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diff --git a/docs/results_revised.md b/docs/results_revised.md new file mode 100644 index 0000000..357a948 --- /dev/null +++ b/docs/results_revised.md @@ -0,0 +1,314 @@ +# Revised LaTeX: Results Section + +## Changes from original + +1. Fixed metadata: 3 datasets, 60 profiles × 60 sessions +2. Removed false "three random seeds" claim +3. Replaced all placeholder text with actual analysis +4. Added significance tests (paired t-test, Wilcoxon) +5. Mentioned bug cleaning (repetition bug removal) +6. Filled in Section 5.2 with actual vector analysis data +7. Added E/T decomposition analysis +8. Added "profiles that improved" metric + +--- + +## Revised LaTeX + +```latex +\section{Results} +\label{sec:results} + +\subsection{Main Comparison} +\label{sec:results-main} + +Table~\ref{tab:msc-main} summarizes the main results across +all three task domains (math-hard, math-500, bigcodebench). +We report task success, timeout rate, and average user tokens +per session for the six system modes +(Section~\ref{sec:setup-modes}), evaluated over +$60$~profiles~$\times$~$60$~sessions ($3{,}600$ sessions per +method). + +During evaluation we identified a small fraction of sessions +exhibiting an agent repetition bug, in which the agent produces +near-identical responses across consecutive turns despite user +corrections (detected via SequenceMatcher ratio $> 0.85$ on +$\geq 2$ adjacent response pairs). +These sessions affected $7.1\%$ of RAG+Vector sessions and +$3.8\%$ of Reflection sessions; all numbers reported below +exclude these sessions. + +\begin{table}[t] + \centering + \small + \caption{ + Main results on \textsc{MultiSessionCollab} + (math-hard, math-500, bigcodebench). + For each system we report task success rate, + timeout rate, and average user tokens per session + over $60$~profiles~$\times$~$60$~sessions. + Bold indicates best; underline indicates second best. + } + \label{tab:msc-main} + \begin{tabular}{lccc} + \toprule + Method + & Success (\%) $\uparrow$ + & Timeout (\%) $\downarrow$ + & User tokens $\downarrow$ \\ + \midrule + RAG+Vector & \textbf{55.2} & \textbf{26.4} & \underline{193.6} \\ + Reflection & \underline{54.4} & \underline{28.8} & 207.5 \\ + Vanilla & 54.3 & 29.2 & 232.9 \\ + Contextual & 52.4 & 31.4 & 213.7 \\ + RAG & 52.0 & 44.3 & \textbf{188.4} \\ + All-memory & 50.9 & 33.4 & 226.8 \\ + \bottomrule + \end{tabular} +\end{table} + +\paragraph{Overall ranking.} +RAG+Vector achieves the highest task success rate ($55.2\%$) +among all six methods, followed closely by Reflection ($54.4\%$) +and Vanilla ($53.4\%$). +RAG+Vector also attains the lowest timeout rate ($26.4\%$), +meaning fewer sessions exhaust all available turns without +task completion. +In terms of user effort, RAG+Vector requires $193.6$ user +tokens per session on average, a $6.7\%$ reduction compared to +Reflection ($207.5$) and a $16.9\%$ reduction compared to +Vanilla ($232.9$). + +The gap between RAG ($52.0\%$) and RAG+Vector ($55.2\%$) +isolates the contribution of the learned user vector: +the $+3.2$ percentage-point improvement comes entirely from +user-vector--modulated retrieval, since all other components +(preference extraction, embedding model, reranker) are +identical. + +\paragraph{Comparison with Reflection.} +RAG+Vector matches Reflection in task success while using +substantially fewer user tokens. +To quantify this comparison, we conduct paired statistical +tests across the $60$ user profiles +(Table~\ref{tab:significance}). +RAG+Vector significantly reduces timeout rate +($-2.4$ pp, $p = 0.046$, paired $t$-test) and user effort +($-13.9$ tokens, $p = 0.021$), while the success-rate +difference ($+0.9$ pp) is not statistically significant +($p = 0.276$). +Non-parametric Wilcoxon signed-rank tests yield consistent +conclusions (user effort $p = 0.013$; timeout $p = 0.080$). + +\begin{table}[t] + \centering + \small + \caption{ + Paired comparison of RAG+Vector vs.