`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 1 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 1 of 9
`
`
`
`UNITED STATES DISTRICT COURT
`SOUTHERN DISTRICT OF NEW YORK
`
`
`
`
`NETWORK-1 TECHNOLOGIES, INC.,
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`v.
`
`
`
`Plaintiff,
`
`GOOGLE LLC and YOUTUBE, LLC,
`
`
`
`
`
`
`
`
`
`
`Defendants.
`
`
`14 Civ. 2396 (PGG)
`
`14 Civ. 9558 (PGG)
`
`
`
`
`
`
`
`PLAINTIFF NETWORK-1 TECHNOLOGIES, INC.’S
`SUPPLEMENTAL BRIEF IN OPPOSITION TO DEFENDANTS’ MOTION FOR
`SUMMARY JUDGMENT
`
`
`
`
`
`
`
`
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 2 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 2 of 9
`
`I.
`
`INTRODUCTION
`
`
`
`Pursuant to the Court’s Order of July 11, 2022 (Dkt. # 266)1, Network-1 submits this
`
`supplemental brief in opposition to Google’s motion for summary judgment of non-infringement.
`
`This supplemental brief relates specifically to Google’s argument that the “Siberia” version of its
`
`ContentID system does not infringe because Google contends that it does not meet the “sublinear”
`
`claim element of the asserted ’988 and ’237 patents.
`
`In its motion for summary judgment (Dkt. # 224), Google argued that its Siberia system
`
`used an allegedly linear search because it “searches a fixed percentage of the index.” Dkt. # 224
`
`at 17. It further characterized Network-1’s assertion that the amount of the index to be searched
`
`was an adjustable variable designed to be adjusted as the size of the index grew as “baseless
`
`speculation” about “hypothetical circumstances.” Dkt. # 224 at 19.
`
`Months after all summary judgment briefing was complete, Google produced additional
`
`discovery revealing that Google’s assertions about its Siberia system were false, or at a minimum
`
`deeply misleading. Documents provided for the first time in June of 2021 showed that Google
`
`had, in fact, made just the sort of adjustment to its Siberia search system that Network-1 had
`
`pointed to, confirming that Google’s system was designed to operate in a sublinear manner.
`
`Moreover, the supplemental discovery obtained by Network-1 long after summary judgment
`
`briefing ended showed that Google had actually made these changes in early 2020 – before it made
`
`the incorrect characterizations in its summary judgment briefing in September 2020. Google
`
`withheld this information from Network-1 and the Court, while making arguments directly
`
`contradicted by the withheld evidence. This evidence, and the parties’ dispute about the facts
`
`
`1 All citations to Docket Numbers refer to the docket of the 2396 case, though the same
`documents may be entered in both coordinated actions.
`1
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 3 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 3 of 9
`
`
`
`regarding how Google’s system actually functions, reflect a genuine issue of material fact
`
`precluding summary judgment.
`
`II.
`
`NEW EVIDENCE CONFIRMS THAT THE SIBERIA VERSION OF GOOGLE’S
`
`CONTENT ID SYSTEM USES A SUBLINEAR SEARCH
`
`The asserted claims of the ’988 patent and the ’237 patent include an element that the
`
`accused system identify an electronic work “based on a non-exhaustive search identifying a
`
`neighbor . . . wherein the non-exhaustive search is sublinear” (’988 claim 17); and using a
`
`“sublinear approximate nearest neighbor search” (’237 claim 33). Google’s motion for summary
`
`judgment of non-infringement argued that the “Siberia” version of its accused Content ID system
`
`did not meet these claim elements because, according to Google, its search is not sublinear. Dkt.
`
`#224 at 16-21.2
`
`Prior to the close of expert discovery, Google’s system searched through
`
`
`
` of its system. Google argued in its summary judgment motion that this
`
`search constituted a “fixed fraction”
`
` Dkt. # 224 at 17. Network-1’s
`
`expert, Professor Mitzenmacher explained in his initial expert report that Google’s Siberia system
`
`did not, in fact, search a “fixed fraction”
`
`. He explained that the search of the
`
`Siberia system was designed to adapt to increases in the size of the data set by allowing it to adjust
`
`the portion of the index that was searched to preserve sublinear scaling. See Dkt. # 240 (Network-
`
`1 Opposition Brief) at 8-12 and evidence cited therein; Dkt. # 240-61 (Resp. Stmt of Genuine
`
`Issues) at ¶¶ 37, 50 and evidence cited therein. Indeed, Professor Mitzenmacher explained that it
`
`was incorrect to characterize the search of the Siberia system as examining a “fixed fraction”
`
`
`
` because that was an adjustable variable in the system. Id.
