retrieve more context. Tool selection is conditioned on belief—different intents trigger different tool calls. It's not a separate system bolted on; it's woven into the agent architecture.

CASEY: 22:39

I'm convinced on the hybrid approach. But what about the implementation lift? This sounds complex to build.

KEITH: 22:45

Start simple. Implement the explicit tracker first—just intent confidence and conversation phase. That alone improves conversations significantly because you can trigger clarifying questions when uncertainty is high instead of guessing. Then layer in the neural embedding as you collect data to train it. The beauty of the two-layer design is you can be incremental.

TAYLOR: 23:08

And what about multi-turn belief dynamics? Users change their minds, context shifts...

KEITH: 23:13

Episodic memory handles the history, but the belief state needs decay and revision mechanisms, there is an important temporal aspect to this. Beliefs from ten turns ago should have less influence than beliefs from the last turn—unless something anchors them. I'd implement a recency-weighted update where older belief signals decay unless reinforced. If you are already using a CoALA based agent memory approach, you likely have temporal variables built into your implementation, and you can just build off of that. Like with LangMem, you can easily implement a temporal mixin class that supports all of your memory types through inheritance and can be carried over into the belief state, just another schema addition, as well. That is one of the reasons I like using LangMem, adding something like this to an existing system is quick and easy, relatively speaking, due to LangMem's modular nature. And use explicit revision when contradictory evidence appears—Bayesian belief revision handles this naturally.

ALEX: 24:14

What about the user's mental state beyond intent—things like frustration, confusion, engagement level?

KEITH: 24:20

Those go in the explicit tracker as parallel distributions. "User frustration: low 60%, medium 30%, high 10%." Update based on sentiment signals, response latency patterns, explicit feedback. This matters because your procedural memory can have rules like "if frustration > 50%, shift to empathetic acknowledgment before problem-solving." Belief states enable emotionally intelligent responses, not just task-focused ones.

MORGAN: 24:47

This is making me rethink how I've seen chatbot architectures designed. The belief layer really is the missing piece that connects memory to action.

KEITH: 24:56

That's exactly it. Memory is the what—what do we know? Belief is the how confident—what do we think is true right now? And together they inform the action—what should we do? Without explicit belief representation, agents either act on assumptions or ask too many questions. With it, you get calibrated confidence that drives appropriately cautious or bold responses.

SAM: 25:18

Let's pressure-test this. What's a scenario where this hybrid approach struggles?

KEITH: 25:23

Novel situations with no training data for the neural layer and no prior patterns in memory. Cold start with a completely new type of user request. Here, your explicit tracker dominates but it's working from generic priors, so confidence stays low. The system correctly identifies "I don't know what's happening" and should defer—ask questions, escalate to human support, acknowledge uncertainty. That's actually the right behavior, but it won't feel magical.

CASEY: 25:51

And compared to pure neural approaches that might hallucinate confidence?

KEITH: 25:56

Exactly. The hybrid fails gracefully. Pure neural might generate a confident-sounding wrong answer because it has no explicit uncertainty representation saying "wait, I actually have no idea."

TAYLOR: 26:08

What about new users specifically? If procedural memory learns from past interactions with a user, a brand new user has no procedural memory to draw from. Does the belief state help there?

KEITH: 26:19

Absolutely—this is one of the most valuable applications. The agent's general belief state, built from patterns across all users, becomes the bootstrap for new user interactions. Think of it this way: your procedural memory has two levels. There's user-specific procedural memory that learns "this particular user responds well to detailed technical explanations." But there's also general procedural memory—patterns learned across your entire user base about how people typically behave, what conversation flows work best, common intent progressions. When a new user arrives with no history, the belief state draws on that general procedural knowledge to inform its initial behaviors. "Users who start with this type of question typically want X, and clarifying questions at this stage usually help." The belief state essentially transfers learned behavioral patterns from the population to bootstrap the individual. Then as you interact with the new user, you start building user-specific procedural memory that gradually overrides or refines the general patterns.

MORGAN: 27:23

So the belief state acts as a bridge—carrying population-level wisdom until individual patterns emerge?

