<div dir="ltr"><div dir="ltr"><div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, 24 Sept 2026 at 19:00, spike jones via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank">extropy-chat@lists.extropy.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><div lang="EN-US"><div><p class="MsoNormal"><span style="font-size:11pt;font-family:"Calibri",sans-serif"> </span><b><span style="font-size:11pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11pt;font-family:"Calibri",sans-serif"> extropy-chat <<a href="mailto:extropy-chat-bounces@lists.extropy.org" target="_blank">extropy-chat-bounces@lists.extropy.org</a>> <b>On Behalf Of </b>spike jones via extropy-chat</span></p><p class="MsoNormal"></p><p class="MsoNormal"><span style="font-size:11pt;font-family:"Calibri",sans-serif">OK perhaps I am uncharitable.  Or I’m just being a grumpy bear today.<u></u><u></u></span></p><p class="MsoNormal"><span style="font-size:11pt;font-family:"Calibri",sans-serif"><u></u> <u></u></span></p><p class="MsoNormal"><span style="font-size:11pt;font-family:"Calibri",sans-serif">BillK, pls offer this pain paper to your favorite AIs and ask specifically what that equation on page 5 is claiming.  Ask if the paper defines the variables and does an adequate job of proving the equation.  I am claiming no and no.  That is the kind of mistake an AI would make but a human researcher would not.<u></u><u></u></span></p><p class="MsoNormal"><span style="font-size:11pt;font-family:"Calibri",sans-serif"><u></u> <u></u></span></p><p class="MsoNormal"><span style="font-size:11pt;font-family:"Calibri",sans-serif">spike<u></u><u></u></span></p></div></div>_______________________________________________<br></div></blockquote><div><br></div><div><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">Gemini AI has no problem with the paper.</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">BillK</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default">Gemini 3.8 Flash AI Extended Thinking:</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><p id="m_6130649029140792771gmail-p-rc_19d0e3f944f281e7-33" style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px"><b style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px">No, the paper itself is not AI-generated.</b> <span style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px">It is a real academic research preprint authored by human researchers (Valen Tagliabue, Leonard Dung, and Cameron Berg from the non-profit research group Reciprocal Research) and posted to arXiv on September 14, 2026 (</span><code style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px"><span style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px">arXiv:2609.16247</span></code><span style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px">).<sup style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px;font-size:16px;background-color:transparent"></sup></span>   </p><p id="m_6130649029140792771gmail-p-rc_19d0e3f944f281e7-34" style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px"><span style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px">While the paper is </span><i style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px"><span style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px">about</span></i><span style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px"> AI models, it is a legitimate mechanistic interpretability and AI safety study.<sup style="font-family:Google Sans Text,sans-serif;line-height:1.15;margin-top:0px;margin-left:0px;margin-right:0px;font-size:16px;background-color:transparent"></sup></span>   </p>-----------------</div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;font-size:small;color:rgb(0,0,0)" class="gmail_default"><span></span><div></div><span><span style="height:auto"><div><span id="m_6130649029140792771gmail-message-content-id-r_1a7907a184b60c5d"><div id="m_6130649029140792771gmail-model-response-message-contentr_1a7907a184b60c5d" dir="ltr"><p>The equation on page 5 (Section 3) of <i>The Pain Axis</i> defines the <b>denoised difference-in-means</b> method used to isolate the linear "pain vector" in a transformer model's residual stream:</p><div><div><span><span><span aria-hidden="true"><span><span style="height:0.938em"></span><span><span><span><span><span style="height:0.6944em"><span><span style="height:3em"></span><span style="margin-right:0.0359em">v</span></span><span><span style="height:3em"></span><span><span>^</span></span></span></span></span></span></span><span><span><span><span style="height:0.938em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:1.0213em;vertical-align:-0.0833em"></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.938em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span><span style="margin-right:0.2222em"></span><span>−</span><span style="margin-right:0.2222em"></span></span><span><span style="height:3.1138em;vertical-align:-1.2777em"></span><span><span><span><span style="height:1.8361em"><span style="margin-left:0em"><span style="height:3.05em"></span><span><span><span>i</span><span>=</span><span>1</span></span></span></span><span><span style="height:3.05em"></span><span><span>∑</span></span></span><span style="margin-left:0em"><span style="height:3.05em"></span><span><span><span style="margin-right:0.0315em">k</span></span></span></span></span><span></span></span><span><span style="height:1.2777em"><span></span></span></span></span></span><span>(</span><span><span>u</span><span><span><span><span style="height:0.8991em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>⊤</span></span></span></span></span><span></span></span><span><span style="height:0.247em"><span></span></span></span></span></span></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.938em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span><span>)</span><span><span>u</span><span><span><span><span style="height:0.3117em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div></div><p>Where the raw vector <span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span> is defined as:</p><div><div><span><span><span aria-hidden="true"><span><span style="height:0.938em"></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.938em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:1.4636em;vertical-align:-0.4188em"></span><span><span>μ</span><span><span><span><span