`
`
`2 Google’s motion made arguments about the same claim elements for the earlier, “LSH” version
`of its system. While Google’s arguments are incorrect for all of the reasons set forth in Network-
`1’s opposition papers, that earlier system is not at issue in this supplemental brief as it was not
`the subject of later-disclosed evidence produced by Google.
`2
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 4 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 4 of 9
`
`
`
`Google characterized Professor Mitzenmacher’s discussion of the design of the Siberia
`
`system’s search algorithm to allow adjustment of the portion of the index searched as “baseless
`
`speculation.” Dkt. # 224 at 19. Google argued that any adjustments would not result in sublinear
`
`scaling because “the source code
`
`
`
`” Dkt. # 224 at 21. Google made similar arguments in its
`
`reply, characterizing Professor Mitzenmacher’s discussion as describing “a hypothetical change
`
`that Google might make to its system.” Dkt. # 227 at 4 (emphasis in original).
`
`A. Google Produced New Evidence After Summary Judgment Contradicting Its
`
`Summary Judgment Arguments
`
`Pursuant to a stipulated order from the Magistrate Judge regarding a late-amendment to
`
`Google’s contention interrogatory responses, Network-1 propounded additional discovery on
`
`Google after the close of summary judgment briefing. In response to that discovery, Google
`
`produced documents in June 2021 showing that the search implemented by Google’s Siberia
`
`system had changed to examine only
`
`, rather than
`
`. Ex.
`
`86 at GOOG-NETWORK-00812409. Google’s witness confirmed in deposition testimony that
`
`this adjustment was made to reduce the computing resources utilized by the system. Ex. 87
`
`(Konrad 2021 Depo) at 30:12-31:23. Thus, Google’s Siberia system was adjusted just as Professor
`
`Mitzenmacher had explained. Professor Mitzenmacher had explained that the supposedly “fixed
`
`percentage”
`
` was not fixed at all. Even under Google’s flawed analysis of the system,
`
`that supposedly fixed percentage was changed
`
` - showing that it was never “fixed” as
`
`Google argued.
`
`Following the supplemental discovery, Professor Mitzenmacher issued a supplemental
`
`expert report explaining that this new evidence provided by Google further confirmed the sublinear
`
`nature of Google’s Siberia system and expressly refuted the arguments Google advanced on
`
`3
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 5 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 5 of 9
`
`
`
`summary judgment. Ex. 88 at ¶¶ 17-26. As Professor Mitzenmacher explained, “[r]educing the
`
` to subject to further consideration) as the
`
`size of the data set increases results in sublinear scaling.” Id. at ¶ 22. Professor Mitzenmacher
`
`explains in detail why this is true. Id. at ¶¶ 23-24. He also explains how the new evidence provided
`
`by Google shows the falsity of Google’s summary judgment arguments. He explained that
`
`“Defendants’ own changes to Content ID Siberia Version reveal that the
`
`
`
`, but rather a changeable parameter that they have in fact changed
`
`for performance reasons.” Id. at ¶ 25. Further, Professor Mitzenmacher explains that far from a
`
`“hypothetical” adjustment as Google argued in its summary judgment briefing, these adjustments
`
`were part of the design of the Siberia System search algorithm in order to allow the search to scale
`
`in a sublinear fashion. Id. at ¶ 26.
`
`B. Google’s Summary Judgment Arguments Were False and Misleading When
`
`Google Made Them
`
`As discussed above, the material produced by Google only long after summary judgment
`
`briefing showed that Google’s summary judgment arguments about the nature and operation of its
`
`Siberia system were incorrect. Google’s summary judgment briefing mischaracterized the
`
`operation of its system in multiple ways, including its arguments that the system only ever searched
`
`a “fixed fraction” of the index, and that any changes to that supposedly “fixed fraction” were purely
`
`hypothetical. The Siberia system search was (and remains) sublinear as a consequence of the
`
`adjustability of the amount of the index searched as the size of the index grows over time.