KEITH: 27:29

Exactly. Without that bridge, every new user is a complete cold start. With it, you're starting from an intelligent prior that represents everything the agent has learned about human behavior in general. The new user benefits from all the conversations that came before, even though those conversations weren't with them.

ALEX: 27:48

That's elegant. The belief state isn't just tracking uncertainty—it's enabling knowledge transfer with confidence.

SAM: 27:55

Here's another scenario to pressure-test: what about multi-agent systems where different agents share the same state? Say you have specialized agents for different tasks that all read from and write to a common graph state. Does this belief architecture still hold up, or does it create conflicts?

KEITH: 28:13

Great question—this is increasingly common in production systems. The short answer is yes, the architecture holds, but you need to be intentional about belief state ownership and scope. There are a few considerations. First, you need to distinguish between shared beliefs and agent-specific beliefs. Some beliefs should be global—"the user's overall intent is financial planning"—and all agents should read from and contribute to that shared belief. But other beliefs are agent-specific—"in my domain of tax optimization, I believe the user wants to discuss deductions." Those shouldn't pollute the shared state or conflict with what the investment agent believes about its domain.

TAYLOR: 28:54

So you partition the belief state?

KEITH: 28:56

Exactly. I'd structure it as a hierarchical belief state in the shared graph. At the top level, you have conversation-wide beliefs that any agent can read and update—user identity, overall session intent, emotional state, conversation phase. Below that, each agent maintains its own belief namespace for domain-specific uncertainty. The tax agent tracks beliefs about tax-related intents, the investment agent tracks beliefs about portfolio goals. They don't step on each other. And again, just like what we do with CoALA-based memories, where they have different scopes, including users, activities, groups, and globally, the belief state should mirror this for the same reason.

MORGAN: 29:36

But what if agents disagree? The tax agent might interpret a question as being about deductions while the investment agent thinks it's about capital gains timing.

KEITH: 29:46

That's where belief aggregation comes in. When agents contribute to shared beliefs, you don't just let them overwrite each other—you aggregate their signals probabilistically. If the tax agent is 80% confident and the investment agent is 60% confident about different intents, you can either maintain both hypotheses in the shared state or use a meta-belief about which agent is most likely relevant given context. An orchestrator agent can read these competing beliefs and decide which specialist to route to, or ask the user a clarifying question if aggregate confidence is low.

ALEX: 30:22

Doesn't this add a lot of complexity compared to single-agent systems?

KEITH: 30:27

It does, but the alternative is worse. Without explicit belief state management in multi-agent systems, you get implicit conflicts buried in agent behaviors. One agent acts on assumptions that contradict another agent's assumptions, and the user sees inconsistent responses. At least with explicit belief states, conflicts are surfaced and can be reasoned about. You can log "agent A believed X while agent B believed Y" and debug coherence issues. Plus, the same two-layer approach applies—your explicit tracker handles the high-stakes shared beliefs with clear ownership and update rules, while neural embeddings handle the nuanced agent-specific pattern matching.

CASEY: 31:07

So the design principle is: explicit ownership of shared beliefs, namespaced isolation for domain-specific beliefs, and probabilistic aggregation when agents need to contribute to common understanding?

KEITH: 31:19

That's the framework. And honestly, this is where the graph-based state architecture really shines. The graph naturally represents these relationships—shared state nodes that multiple agents connect to, private state nodes scoped to individual agents, and edges that define read and write permissions. The belief state isn't floating separately; it's embedded in the graph structure with clear semantics.

TAYLOR: 31:43

I'm sold. The integration with existing CoALA memory, the two-layer explicit-plus-implicit design, the incremental implementation path, and now the multi-agent considerations—it addresses the practical concerns while getting the theoretical benefits.

ALEX: 31:58

Agreed. And keeping the explicit tracker lightweight means we're not adding significant latency to conversation turns.

MORGAN: 32:06

Keith, final word—what's the single most important thing for practitioners to remember when adding belief states to their agents?