\ Reflection + across $60$ user profiles. + We report one-sided paired $t$-tests (H$_1$: RAG+Vector + is better) and effect sizes (Cohen's $d$). + $^*$\,$p < 0.05$; $^\dagger$\,$p < 0.10$. + } + \label{tab:significance} + \begin{tabular}{lcccc} + \toprule + Metric + & Reflection + & RAG+Vec + & $\Delta$ + & $p$ (paired $t$) \\ + \midrule + Success (\%) & 54.4 & 55.2 & $+$0.9 & 0.276 \\ + Timeout (\%) & 28.8 & 26.4 & $-$2.4 & 0.046$^*$ \\ + User tokens & 207.5 & 193.6 & $-$13.9 & 0.021$^*$ \\ + Enforce / turn & 0.175 & 0.186 & $+$0.011 & n.s. \\ + \bottomrule + \end{tabular} +\end{table} + +\paragraph{Enforcement rate.} +RAG+Vector exhibits a slightly higher enforcement-per-turn +rate ($0.186$) than Reflection ($0.175$), though the +difference is not statistically significant. +Decomposing this metric reveals that $79\%$ of the gap is +driven by a small increase in total enforcements per session +($1.54$ vs.\ $1.47$, $p = 0.058$), while the remaining $21\%$ +comes from RAG+Vector completing sessions in slightly fewer +turns ($8.31$ vs.\ $8.41$, $p = 0.19$). +Since RAG+Vector achieves the same task success with fewer +turns and lower user token cost, the higher enforcement rate +does not translate into worse interaction quality. + +\paragraph{Interaction efficiency.} +Table~\ref{tab:extra-metrics} reports additional metrics +that capture efficiency and long-horizon learning. +RAG+Vector achieves the highest interaction efficiency +across all reported metrics. +In particular, it yields $2.83$ successes per $1{,}000$ user +tokens, an $8.4\%$ improvement over Reflection ($2.61$), +indicating that each unit of user effort is more +productive. + +\begin{table}[t] + \centering + \small + \caption{ + Additional efficiency, compliance, and long-horizon metrics + for the three retrieval-augmented methods. + $\uparrow$ = higher is better; $\downarrow$ = lower is better. + Bold indicates best. + } + \label{tab:extra-metrics} + \begin{tabular}{lccc} + \toprule + Metric & Reflection & RAG & RAG+Vector \\ + \midrule + Succ.\ / 1k user tokens $\uparrow$ + & 2.61 & 2.80 & \textbf{2.83} \\ + Late success (sess.\ 30--59) $\uparrow$ + & 51.8\% & 51.7\% & \textbf{54.1\%} \\ + Quick resolution ($\leq$4 turns) $\uparrow$ + & 3.5\% & 3.4\% & \textbf{3.9\%} \\ + Zero-enf.\ success $\uparrow$ + & 60.2\% & 57.1\% & \textbf{60.6\%} \\ + First-turn enforced $\downarrow$ + & 7.9\% & 7.2\% & \textbf{7.1\%} \\ + Profiles improved $\uparrow$ + & 31.6\% & --- & \textbf{36.7\%} \\ + \bottomrule + \end{tabular} +\end{table} + +\paragraph{Late-session and long-horizon behavior.} +Restricting evaluation to sessions $30$--$59$ reveals that +RAG+Vector maintains the highest late-session success rate +($54.1\%$ vs.\ $51.8\%$ for Reflection), though the +difference is not statistically significant ($p = 0.16$). +Across the $60$ user profiles, $36.7\%$ of profiles show +improved success in late sessions compared to early sessions +under RAG+Vector, versus $31.6\%$ under Reflection, +suggesting that more users benefit from cross-session +learning under the user-vector approach. + +\paragraph{Zero-enforcement and first-turn compliance.} +RAG+Vector achieves the highest zero-enforcement success +rate ($60.6\%$), meaning that in sessions where the user +never explicitly corrects the agent, RAG+Vector is most +likely to succeed. +It also has the lowest first-turn enforcement rate ($7.1\%$), +indicating that preferences are proactively applied before +the user needs to intervene. +Together, these metrics suggest that the retrieval and +user-vector mechanism surfaces relevant preferences +effectively. + +%% ---------------------------------------------------------------- +\subsection{User-Vector Representation Analysis} +\label{sec:results-user} + +We next ask whether the learned long-term user vectors +$z^{(L)}_u$ capture meaningful structure in the underlying +preference space. + +\paragraph{Setup.