`
`Network-1 only learned about these additional facts beginning in June 2021, when Google first
`
`produced documents referring to them, and later in November 2021 when it was finally able to
`
`take the deposition of a Google witness regarding those changes.
`
`4
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 6 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 6 of 9
`
`
`
`But Google had actually made these changes long before it made the incorrect assertions
`
`in its summary judgment briefing. Google’s witness admitted that the change to the amount of the
`
`index examined in a search was made in early 2020. Ex. 87 Konrad 2021 Depo. at 30:12-31:23.
`
`By that time fact discovery had ended, but Google did not serve its opening summary judgment
`
`brief until September 2020. Thus, not only were Google’s summary judgment arguments about
`
`the operation of the Siberia system false and misleading in light of the evidence Google only later
`
`produced, but those arguments were false and misleading at the time that Google made them.
`
`Google’s own actions in early 2020 show that Google’s September 2020 summary judgment
`
`assertions were incorrect, but Google continued to conceal those facts from Network-1 until long
`
`after summary judgment briefing had closed.
`
`C. Google’s Supplemental Expert Opinions Do Not Support Its Summary Judgment
`
`Motion
`
`Google’s expert has submitted a supplemental report attempting to dispute Professor
`
`Mitzenmacher’s descriptions of Google’s Siberia system. At most, these new opinions merely
`
`confirm that this issue presents a genuine issue of material fact precluding summary judgment.
`
`Google’s expert and Professor Mitzenmacher disagree about the design and operation of the
`
`Siberia system. While Network-1 submits that Google’s expert opinions lack proper factual
`
`support, that is an issue that the trier of fact must resolve and that cannot properly be addressed by
`
`summary judgment. Further, Google’s expert assertions do not withstand even cursory scrutiny.
`
`Initially, Google’s expert continues to characterize Professor Mitzenmacher’s opinions
`
`about the adjustability of the Siberia search algorithm as “theoretical” despite clear evidence
`
`proving that, just as Professor Mitzenmacher has repeatedly explained,” the search algorithm was
`
`designed to adjust in order to maintain the sublinear scaling of the search system. Indeed, much
`
`of Google’s expert analysis seems to utilize the wrong focus in understanding the system. He
`
`5
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 7 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 7 of 9
`
`
`
`argues that before parameters were adjusted, each individual search examined
`
`, and after the adjustment, each individual search examined
`
`
`
`
`
`. What he fails to acknowledge or discuss is the nature of sublinear
`
`scaling. As the parties agreed claim construction reflects, sublinearity refers to the scaling of
`
`search time as the size of the index increases. Thus, the amount of the index interrogated in a
`
`particular individual search (the question addressed by Google’s expert) is the wrong frame.
`
`Rather, sublinearity involves the question of whether, over time, the work to be done grows in a
`
`linear fashion along with growth of the index. As Professor Mitzenmacher has explained,
`
`Google’s Siberia search algorithm is designed to be adjustable so that over time, the amount of the
`
`index to be interrogated can be reduced (
`
`) to reduce the work to be
`
`done relative to the size of the index. Thus, Google’s expert analysis focuses on the wrong inquiry.
`
`Google’s expert also resorts to the non-sensical argument that Network-1 did not show an
`
`expansion in the size of the index to be searched, and thus the change in parameters is irrelevant.
`
`First, this argument completely misses the relevant point. Regardless of the current size of the
`
`index, the new evidence clearly shows (contrary to the false arguments previously advanced by
`
`Google) that the Siberia system is designed to be adjustable so that the work done in the search
`
`will not scale in a linear fashion with the growth of the index. Google previously disputed this
`
`adjustability as a design feature of the system. The new evidence even more conclusively shows
`
`that Google’s characterizations of the system were wrong. Additionally, however, Google’s expert
`
`ignores the clear evidence that the index is always growing. Google’s witnesses admitted as much
`
`in sworn deposition testimony. See, e.g., Dkt. # 240-5 (Pasula Deposition) at 91:14-17, 42:7-17.