KEITH: 32:14

Beliefs must be actionable. Don't track uncertainty for its own sake—track it because it changes what the agent does. If high uncertainty triggers clarifying questions, if low uncertainty enables direct action, if specific belief patterns activate specific procedural memories—then your belief states are earning their computational cost. Otherwise, you've built a sophisticated monitoring system that doesn't actually improve conversations.

SAM: 32:40

Perfect framing. The takeaway: for CoALA-based conversational agents, a hybrid belief architecture with explicit probabilistic tracking of key variables plus neural implicit embeddings for nuanced patterns, tightly integrated with your memory systems, gives you interpretable, calibrated, and actionable uncertainty that makes agents genuinely smarter about handling ambiguous conversations.

SAM: 33:04

For AI practitioners building belief state systems, here’s some practical advice.

MORGAN: 33:10

Really useful patterns. Anything to avoid?

SAM: 33:12

Avoid naïve particle filter implementations in very high dimensions without careful resampling and proposal designs. Also, neural methods shouldn’t be black boxes—use explainability tools where possible.

CASEY: 33:25

Solid grounding in your problem domain and data characteristics remains key to selecting the right belief representation.

MORGAN: 33:33

Before we move on, a quick shout-out to Keith Bourne’s book again. It’s a must-have if you want solid foundations on these topics with practical code and diagrams to really get under the hood. The book starts with building a very solid and thorough foundation in RAG, and over 19 chapters it ramps all the way up to the most advanced agentic memory systems you can implement. And you do, there are code labs, you will be implementing these advanced agentic memory systems yourself! So really, just highly recommended for any AI practitioner.

MORGAN: 34:05

This podcast is produced by Memriq AI, an AI consultancy and content studio building tools and resources for AI practitioners.

CASEY: 34:13

Our goal is to help engineers and leaders stay current in this fast-moving AI landscape.

MORGAN: 34:19

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SAM: 34:25

Despite advances, belief-space planning remains challenging due to continuous, high-dimensional belief representations. Efficient approximation methods are a hot research area.

MORGAN: 34:36

And multi-agent recursive beliefs still hit a combinatorial wall with nesting depth. Practical solutions are needed there.

CASEY: 34:43

Neural-symbolic integration is another frontier—combining interpretability with the scalability of neural methods.

SAM: 34:51

Calibration of learned beliefs is critical. Overconfident or poorly calibrated models can cause catastrophic failures in safety-critical systems.

KEITH: 34:59

And adding to that, explicit Theory of Mind modeling using belief states in large language models is emerging. Understanding how AI models others’ beliefs is key for trustworthy interactions.

MORGAN: 35:11

Keith, from your work, what should listeners watch for in these open problems?

KEITH: 35:16

Focus on robustness and interpretability. As systems grow more complex, ensuring that belief representations are both reliable and understandable will be crucial for adoption in industry.

MORGAN: 35:27

Belief states transform abstract uncertainty into actionable representations—essential for planning under partial observability.

CASEY: 35:36

But beware: computational costs and model assumptions can limit their effectiveness in complex real-world settings.

JORDAN: 35:43

Remember, belief states connect theory to practice—they’re the mental maps AI agents use to navigate uncertainty every second.

TAYLOR: 35:51

Choosing the right belief representation depends on your domain’s noise characteristics, scalability needs, and interpretability requirements.

ALEX: 36:00

The elegance of Bayesian updates and the power of neural implicit beliefs show how math and learning intertwine in modern AI.

SAM: 36:08

Practical deployment demands balancing approximation, scalability, and clarity—no one-size-fits-all here.

KEITH: 36:14

Ultimately, mastering belief states unlocks sophisticated AI capable of reasoning about the unknown—and that’s where real intelligence begins.

MORGAN: 36:23

Keith, thanks so much for giving us the inside scoop today—your insights really brought belief states to life.

KEITH: 36:30

My pleasure. This is such an important topic, and I hope listeners dig deeper into it—it’s foundational for robust AI.

CASEY: 36:38

Thanks to everyone for listening and pushing us to think critically about uncertainty in AI.

MORGAN: 36:44

Until next time, stay curious and keep exploring the frontier of AI.

CASEY: 36:48

See you soon!