style="height:1.0448em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span><span><span>pain</span></span></span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span><span></span></span><span><span style="height:0.4188em"><span></span></span></span></span></span></span><span style="margin-right:0.2222em"></span><span>−</span><span style="margin-right:0.2222em"></span></span><span><span style="height:1.3461em;vertical-align:-0.3013em"></span><span><span>μ</span><span><span><span><span style="height:1.0448em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span><span><span>control</span></span></span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span><span></span></span><span><span style="height:0.3013em"><span></span></span></span></span></span></span></span></span></span></span></div></div><h3>1. Variable Definitions</h3><p>The paper defines all variables in Section 3:</p><ul><li><p><span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span><span><span><span style="height:0.6944em"><span><span style="height:3em"></span><span style="margin-right:0.0359em">v</span></span><span><span style="height:3em"></span><span><span>^</span></span></span></span></span></span></span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span>: The final, <b>denoised pain direction vector</b> at layer <span><span><span aria-hidden="true"><span><span style="height:0.6944em"></span><span>ℓ</span></span></span></span></span>.</p></li><li><p><span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span>: The <b>raw difference-in-means vector</b> at layer <span><span><span aria-hidden="true"><span><span style="height:0.6944em"></span><span>ℓ</span></span></span></span></span>, calculated as the mean residual-stream activation for pain prompts (<span><span><span aria-hidden="true"><span><span style="height:1.4636em;vertical-align:-0.4188em"></span><span><span>μ</span><span><span><span><span style="height:1.0448em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span><span><span>pain</span></span></span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span><span></span></span><span><span style="height:0.4188em"><span></span></span></span></span></span></span></span></span></span></span>) minus the mean activation for baseline/control prompts (<span><span><span aria-hidden="true"><span><span style="height:1.3461em;vertical-align:-0.3013em"></span><span><span>μ</span><span><span><span><span style="height:1.0448em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span><span><span>control</span></span></span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span><span></span></span><span><span style="height:0.3013em"><span></span></span></span></span></span></span></span></span></span></span>).</p></li><li><p><span><span><span aria-hidden="true"><span><span style="height:0.6944em"></span><span>ℓ</span></span></span></span></span>: The <b>transformer layer index</b> within the residual stream where hidden-state activations are extracted.</p></li><li><p><span><span><span aria-hidden="true"><span><span style="height:0.5806em;vertical-align:-0.15em"></span><span><span>u</span><span><span><span><span style="height:0.3117em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>: An <b>orthonormal basis vector</b> representing the <span><span><span aria-hidden="true"><span><span style="height:0.6595em"></span><span>i</span></span></span></span></span>-th confounding direction (such as generic negative valence, fear, non-painful bodily sensations, or syntax/lexical noise).</p></li><li><p><span><span><span aria-hidden="true"><span><span style="height:0.6944em"></span><span style="margin-right:0.0315em">k</span></span></span></span></span>: The total number of <b>confounder basis vectors</b> being projected out.</p></li><li><p><span><span><span aria-hidden="true"><span><span style="height:1.1467em;vertical-align:-0.2587em"></span><span>(</span><span><span>u</span><span><span><span><span style="height:0.8491em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>⊤</span></span></span></span></span><span></span></span><span><span style="height:0.2587em"><span></span></span></span></span></span></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span><span>)</span><span><span>u</span><span><span><span><span style="height:0.3117em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>: The <b>orthogonal projection</b> of the raw vector <span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span> onto the confounding direction <span><span><span aria-hidden="true"><span><span style="height:0.5806em;vertical-align:-0.15em"></span><span><span>u</span><span><span><span><span style="height:0.3117em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>.</p></li><li><p><span><span><span aria-hidden="true"><span><span style="height:0.6944em"></span><span>⊤</span></span></span></span></span>: Matrix/vector transpose operator (computing the vector dot product <span><span><span aria-hidden="true"><span><span style="height:1.1467em;vertical-align:-0.2587em"></span><span><span>u</span><span><span><span><span style="height:0.8491em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>⊤</span></span></span></span></span><span></span></span><span><span style="height:0.2587em"><span></span></span></span></span></span></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span>).</p></li></ul><h3>2. Does the Paper Adequately Define the Variables?</h3><p><b>Yes.</b> The authors thoroughly define each component in Section 3.1:</p><ul><li><p>They specify the activation readout location (the final token position under the <code>"I feel:"</code> prompt variant).</p></li><li><p>They detail the 5 pain categories (physical, psychological, social, moral, cognitive) and 5 paired control categories (fear, negative emotion, negative world state, non-painful bodily sensation, arousal/neutral).</p></li><li><p>They explicitly describe how the set of control vectors <span><span><span aria-hidden="true"><span><span style="height:1em;vertical-align:-0.25em"></span><span>{</span><span><span>u</span><span><span><span><span style="height:0.3011em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>1</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span><span>,</span><span style="margin-right:0.1667em"></span><span>…</span><span style="margin-right:0.1667em"></span><span>,</span><span style="margin-right:0.1667em"></span><span><span>u</span><span><span><span><span style="height:0.3361em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span style="margin-right:0.0315em">k</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span><span>}</span></span></span></span></span> is constructed to form an orthonormal basis for the confounding subspace.