`
`Finally, Google’s expert tries to argue that Professor Mitzenmacher’s explanation of the
`
`kind of ongoing adjustments that will continue to be made to the system parameters over time are
`
`merely “hypothetical.” As shown above, this is hardly the first time that Google’s expert has
`
`6
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 8 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 8 of 9
`
`
`
`incorrectly described the reality of Google’s system as merely “hypothetical.” Moreover, the
`
`ongoing adjustments that Professor Mitzenmacher describes are precisely what Google’s own
`
`design documents (discussed in Professor Mitzenmacher’s initial expert report) confirm was the
`
`design goal of the system – to preserve a sublinear-scaling search system. Professor Mitzenmacher
`
`merely illustrates the nature of the adjustments that will continue to achieve those design objectives
`
`– confirming that the search algorithm is a sublinear search. Google’s arguments incorrectly seek
`
`to excise the adjustable parameters (which Google can no longer deny is a part of the system) from
`
`the search system. The adjustability of parameters that Professor Mitzenmacher examined is an
`
`integral part of the Siberia system search algorithm, and that adjustability makes the algorithm
`
`sublinear. Google’s own design documents confirm that this was the design goal of the system.
`
`See Dkt. # 240-2 (Mitzenmacher Initial Report) at ¶¶ 231-236.
`
`D. Genuine Issues Of Material Fact Preclude Summary Judgment
`
`As shown above, Google’s expert and Network-1’s expert disagree about the design and
`
`functioning of Google’s Siberia Content ID system. While Network-1 respectfully submits that
`
`only Professor Mitzenmacher’s opinions are properly grounded in the evidence, resolution of this
`
`question is clearly not appropriate for summary judgment. The trier of fact must decide whether
`
`Google’s system is designed with a sublinear search algorithm, as Professor Mitzenmacher has
`
`explained, or whether the sublinearity of the search is merely “hypothetical” as Google’s expert
`
`argues. Network-1 respectfully submits that even prior to Google’s production of new evidence,
`
`this issue was not appropriate for summary judgment. However, Google’s new evidence further
`
`confirms that Google’s characterizations of its system were false and misleading. The evidence
`
`contradicts the arguments Google relied on, and shows that those arguments were false even when
`
`Google made them.
`
`7
`
`

`

`
`
`Case 1:14-cv-02396-PGG-SN Document 274 Filed 09/23/22 Page 9 of 9Case 1:14-cv-02396-PGG-SN Document 276 Filed 09/26/22 Page 9 of 9
`
`III. CONCLUSION
`
`
`
`The new evidence produced by Google further confirms that its accused Siberia system
`
`utilizes a sublinear search algorithm as required by the asserted claims. At a minimum, the
`
`evidence submitted by both parties reveals a genuine issue of material fact as to the design and
`
`operation of Google’s accused system. Such issues cannot be resolved on summary judgment.
`
`Accordingly, Google’s motion for summary judgment on this issue should be denied for the
`
`additional reasons set forth above.
`
`Dated: September 23, 2022
`
`
`
`
`
`
`/s/ Brian D. Ledahl
`Marc A. Fenster (pro hac vice)
`Brian D. Ledahl (pro hac vice)
`Adam S. Hoffman (pro hac vice)
`Paul A. Kroeger (pro hac vice)
`Amy E. Hayden (pro hac vice)
`RUSS, AUGUST & KABAT
`12424 Wilshire Boulevard 12th Floor
`Los Angeles, California 90025
`Telephone: (310) 826-7474
`Facsimile: (310) 826-6991
`mfenster@raklaw.com
`bledahl@raklaw.com
`ahoffman@raklaw.com
`pkroeger@raklaw.com
`ahayden@raklaw.com
`
`Charles R. Macedo
`AMSTER, ROTHSTEIN & EBENSTEIN LLP
`90 Park Avenue
`New York, NY 10016
`Telephone: (212) 336-8000
`Facsimile: (212) 336-8001
`cmacedo@arelaw.com
`
`Attorneys for Network-1 Technologies, Inc.
`
`
`
`8
`
`