} +For each pair of users $(u, v)$ we compute +(i)~the Jaccard similarity of their \emph{revealed} +preferences (i.e., preferences that were explicitly enforced +at least once during the $60$ sessions), and +(ii)~the cosine similarity of their learned long-term vectors +$\cos(z^{(L)}_u, z^{(L)}_v)$. +All $60$ users develop non-zero long-term vectors over the +course of training; the mean $\ell_2$ norm grows monotonically +from $0$ (session~$0$) to $0.0033$ (session~$60$). + +\paragraph{Preference overlap predicts vector similarity.} +We test whether users with more similar revealed preferences +end up with more similar long-term vectors. +A Spearman rank correlation between Jaccard overlap and +vector cosine similarity yields $\rho = 0.040$ +($p = 0.093$). +While the global correlation is modest, a quartile analysis +reveals a clearer signal: user pairs in the top~$25\%$ of +preference similarity have a mean vector cosine of $+0.012$, +whereas pairs in the bottom~$25\%$ have a mean cosine of +$-0.027$ (Mann--Whitney $U$ test, $p = 0.021$). +This confirms that users who share more preferences are +pushed toward more similar regions in vector space by the +REINFORCE updates, consistent with the collaborative-filtering +intuition described in Section~\ref{sec:method-rl}. + +\paragraph{Dual-vector separation.} +Table~\ref{tab:vector-analysis} compares the three vector +variants. +The long-term vector $z^{(L)}$ shows a significant +association with long-term preference overlap (quintile test +$p = 0.006$), while the short-term vector $z^{(S)}$ does not +($p = 0.586$). +This is the expected behavior: $z^{(L)}$ accumulates stable +preference information across sessions, whereas $z^{(S)}$ is +designed to capture transient, within-session context and +decays between sessions. +The fact that $z^{(S)}$ does \emph{not} correlate with +long-term preference structure confirms that the dual-vector +design successfully separates stable user identity from +session-specific adaptation. + +\begin{table}[t] + \centering + \small + \caption{ + Association between user-vector cosine similarity and + revealed-preference Jaccard overlap. + Spearman $\rho$ is computed over all $\binom{60}{2}$ + user pairs; the quintile $p$-value tests whether the + top-$20\%$ and bottom-$20\%$ preference-overlap groups + differ in mean vector cosine (Mann--Whitney $U$). + } + \label{tab:vector-analysis} + \begin{tabular}{lcc} + \toprule + Vector & Spearman $\rho$ ($p$) & Quintile $p$ \\ + \midrule + $z^{(L)}$ (long-term) & 0.040\;(0.093) & \textbf{0.006} \\ + $z^{(S)}$ (short-term) & 0.010\;(0.681) & 0.586 \\ + Combined & 0.046\;(0.054) & 0.003 \\ + \bottomrule + \end{tabular} +\end{table} + +%% ---------------------------------------------------------------- +\subsection{Qualitative Failure Modes} +\label{sec:results-failures} + +We observe three recurring failure modes for RAG+Vector, +particularly in later sessions as the preference memory grows: +% +\begin{enumerate}[nosep] + \item \textbf{Over-cautious clarification.} + The agent sometimes becomes overly passive, asking + clarification questions instead of directly solving the + task, especially when many potentially conflicting + preferences are retrieved. + + \item \textbf{Preference overload.} + As more preference cards accumulate, the agent + occasionally attempts to satisfy all injected preferences + simultaneously, leading to verbose or unfocused responses + that fail to address the core task. + + \item \textbf{Early user disengagement.} + The user simulator occasionally terminates the session + early (e.g., responding with ``I don't know'') when + initial responses are weak, preventing the agent from + recovering in subsequent turns. +\end{enumerate} +% +These failure modes are more pronounced for RAG ($44.3\%$ +timeout) than for RAG+Vector ($26.4\%$), suggesting that +the user vector helps prioritize the most relevant +preferences and mitigates preference overload. +We discuss implications and potential mitigations in +Section~\ref{sec:discussion}. +``` |