Research
A working record of the research underneath the product. Each paper ships with a public reproduction kit so the numbers can be checked, not just cited.
Analysis of Conversation Trajectory Representations: Orthogonal Projections versus Scalar Geometry for Satisfaction Prediction
Jacob Sussmilch
Heya Enterprises Pty Ltd
A conversation can be represented as a trajectory through high-dimensional semantic space — one point per turn — and a common way to use it is to summarize that trajectory as a fixed-size vector for a simple learner; which summary to use is the question this paper studies. We compare hand-crafted conversational geometry — scalar features of the trajectory, most prominently in TRACE (Gooding and Grefenstette, 2025) — against projecting the trajectory onto a low-order orthogonal-polynomial basis and keeping the coefficients, evaluating both on conversation-level user satisfaction. First, which representation wins is regime-dependent: the projection beats TRACE's geometric features by 5-12 points on all three corpora, but on short, first-person-rated chats the trajectory-shape channels collapse and hand-crafted scalars become a genuine complement.
Jacob Sussmilch · Heya Enterprises Pty Ltd
The first public-data benchmark of TRACE's hand-crafted conversational geometry, measured against a low-order orthogonal projection of the same turn-embedding trajectory. The projection leads by 5–12 points across three satisfaction corpora, and splitting the trajectory by speaker — a per-role mean plus drift, no training and no feature selection — is never distinguishably worse than any measured alternative in either regime. The boundary is reported as a result: on short, first-person-rated chats trajectory shape collapses and curated scalars become a genuine complement.
Gram Projections for Conversation Trajectories: A Polynomial Equivalent of the DCT
Jacob Sussmilch
Heya Enterprises Pty Ltd
Fixed orthogonal transforms are a standard way to turn a variable-length sequence of embeddings into a fixed-size vector: keep the first few transform coefficients. The DCT is the default choice. We introduce the Gram (discrete orthogonal polynomial) projection as its polynomial equivalent for short, aperiodic, drifting sequences such as conversation trajectories, and measure whether the choice matters. The Gram coefficients have stable semantics: degree 0 is exactly the mean of the sequence, truncation never changes retained coefficients, degree 1 is the least-squares drift, and the drift coefficient reports the same end-to-end drift at every sequence length.
Jacob Sussmilch · Heya Enterprises Pty Ltd
Introduces the Gram (discrete orthogonal polynomial) projection as a polynomial equivalent of the DCT for turning short, aperiodic embedding sequences into a fixed-size vector. The coefficients have stable semantics — degree 0 is the mean, degree 1 is the least-squares drift, and the drift coefficient reports the same end-to-end drift at every sequence length. On three conversation-satisfaction corpora the bases tie almost everywhere; the exception favours the polynomial basis on populations dominated by very short per-role sequences, by a measured 2.3 points.
Manipulability of Trajectory-Geometric Conversation Rewards and a Role-Restricted, Task-Conditioned Construction
Jacob Sussmilch
Heya Enterprises Pty Ltd
A dense reward that scores a conversation on every turn is what reinforcement learning wants where the true outcome is sparse and late — and what Goodhart's law warns will be gamed. We show it need not be. Trajectory geometry is a genuine within-domain failure signal — it predicts failure before a task-oriented call ends — but as a reward it is gameable by selection over real turns alone. Its exploitability, however, is not a property of "content": it is a property of which role the adversary can write.
Jacob Sussmilch · Heya Enterprises Pty Ltd
A dense reward that scores a conversation on every turn is what reinforcement learning wants where the outcome is sparse and late — and what Goodhart's law warns will be gamed. We show it need not be. Exploitability is a property of which role the adversary can write, not of content. Score the fixed evidence — user turns, tool calls, tool results — admit the model's reasoning and response only as its consistency with that evidence, and condition on the task: the construction recovers 97–99% of the predictor's accuracy while remaining un-gameable by the selection adversary that breaks the naive proxy.