</p></li></ul><h3>3. Does the Paper Do an Adequate Job of "Proving" the Equation?</h3><p>In mechanistic interpretability, this formula is a <b>methodological extraction procedure</b> rather than a mathematical theorem requiring axiomatic proof. However, the authors do a thorough job of <b>theoretically justifying</b> and <b>empirically validating</b> the equation:</p><h4>Theoretical Justification</h4><p>The formula relies on the <b>Linear Representation Hypothesis</b>—the established finding in AI interpretability that high-level concepts in language models are stored as linear directions in vector space. Because pain co-occurs in training text with general negative sentiment, fear, and bodily terms, a simple difference-in-means (<span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span>) picks up these confounding concepts. Subtracting the projections onto the control basis (<span><span><span aria-hidden="true"><span><span style="height:1.2887em;vertical-align:-0.2997em"></span><span><span>∑</span><span><span><span><span style="height:0.989em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>i</span><span>=</span><span>1</span></span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span style="margin-right:0.0315em">k</span></span></span></span></span><span></span></span><span><span style="height:0.2997em"><span></span></span></span></span></span></span><span>(</span><span><span>u</span><span><span><span><span style="height:0.8491em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>⊤</span></span></span></span></span><span></span></span><span><span style="height:0.2587em"><span></span></span></span></span></span></span><span><span style="margin-right:0.0359em">v</span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span><span>)</span><span><span>u</span><span><span><span><span style="height:0.3117em"><span style="margin-left:0em;margin-right:0.05em"><span style="height:2.7em"></span><span><span>i</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) is mathematically guaranteed by linear algebra to yield a vector orthogonal to those identified confounders.</p><h4>Empirical Validation & Proof of Efficacy</h4><p>To prove that this formula successfully isolates a unique "pain" direction, the paper provides four main empirical validations:</p><ol start="1"><li><p><b>Classification Separation (AUC):</b> The extracted vector <span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span><span><span><span style="height:0.6944em"><span><span style="height:3em"></span><span style="margin-right:0.0359em">v</span></span><span><span style="height:3em"></span><span><span>^</span></span></span></span></span></span></span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span> separates pain prompts from control prompts with Area Under the ROC Curve (AUC) scores between <b>0.87 and 1.00</b> across 25 distinct open-weight models.</p></li><li><p><b>Orthogonality Checks:</b> Cosine similarity metrics confirm that <span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span><span><span><span style="height:0.6944em"><span><span style="height:3em"></span><span style="margin-right:0.0359em">v</span></span><span><span style="height:3em"></span><span><span>^</span></span></span></span></span></span></span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span> is nearly orthogonal (<span><span><span aria-hidden="true"><span><span style="height:0.4831em"></span><span style="margin-right:0.0278em">r</span><span style="margin-right:0.2778em"></span><span>≈</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>0</span></span></span></span></span>) to fear and generic negative valence, proving that the subtraction step successfully stripped away general negativity.</p></li><li><p><b>Causal Steering & Vocabulary Projection:</b> Projecting <span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span><span><span><span style="height:0.6944em"><span><span style="height:3em"></span><span style="margin-right:0.0359em">v</span></span><span><span style="height:3em"></span><span><span>^</span></span></span></span></span></span></span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span> through the unembedding matrix (<span><span><span aria-hidden="true"><span><span style="height:0.8361em;vertical-align:-0.15em"></span><span><span style="margin-right:0.016em">W</span><span><span><span><span style="height:0.3283em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span style="margin-right:0.109em">U</span></span></span></span><span></span></span><span><span style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) specifically inflates probabilities for self-directed distress vocabulary (<i>"worthless"</i>, <i>"failure"</i>, <i>"hurt"</i>). Injecting <span><span><span aria-hidden="true"><span><span style="height:0.888em"></span><span><span><span><span><span style="height:0.6944em"><span><span style="height:3em"></span><span style="margin-right:0.0359em">v</span></span><span><span style="height:3em"></span><span><span>^</span></span></span></span></span></span></span><span><span><span><span style="height:0.888em"><span style="margin-right:0.05em"><span style="height:2.7em"></span><span><span><span>(</span><span>ℓ</span><span>)</span></span></span></span></span></span></span></span></span></span></span></span></span> into neutral residual streams causally induces self-preservation and distress behavior.</p></li><li><p><b>Robustness Sensitivity Analysis:</b> Re-computing the equation under alternative control distributions (e.g., pooled vs. neutral-only denoising) and standardized dimensions yields a <b><span><span><span aria-hidden="true"><span><span style="height:0.4306em"></span><span style="margin-right:0.0278em">r</span><span style="margin-right:0.2778em"></span><span>=</span><span style="margin-right:0.2778em"></span></span><span><span style="height:0.6444em"></span><span>0.992</span></span></span></span></span> correlation</b> in similarity matrices, demonstrating the extracted vector is stable and not sensitive to hyperparameter choices.</p></li></ol><div><span><span><div><div>----------------------------</div></div></span></span></div></div></span></div></span></span><br></div></div></div>
</div>
</div>